Funny how things work sometimes. I neglect this blog for a couple of years and of course it gets hacked, as outdated WordPress does. Luckily I discovered the defacement within hours, moved the site over to a new server and did some quick maintenance. While updating, re-uploading stuff and poking around old posts I get inspired to write this new post. The proverbial creation within destruction is doing overtime here. It's almost midnight.
I've been busy building SatoshiPay, starting around the end of 2014. It's a fun ride and we are only getting started. Growing the idea into a company kept me pretty occupied and not updating my beloved blog (est. 1999) was the smallest thing I neglected. Part of creating our nanopayments empire was releasing a pretty sweet WordPress plugin. It allows easy monetisation of content and I might do some more dogfooding here in the future.
Screenshot of my site from earlier today. A bloody cat with headphones hacked my blog?!
OK, back to the "hack". Somehow the "attackers" gained access to files that are writeable by the web server and replaced one single file: index.php. Obviously, I blame the Russians! Possibly with the help of some North Koreans. The previous server being an old PHP box, I didn't even bother looking into the root cause of the breach, but abandoned it faster than you can say "who is still using PHP". Turns out half of the world is, so I will keep this site running on WordPress for now, but on a fully managed web hosting instead.
Just in case you are wondering what I am up to these days, read Beatcoin Is A Music Jukebox Hack Powered By Bitcoin Micropayments. 🙂 Well, actually this was all created within the last 24 hours by a team of 5 and I only played a relatively small part, working on the Android app and doing some minor design work.
To read the rest of this article, I am asking you to pay a small fee, via SatoshiPay.
Last night I arrived to Hong Kong. For my way into the city I decided to take the bus – a slooow magical carpet ride with lots of bumpy stops on the upper deck of the cheapest option, the local "tower cruiser" line E21. It reminded me of my time in the UK a lot: exact same buses, road signs, round-abouts, people from all over Asia getting on and off all the time. But in a place that has palm trees instead of weeping willows. Bewildering.
To get to Hong Kong I took my first flight on this trip. I would have preferred the ferry to Qingdao again, but because it is no longer possible to get a China visa for tourists in South Korea and I wanted to go to a warmer climate I had not other option. If you look at a map you realise I was stuck, sandwiched by water and countries with difficult-to-get visas.
Since I am spending some time in this lovely country I looked into connecting to my environmental activism roots a few days ago and checked out what's going on with tree huggers in the Chaebol kingdom.
It came as a small surprise that green opposition politics don't really exist here or are at least gravely underdeveloped for a country with recent annual GDP growth around 5%, dramatically growing energy needs and ever increasing urbanisation – a country that is member of the friendly G20 and that features beautiful nature all around.
There was an attempt to establish a Korean Greens party starting in 2003, which failed in 2008. Right now the party is re-establishing itself, after being terminated yet again following a meagre 0.43% result in general elections earlier this year. It looks like the general public in South Korea has no interest in a green party. Now, why is that?
It appears that the current government lulls the population with plans like Green Growth (which Green Korea has solid criticism on) and tries to silence foreign critics of their nuclear energy strategy by simply not allowing them into the country. Details on the recent Greenpeace activist deportation also mention a 30% budget increase to more than $10 million USD after the Fukushima disaster for KONEPA, the South Korean agency for promoting nuclear energy with faces of playing children. This money will most likely not go into spreading information about incidents like the recent shut-down of two reactors in the south of the country on 2 Oct 2012.
The Energy Korea portal aggregates an interesting mix of general environmental news, including critical Greenpeace reports and at the same time greenwashes fossil fuels and nuclear energy, both of which -oops- the maintainer of the site, Daesung Group is heavily invested in.
However, there are people working on change for the better, for example prize-winning Yul Choi, a white-collar activist involved in various South Korean environmental projects since many years. Aforementioned Greenpeace Korea twitters daily, organic farming definitively exists and the Asia-Pacific Economic Cooperation Virtual Center for Korean Environmental Exchange (catchy name!) helps to flog off green technology. Friends of the Earth Korea also seem to be doing a lot of things including information centres and an organic online shop, but unfortunately don't have an English website at the moment.
When writing this I relied mostly on websites written in English. If you have pointers to websites in Korean or other languages, please send them to me and I will include links here!
A week ago various "makers" from around Moritzplatz in Berlin Kreuzberg hacked the public space surrounding them and celebrated Makerplatz. During two days dozens of micro events and performances took place between different locations in the area. To capture the decentralised nature of Makerplatz, to document and to give orientation while things are happening throughout the day, performer Brina Stinehelfer inspired a live internet broadcast performance.
Following the everyone-is-a-publisher spirit of the early internet days a DIY set-up was quickly cooked up using available technology: A smartphone with a free live-streaming app, the app's website repeating and archiving the streams and the Makerplatz website to announce content. Done. The videos were played live on a battery-powered mobile info point and projected in the Betahaus café. All what was needed now was Brina to walk around and report live. See the 83 videos she took at qik.com/makerplatz.
Initially I was not even going to be at Makerplatz, but invited by Judith of Trial&Error and lured by free food I hung around a preparation meeting hosted by Platoon in Mitte three days before the event. Suddenly I found myself in a discussion about wireless mesh clouds on Moritzplatz and video streams from mobile phones. I decided quickly that I want to be part of the performance, shuffled around my travel plans a little and agreed to give technical support on site.
After a quick evaluation of alternatives the centrepiece of the broadcast became Qik, a freemium live video sharing site with apps for all major mobile platforms, recently bought by $kype. We used a recent Android phone by HTC with 2 cameras. Once the app was installed and a Qik account was created we could already record video on the phone and view it on qik.com a few seconds later. We tested with a free Qik account first, but it's limited to 20-something clips, so we upgraded to a free premium trial. Note to self: Don't forget to cancel premium account in 2 weeks from now.
Brina's phone was connected to the internet via roaming between 3G, HSDPA and wireless, which worked out quite well. The screen at the mobile info-point however was relying on a wireless connection of a café at Moritzplatz, which faded away in the afternoon. Next time we'll make sure to have a USB dongle for mobile internet and then be able to move around independently.
Yesterday I was invited to join some friends visiting the Good Goods trade fair about sustainable consumption here in Hamburg. Next to the usual suspects such as clothing manufacturers, financial services vendors, energy traders, governmental organisations, publishers, food producers and about half a dozen different organic lemonade brands (samples, yeah!), my personal highlight was the tiny booth of PHeFE (de). Phefe is the ambitious project of researcher Susanne Jordan, aiming to create fair (as in fair-trade) alternatives for consumer electronics, starting with a self-designed computer mouse.
Phefe continues where Goliath corporations fail to deliver again and again, to go beyond labelling energy saving and recyclable devices as "Green IT" and make the entire production of electronics a process that respects basic human rights. As an example the documentary Blood in the Mobile illustrates vividly how mining minerals used in mobile phones is directly linked to local wars. But also sweatshop like labour conditions in product assembly lines are very common, with Foxconn (Apple, Asus, Nokia, Sony Ericsson) controversies unfortunately only being the tip of the iceberg.
The fair PC mouse is not yet available for purchase, but production is planned to start in 2011. So look forward to the Phefe mouse becoming what coffee was to fair-trade foods and hopefully initiating a paradigm shift in the consumer electronics sector. I will keep you updated!
Today a dream of mine came true – I was passenger in a 39 minutes glider flight! We were lucky with thermal updraft and reached 1800 metres within a few minutes. "Yeehaa, this one is like an elevator!", Bernd, the pilot cheered while spiraling us up into the sky.
I am fascinated by how gliders fly with updraft just like big birds. The glider is pulled up by a winch on the ground, unlinks the metal rope (drops a good bit right afterwards, ugh!) and then it's up to the skill of the pilot and the weather conditions how long you will stay in the air. Free like a bird. No fumes, no noise.
One of the things that made this trip so unreal is how fast you move around space. You are circling over the old city one minute, then a few moments later you are racing down towards the runway and before you can think you are standing on grass again and hear birds twitter. That seriously messes with your head, man. Well, that and the large quantities of adrenalin in your system I assume.
Enjoy some nice views of my home town from above and lots of whistling and howling in this video that I made with my phone.
Replace "myclient" and "myclient:prefs" with your own invented namespace and use your key/value names instead of "mypreference"/"yes".
I am so glad to have met Robin Upton at this year's FOSDEM conference in Brussels. Robin initiated Altruists International a few years back and is doing elaborate non-formal research in the field of gift economies.
While at FOSDEM (where the only other talk I attended was about strophe.js, an XMPP library designed for the real-time web I was playing with recently) and visiting a chocolate factory outlet a bit outside Brussels, Robin, Dante and I mainly discussed his ongoing project Friend2Friend — a possible technical back-end to a fully independent and distributed gift economy. The software is still a prototype, but I believe it is important pioneering work that encourages new ways of thinking about our data, how it is processed and stored.
Robin is a kind and loving altruist and an inspiring thinker with a strong mathematics background. Believe it or not, his black framed glasses are actually fixed with sticky tape, hehe. Please do invite him to talk about his ideas! He will roam about Europe a bit longer and return to East Asia at some point.
Thanks to Petter, Dante and Kasper for connecting us.


text:
Q: Image loop only returns one image but should return them all function all_images(&$post){
$content = $post->post_content;
if(preg_match_all('/<img[^>]+src="(.*?)"[^>]*>/', $content, $results)){
    $i = 0;
    $count = count($results);
    $count = $count - 1;
    while($i < $count)
    {
        foreach($results as $result){
            echo $result[$i];
        }
        $i++;
    }
  }
}

The above loop manages to get all of the images out of the original text. However, it only returns one image. I have tried several different combinations of while() and foreach() but it only ever returns one image. Does anyone know what i am doing wrong? Thanks

A: $results[1] should be an array of all the matches on the first parenthesized subpattern, so something as simple as this should work:
if(preg_match_all('/<img[^>]+src="(.*?)"[^>]*>/i', $content, $results)){
    foreach($results[1] as $src)
    {
       echo "src is $src<br>";
    }
}

Note I've used the /i modifier to make the match case insensitive, which might help you.
You might also want to supply some sample content you are trying to match against.

A: Why are you doing $count = $count - 1?
You should be able to just do this:
if(preg_match_all('/<img[^>]+src="(.*?)"[^>]*>/', $content, $results)){
    foreach($results[1] as $result)
    {
        echo $result;
    }
  }
}

A: You have to consider the structure of the array returned by preg_match_all. So try this:
function all_images(&$post)
{
    $content = $post->post_content;
    if (preg_match_all('/<img[^>]+src="(.*?)"[^>]*>/', $content, $results)) {
        // $results[0] contains the whole match of the regular expression
        foreach ($results[0] as $result) {
            echo $result;
        }
    }
}

redpajama_set_name: RedPajamaStackExchange


The controlled source experiment investigates the Seychelles margin and its conjugate equivalent near the Laxmi ridge off the coast of India. The RRS Charles Darwin, a British research vessel, acquired controlled-source seismic data in both areas during a period between late January and the middle of February, 2003. The source was a low energy, but finely tuned air gun array. The signals were recorded by hydrophones towed behind the ship, ocean bottom seismometers and seismometers located on various islands. Stations were deployed on Mahé and the surrounding islands, the Praslin islands, Bird and Denis. The portion of the experiment on the Seychelles side of the margin lasted ten days in mid February.
Above - Map of ship track and land stations on the Seychelles plateau. Red circles show locations of short period stations and blue triangles show locations of broad band stations (all are 3-component). The straight black line shows the proposed ship track, whilst the more variable line shows the track that was eventually sailed due to shallow water around Ile Aride.
The plot above shows an example of the raw data in the form of a record section (common receiver gather). The example shows air gun sources recorded at a station on Mahé. Pg (Sg) refers to P-wave (S-wave) energy that propagates through the lower crust.
Air guns behind the RRS Charles Darwin.


Art can be a very controversial subject, so just ripe for vents, here are some of ours.
Tracey Emin is reporting that she may have to leave Britain for France in order to avoid paying Tax. Oh dear my heart bleeds for her.
So Tracy are you really telling me you work hard to produce what you do….wow.
I think you should really reflect on the nature of "hard work". A nurse in a hospital works hard for very little reward. The only thing you have in common is that you both work with s*** all day long.
You should think yourself lucky that you have a 'job' that earns you large amounts of money and that you enjoy.
Tracy the only cultural contribution you and your fellow Art Marketeers have made is to be another marker in the decay of Western Art Criticism where B***s*** is recognised as genius!
1. Artists who copyright public art.
2. Artists with no technical skills – who think Art is stuffing a dead mouse in a cotton wool box or some such nonsense.
3. Artists who get other people to make their art.
4. Artists who are more into self publicity than the work itself.
5. Art that is a blight on the surrounding landscape, this can apply to both badly done graffiti and art installations that just jar.
Councils with no sense of humour – e.g., the damaged Banksy in Hackney.
Bar owners who destroy/paint over original commissioned art in favour of catalogue style decor.
Art destroyed for political reasons – e.g., the Diego Rivera mural in the Rockefeller Centre.
I should however point out that I definitely do not include the cleaner who threw out Damien Hursts work in this category, I would suggest that cleaner is co-opted to judge the Turner Prize.
8. Conceptual art that is simply pretentious – a prime example of this is Colombian artist Doris Salcedo's work Shibboleth, nick-named Doris's crack.
This work in my view also qualifies as an example for Vents 2,3,4,5 and 7.
9. Art as a Market commodity.
10. People who buy art and keep it in a vault.
11. Art that is big just for the sake of it.
12. Art galleries that are so busy that checking out the art is next to impossible – it's like being on a conveyor belt.
13. Art that is so badly constructed that it decays within the Artists life time (that does not include temporary Art in a medium that is meant to decay, like Pumpkin Carving or Ice Sculptures).
14. Art that needs an essay in order to impart its meaning.
15. Art NewSpeak – pretentious and pompous explanations of an "art work".


Clutter can be overwhelming. The new move into a more minimal lifestyle emphasizes that when we get rid of a life of too much 'stuff', we live more freely. Keep clutter away and you will be able to focus on what really matters. Whether this is a hobby we really love, a spiritual path we would love to embark upon or a debt (and anxiety) free lifestyle, we improve our quality of life when we reduce clutter.
The idea of keeping clutter away may seem unconventional at first. However, writers such as Oliver James have explored how 'Affluenza' or the search for more – more belongings, a higher level of success, or even a more youthful appearance – leads to unhappiness, anxiety and stress. Clearly, clutter is not the answer to a happier or more fulfilled mind. With this in mind, we may ask ourselves about the best ways to keep clutter away.
The psychologist James Hillman once wrote that we cannot get enough of what we don't need. When we search for happiness in products like a hardwood floor vacuum (which is marketed to us), we often search for happiness in the items we acquire. When we feel dissatisfied, we carry on the search. Marketing messages may also make us feel ashamed of some of the products we already own. Focusing on what we love gives us immunity. When we spend time on our passions, we make ourselves happy. We don't need to search for the answers by acquiring new products or searching for new solutions. Whether it is cycling, photography, art, reading, walking in nature, swimming or playing music, spend time doing what you love. This will help to keep your life clutter-free.
Oliver James explains that we often wish to feel attractive, and so will buy a great many products in order to come across well to others. These include new, trendy, clothes, styling products, creams and potions. By embracing our natural beauty, eating well and keeping ourselves healthy from the inside, we are able to take better care of our physical bodies. Rather than see our bodies as objects, we can focus on the wonders our bodies achieve all of the time. By staying in touch with our bodies, we are able to explore our own natural beauty. This helps us to reduce clutter, improve our self-esteem and save money while keeping our lives clutter free.
Ecopsychologist Theodore Roszak explains that human beings have a natural sense of belonging to outdoor spaces. Nature often helps us feel better during times of crisis. It will also help us to feel sensuous and alive. Whether it is the sound of birds in the morning, the babble of a brook or a walk in the woods, being outside soothes us. Organic shapes feel comfortable and enjoyable. While we spend time in nature, there is no real need to own what we see. We may pick wild strawberries or harvest nuts, but we often gain deep enjoyment simply by being out of doors. This will assist us in clearing our thoughts. We can also satisfy ourselves without spending time in the mall.
Researcher Brene Brown shares that in order to live a wholehearted life, we need to embrace our playful sides. Play helps us to laugh, dance, enjoy our relationships and take a break from our worries. When we play, we clear our minds of clutter. We also create a sense of joy or celebration. Play lets go of tension and assists us to embrace the joy that already exists within us. As Dr Patch Adams showed us, we can find joy and happiness even in difficult circumstances. When we are tired, when we have been overworking, when we simply want to connect with those around us, play is the answer.
Once you've found what brings you joy and you no longer search for happiness in products, you will be free to live a clutter filled life. In The Life Changing Magic of Tidying Up, writer Marie Kondo shares that we often feel most relaxed when our homes are free of clutter, well organized and efficient. While we spend time on holiday, we often feel relaxed and free. We enjoy good food, basic necessities, comfortable furniture and lots of recreation time. We are free to enjoy ourselves. Marie Kondo stresses that by purging what we do not need, we are able to fully appreciate those items we either need or truly love. A minimalist life does not mean that we deprive ourselves. Instead, we are often free to feel a deeper appreciation of what we have. When we feel a deep appreciation for what we own, we feel settled in our lives. Extra space gives us room to think. Understanding what we need and love reduces the pressure on our bank balances. This, in turn, reduces our stress.
There are many different ways to reduce clutter. Whether we have cluttered homes, cluttered thoughts or feel overburdened by our duties, by embracing our joys, we are able to free ourselves of the Affluenza virus, embracing our true freedom. This will reduce our stress, help us to create order and harmony in our lives and bring us joy. What more could we ask for than a clutter-free life?
Liz is a part of the Content team at Best Vacuum Expert, sharing expert knowledge and best tips on how to have a clean house.
Meal Plan Monday: Week 3 is Easier than Ever!


Are you a runner? Learn how Recover can help!
What you do immediately after a workout is critical for long-term performance. Recover post-workout gummies rapidly recharge your muscles, so you can recover faster. The combination of active ingredients supports muscle synthesis, facilitates energy storage, repairs muscle cells, and reduces soreness. Recover faster and maximize your training with Recover post-workout gummies.
Other Ingredients: Tapioca Syrup, Maltose, Cane Sugar (Sucrose), Pectin, BCAA mix (L-valine, L-leucine, L-isolucine), Citric Acid and/or Malic Acid, Glycerol, Coconut Oil, Natural Flavors, Natural Blue Color (Spirulina), Ginger Extract.
What you do immediately after a workout is just as important as the workout itself. Consuming a high GI carbohydrate right after an intense workout has a compounding effect: spiking insulin and replenishing muscle glycogen. Insulin helps speed the delivery and absorption of nutrients, and because it reduces muscle breakdown, it improves net protein balance. Glycogen is the fuel reserve for your muscles. Consuming high GI carbohydrates after intense training quickly replenishes glycogen stores and repairs muscle tissue. The faster you can replenish glycogen, the more beneficial it is for your muscles and recovery. Vigorous exercise also increases systemic inflammation and oxidative stress. Antioxidants should be consumed after training to neutralize cell-damaging free radicals and speed recovery.


text:
TriStar Centennial Medical Center Welcomes New Physician Jeremy Pantin, M.D. to Medical Staff
TriStar Centennial Medical Center...
TriStar Centennial January 25, 2019
Dr. Jeremy Pantin specializes in hematology and blood marrow transplantation.
TriStar Centennial Medical Center is proud to welcome Jeremy Mark Alexander Pantin, M.D., FACP to Sarah Cannon Center for Blood Cancer at TriStar Centennial. Dr. Pantin specializes in hematology and blood marrow transplantation.
Dr. Pantin attended Medical School at The University of the West Indies in St. Augustine, Trinidad. He completed his residency in internal medicine at Howard University Hospital in Washington D.C. before completing a fellowship in hematology, medical oncology, and blood and marrow transplantation at the National Heart Lung and Blood Institute in Bethesda, Maryland.
"I am pleased to welcome Dr. Jeremy Pantin to our BMT team," said Scott Cihak, CEO of TriStar Centennial Medical Center. "Dr. Pantin is committed to using his vast expertise in blood and marrow transplantation in helping patients here in middle Tennessee have access to the latest in life-saving therapies and surgical treatment options in the fight against blood cancer."
Dr. Pantin comes to TriStar Centennial from Augusta University in Augusta, GA where he was an associate professor in the Division of Hematology, Medical Oncology and Bone Marrow Transplantation.
For more information and to make an appointment, please go to TriStarCentennial.com or call (615) 342-7440.

redpajama_set_name: RedPajamaCommonCrawl


Encountering a bear in a place still untrampled enough to be called 'wild' is an experience completely different than seeing a bear in a human-dominated locale. At least, I always thought so.
I've visited zoos and admired Black bears and Grizzlies, Polar bears sporting underwater, separated from me by inches of reinforced glass, and felt wowed. I've seen bears digging through garbage (like racoons in altogether too urbanized a place) and felt sad. My first time in Denali National Park, though, I saw bears in an utterly different light. A mother Grizzly pausing on a hill to sniff the air, trailed by her two trundly but also-cautious cubs. How amazing. A bear in a zoo is still a bear of course; somehow, a bear in a more natural habitat seems altogether enigmatic and complete. We are left to shoot pictures, knowing we're capturing just a fragment of their lives.
Humans are fascinated by bears, enamored of them. They are powerful creatures and we admire power. Bears are a symbol of steadfast strength. Often, we try to capture this sense of them in our sports teams: the Bears, the Bruins. For those who've encountered these animals coexisting with our present-day society, I think bears can represent adaptability as well.
You can find bears in our mythos. In the constellations, Ursa Major and the Big Dipper are familiar features of the night sky. Polar bears embody the arctic; I've heard them called the 'Spirit of the North'. Bears even play a role in politics, as represented in this comic featuring Theodore Roosevelt 'Drawing the Line' and refusing to shoot a bear which had been purposefully injured and bound to a tree for hunting sport. The incident inspired the name 'Teddy Bears'. Those sewn critters are part of many of our childhoods. Teddy bears are plush counterparts to what bears are in the wild. Teddy bears can reflect love and compassion back on a child, and offer security. Something ferocious turned into a fluffy protector.
Still, bears can be protectors. Smoky the Bear teaches us to prevent wildfires. And bears in childrens' tales teach lessons: Goldilocks and the Three Bears, Winnie the Pooh, Yogi Bear, the Berenstein Bears. In novels, too, bears roam. In Hal Borland's When the Legends Die (1963) a rescued bear cub serves as a guide on the road to self-identity, as an entity worthy of empathy and care. Bears serve incredibly versatile roles in many other books as actors and as metaphors, like in author John Irving's books.
Irving's The Hotel New Hampshire (1981) references another aspect of bears in human culture when it introduces a character named Freud, an entertainer who performs with his pet bear, State o' Maine. Performing animals are a big part of the circus tradition. Ursari, animal trainers from among the Roma people, were among those who trained bears for circuses in Europe. People are enchanted by the distraction of the circus, and I think acts with bears performing feats entertained so many because humans like to see our behavior echoed in other species. We also like to feel endangered but be safe.
We should remember that humans are the ones endangering bears.
Real bears aren't Teddy bears, fluffy protectors. They need our protection. It is hard to remember that something so wild and fierce and capable is so strongly affected by humans. Bears can coexist with us, they have a broad ecological niche, but really they need wild places. And when we do not preserve truly wild places which make good habitat, wild creatures suffer. Polar bears, for instance, are facing a wide variety of threats including habitat fragmentation and toxic chemicals, which you can read about on the WWF facts sheet here.
"Polar bears are already predicted to die out in a century," (The Sunday Times, 2006). I think it's safe to say that's not what we want- for any bear species. I think we love the idea that is bears. We should also pay heed to their reality.
Beyond just the ecological concerns of biodiversity conservation, I think there are cultural concerns. We live in our cities and think we are urbanized- that we don't need wild places. But it has been proposed that humans do… that wilderness is precious. And recognizing that humans are one part of the natural system is healthy and good. Aldo Leopold said: "We abuse land because we regard it as a commodity belonging to us. When we see land as a community to which we belong, we may begin to use it with love and respect," (A Sand County Almanac, 1949).
He is right about community. We are ever more connected. Technology connects us. We can root wildly for the survival of orphaned Polar bear cub Qannik and follow her on the first legs of her new life at the Alaska Zoo, learn about her in the news as she recovers and heads to Louisville. Nature also connects us. We can travel and encounter bears in wild places. That means learning and practicing bear safety, so that we can share wild spaces with bears with more surety.
Strong and proud, capable, loveable, and fierce, a bear embodies many things for us. Bears need the wild, and so do humans. Though we are very different, I think that fellowship is one reason for our fascination with the animals. What do you think?
To see how bears and humans interact at Denali, watch Frontier Scientists vodcast 'Grizzlies: Preserving Bear & Visitor Experiences' with wildlife biologist Pat Owen of Denali National Park and Preserve.


text:
COUNTY NEWS: Suspect further held in St Leonards murder probe
Police at the scene. Photo by Eddie Mitchell.
Huw Oxburgh
Published: 17:50 Friday 28 July 2017
A man arrested on suspicion of murder has been further detained for another 36 hours, police say.
The man, a 21-year-old from London, was arrested after police were called to the incident in Clyde Road, St Leonards at about 12.41pm on Thursday (July 27). After officers arrived on scene, further enquiries led them to Wishing Tree Road where they found a 37-year-old local man with serious injuries.
The victim had driven himself from Clyde Road to Wishing Tree Road where, despite the best efforts of paramedics, he was pronounced dead at the scene.
Police say they are not looking for anyone else in connection with the incident, however anyone with any information is asked to report it online at https://sussex.police.uk/appealresponse quoting Operation Lexus.
Photos by Eddie Mitchell.
Disruption to trains between Bognor Regis and Littlehampton


text:
Q: $n \ge 2, (p,n) \ne (2,2).$ Prove that for any $v \in \mathbb{F}_p^n,$ the sequence $v, (I+M)v, (I+M+M^2)v, \dots$ has period $
Let $p$ be prime and $n \ge 2, (p,n) \ne (2,2), M \in \mathbb{M}_{n \times n}(\mathbb{F}_p).$ Prove that for any $v \in \mathbb{F}_p^n,$ the sequence $v, (I+M)v, (I+M+M^2)v, \dots$ has period $<p^n.$
My attempt: Let $M = AJA^{-1}.$ Then $(1+M+\dots+M^{r-1})v = (1+M+\dots+M^{s-1})v \Rightarrow M^r v = M^s v \Rightarrow A(J^r - J^s)A^{-1}v = 0 \Rightarrow J^r w = J^s w$ where $w = Av.$
Let $f \in \mathbb{F}_p[x]$ be the characteristic polynomial of $M.$ Let $f = qr$ where $q$ fully factors in $\mathbb{F}_p$ and $r$ is irreducible. Since $r$ is irreducible, it has no double roots. Thus, we can write $J = \text{diag}(J_1, \dots, J_k, D)$ where $D$ is a diagonal matrix, $J_i = \lambda_i I + N_i, \lambda_i \in \mathbb{F}_p,$ and $N_i$ is the matrix of ones above the diagonal of $J_i.$
Since $J_i$ has size $\le n,$ we have $N^n = 0.$ So if $p^k \ge n,$ then $J_i^{p^k} = \lambda_i I + N_i^{p^k} = \lambda_i I,$ hence $J_i^{p^k} w = \lambda_i w$ for all such $k.$
Write $D = \text{diag}(\beta_1, \dots, \beta_{\deg r})$ where the $\beta_i$ are roots of $r$ and note that $m = [\mathbb{F}(\beta_1, \dots, \beta_{\deg r}) : \mathbb{F}] \le \deg r \le \deg p = n.$ All roots lie inside $\mathbb{F}_{p^m},$ so $D^{p^m} = D.$
$J^r w = J^s w$ if and only if $J_i^r w' = J_i^s w', D^r w' = D^s w'$ where $w'$ is a portion of $w$ corresponding to $J_i$ or $D.$ Since $p^{n-1} \ge 2^{n-1} \ge n,$ we may take $r = n-1, s = n$ to ensure the first equation holds. The 2nd equation holds if $r = p^m, s = 1.$ However, I'm having trouble satisfying both equations simultaneously. What choice of $1 \le r \ne s \le p^n$ will make both equations hold, thereby proving the period is $\le s-r < p^n,$ and how could we derive or motivate the choice? If the choice depends on $v,$ that's bad news for my approach so far, but at least I've made tons of progress.

A: It turns out a different approach is needed. As mentioned earlier, we need to rule out the case that the period is exactly $p^n.$ Suppose this is the case, and define $f_k(v) = (I+M+\dots+M^{k-1})v$ so that $\mathbb{F}_p^n = \{f_0(v), \dots, f_{p^n}(v)\}.$ If $g$ is a polynomial and $g(M)v = 0,$ then $g(M)f_k(v) = 0$ for all $k,$ hence $g(M) = 0$ identically. Note that $f_{k+1}(v) = h(f_k(v))$ where $h(v) = v+Mv,$ so $h$ has period exactly $p^n.$
Since $h(0) = v = f_1(v),$ we must have $f_{p^n}(v) = 0,$ so $(I-M)(1+M+\dots+M^{p^n - 1}) = M^{p^n} - 1$ by our earlier observation. Let $q(t)$ be the minimal polynomial of $M.$ Then $q(t+1)$ divides $(t+1)^{p^n} - 1 = t^{p^n} \mod p,$ so $q(t) = (t-1)^a$ for some $a.$ By Cayley-Hamilton, $a \le n.$ It follows $N = M-I$ is nilpotent with $N^n = N^a N^{n-a} = 0$ specifically.
Now $f_{p^{n-1}}(v) = \sum\limits_{i=0}^{p^{n-1}-1} (N+I)^i v = \sum\limits_{i=0}^{p^{n-1}-1} \sum\limits_{j \in \mathbb{Z}} \binom{i}{j} N^j  v = \sum\limits_{j \in \mathbb{Z}} \binom{p^{n-1}}{j+1} N^j v = N^{p^{n-1}-1} v$ since the other binomial coefficients vanish. If $n=2, p>2,$ then $p^{n-1} = p > n,$ and if $n \ge 3,$ then $p^{n-1} \ge 2^{n-1} > n$ as well. Thus, the remaining term is also zero and $f_{p^{n-1}}(v) = f_{p^n}(v) = 0,$ contradiction.


Should young adults pay board to their parents?
Soaring house prices and the rising cost of living are prompting young adults to stay in the family nest longer - but at what cost? While in generations past it was common practice for young Australians working full-time and living at home to help cover household expenses, paying board appears to be out of favour.
Running an airport in Australia: a licence to print money?
Is running an airport a license to print money? Australian airports are so profitable, there are calls for greater regulation.
As founder and executive chairman of IBISWorld, an international research firm that predicts industry and economic trends, Phil Ruthven looks to the past to know what to expect tomorrow.


To post an ad selling or renting a property, click here!
Look for a property that you cannot find, click here!
Please complete the following form with your request. This request will be sent to the eGo Realestate network of property agents, who will in turn contact you.


text:
\section{Introduction}
There is a number of quantum many-body problems that are of paramount
importance for condensed matter physics and, at the same time,
possess an exact solution.
These are the Anderson orthogonality catastrophe\cite{Anderson}, Fermi edge
singularity\cite{Nozieres} (FES), Luttinger liquid\cite{Tomonago} (LL)
zero-bias anomaly\cite{Luther}, and Kondo problems\cite{Kondo}.
It has been realized long ago   that  these problems  are,  in fact,
inter-connected,
both vis-a-vis   the  underlying physics and the  mathematics  involved.
Such connections have been used, e.g.,  for the
representation of  the dynamics of the  Kondo problem
as  an infinite sequence of  Fermi-edge-singularity events\cite{Yuval}.

In our recent works\cite{GGM_long2010,GGM_short2010}
we have addressed some of these problems away
from equilibrium.  To achieve this goal,
we  have developed a non-equilibrium bosonization technique
generalizing the conventional bosonization
\cite{stone,Delft,Gogolin,giamarchi,maslov-lectures} onto problems
with non-equilibrium distribution functions.
We have shown that the relevant correlation functions  can be
expressed through
Fredholm determinants of a ``counting'' operator.
The information on the specific type of the problem, as well as on different
aspects of the interaction,
is  encoded  in the time-dependent scattering phase of the counting operator.
The results of
Refs.~\onlinecite{GGM_long2010,GGM_short2010} have demonstrated  that those
classic many-body problems are more closely connected than has been
previously understood, extending the interrelations into  the
non-equilibrium regime.

The purpose of the present  paper is twofold.
First, we present the  relation between the LL tunneling
spectroscopy, the full
counting statistics, and the  Fermi-edge singularity problems in a
systematic way. We also include in this scheme the generalization of
the LL problem to a non-equilibrium gas of  strongly repulsive
bosons (Tonks-Girardeau gas). These results are summarized in
Table~\ref{table1}.
Second, we apply the general theory of
asymptotic behavior of
Toeplitz determinants to the present problems. This allows us to
extract important  information on the  many-body physics of these models,
including non-equilibrium dephasing rates and
the modification of power-law exponents due to
non-equilibrium conditions.

\setlength{\tabcolsep}{7pt}
\begin{table}
\begin{center}
\resizebox{9cm}{!}{
  \begin{tabular}{ | c  | c |  c |  c | c | }
    \hline
       & $c_R$ & $c_L$ & $\delta_R$ & $\delta_L$ \\ \hline \hline
    $G_{\rm FES}^>$ & $-1+
\frac{\delta_0}{\pi}$  & $0$ &  $2(\pi -\delta_0)$ & $0$ \\ \hline
    $G_{FR}^>$  &  $-1$  &  0  &  $2\pi \frac{1+K}{2\sqrt{K}}$   &
    $2\pi\frac{1-K}{2\sqrt{K}}$  \\ \hline
   $G_{FL}^>$  & 0 & $-1$ & $2\pi\frac{1-K}{2\sqrt{K}}$ &
   $2\pi\frac{1+K}{2\sqrt{K}}$ \\ \hline
   $\chi_\tau(\lambda)$ & $-\frac{\lambda}{2\pi}$ &
   $\frac{\lambda}{2\pi}$ & $\lambda\sqrt{K}$ & $-\lambda\sqrt{K}$ \\
    \hline
$G_B^>$& $-\frac{1}{2}$ & $-\frac{1}{2}$ & $\frac{\pi}{\sqrt{K}}$ &
$\frac{\pi}{\sqrt{K}}$ \\
\hline
 \end{tabular}
}
\label{table1}
\caption{Non-equilibrium correlation functions of many-body
  problems: Fermi edge singularity ($G^>_{\rm FES}$),  Green functions
  of right- and left-moving fermions in a LL ($G^>_{\rm FR}$ and
  $G^>_{\rm FL}$), full counting statistics of a LL
  ($\chi_\tau(\lambda)$), Green function of the Tonks-Girardeau gas
  ($G^>_{\rm B}$). All these correlation functions can be cast in the
  form $G^> = \langle e^{-i{\cal O}_-(\tau)}e^{i{\cal O}_+(0)}\rangle$,
  where ${\cal O} = \sum _{\eta=R,L} c_\eta\phi_\eta$ and $\phi_\eta$
  are free bosonic fields. The coefficients $c_\eta$ are shown in the
  second and third columns of the table.
Evaluation of these correlation functions
  yields the results in the form of Fredholm-Toeplitz determinants
  $\Delta_R[\delta_R]\Delta_L[\delta_L]$. The corresponding phases
  $\delta_{R,L}$ are presented in the last two columns for the case
  where the LL is adiabatically connected to the  reservoirs.}
\end{center}
\end{table}

The structure of the present  paper is the  following:
In Sec.~\ref{fermionic_problems} we  summarize the results  of our
earlier works \cite{GGM_long2010,GGM_short2010} for the FES problem,
as well as the
tunneling spectroscopy and the  counting statistics problems  in the LL, all
underlined
by interacting fermions.
Section \ref{bosonic_problems} is devoted to the
tunneling spectroscopy problem  for a non-equilibrium Tonks-Girardeau gas.
In Sec.~\ref{Fredholm_determinant} we  study the long-time behavior of
emerging Fredholom determinants, employing   Szeg\H{o} and
Fisher-Hartwig theorems.  For completeness, properties of the
Tonks-Girardeau gas at
equilibrium are
summarized  in Appendix \ref{Tonks_girardo_equilibrium}, while
relevant mathematical  theorems from the theory of Fredholm determinants
 are  presented
 in Appendix \ref{Fisher-Hartwig-conjecture}.

\section{Many-body problems as Fredholm Determinants}

\subsection{Fermionic problems}
\label{fermionic_problems}

\subsubsection{Free fermions}
\label{free_fermions}

We first discuss   non-interacting electrons.
Evidently,  the  Green functions of free fermions $G_0^>$, $G_0^<$ (we
use the standard notations of Keldysh formalism \cite{Kamenev}
can easily  be  calculated within a fermionic description.
However,  it is insightful to recalculate it  employing the
non-equilibrium bosonization\cite{GGM_long2010}. The result reads
\begin{equation}
\label{a1}
G_{0,\eta}^\gtrless(\tau)=-\frac{1}{2\pi v}\frac{1}{\tau\mp i/\Lambda}
\overline{\Delta}_\eta[\delta_\eta(t)]\:.
\end{equation}
Here  $\eta$ is the chirality index ($\eta=L$ for left and $\eta=R$
for right movers), the phase $\delta_\eta(t)=\lambda\omega_\tau(t,0)$,
where
\begin{equation}
w_\tau(t,\tilde{t})=\theta(\tilde{t}-t)-\theta(\tilde{t}-t-\tau)
\end{equation}
is a ``window function'', and
$\lambda=2\pi$. Further,
$\Delta_\eta[\delta_\eta(t)]$  is
the Fredholm determinant of a counting operator
\begin{equation}
\label{determinant_definition}
\Delta_\eta[\delta_\eta(t)]=
{\mathrm{det}}[1
  + (e^{-i{\hat{\delta}_\eta}}-1)\hat{n}_\eta]\,,
\end{equation}
and we denote by $\overline{\Delta}_\eta$ the determinant normalized
to its value for zero-$T$ equilibrium distribution.
As we see, in the bosonic description, a  free fermion is represented
by a $2\pi$ phase soliton entering the counting operator.
The latter consists of a  fermionic distribution function $n_\eta(\epsilon)$,
and
a time-dependent scattering phase $\delta_\eta(t)$, with $\epsilon$
and $t$ to be understood as canonically conjugate variables.
Since the matrices $\hat{\delta}$ and $\hat{n}$
can not be diagonalized simultaneously,
the task of calculating   $\Delta_\eta[\delta_\eta(t)]$ is non-trivial.
In most cases the analysis of such determinants can be done only numerically.
However, the long time asymptotic properties can be studied analytically,
by means of  Szeg\H{o} and Fisher-Hartwig theorems,
as discussed in Sec.~\ref{Fredholm_determinant}.

When read from right to left, Eq.~(\ref{a1}) can be viewed as a
remarkable identity for Fredholm determinants. It yields an exact
value of such a determinant for an  arbitrary distribution function
$n_\eta(\epsilon)$, and for the phase function $\delta(\tau)$ given by
a window function with amplitude $2\pi$. It is worth mentioning that
the determinat should be considered as analytically continued from the
region of small phases $\delta$.

\subsubsection{Fermi edge singularity}

The FES problem describes the  scattering of conduction  electrons off a
localized hole, which  is left behind by  an electron excited into the
conduction band.
Historically, the FES problem was first solved by exact summation of an
infinite diagrammatic series \cite{Nozieres}.
While in the FES problem there is no interaction between electrons
in the conducting band, it has many features characteristic of genuine
many-body physics.
Despite the fact that conventional experimental realizations of FES are
three-dimensional, the problem can be reduced (due to the local and isotropic
character of the interaction with the core hole) to that of
one-dimensional chiral fermions. For this reason,  bosonization
technique can be effectively applied, leading
to  an alternative and very elegant solution \cite{Schotte}.

One can consider the FES out of equilibrium\cite{Abanin},
with an arbitrary electron distribution function $n(\epsilon)$.
This problem can be solved within the framework
of non-equilibrium bosonization\cite{GGM_long2010}, with the following
results for the  emission/absorption rates:
\begin{equation}
\label{b1}
G^\gtrless_{\rm FES}(\tau)=\mp
{ i\Lambda{\overline{\Delta}}_{\tau}(2\pi-2\delta_0) \over
2\pi v (1\pm i\Lambda\tau)^{(1-\delta_0/\pi)^2}}.
\end{equation}
Here $\delta_0$ is the $s$-wave electronic phase shift  due to the
scattering of conduction electrons off the core hole.

\subsubsection{Luttinger liquid: Tunneling spectroscopy}

The tunneling spectroscopy technique allows one to explore
experimentally Keldysh
Green functions of an interacting system that carry information about
both tunneling density of states and energy distribution.
Recent experiments on carbon nanotubes and quantum Hall edges have
proved the efficiency of this technique in the context of 1D
systems\cite{tunnel-spectroscopy,tunnel-spectroscopy-qhe}. The
technological and experimental
advances motivate the theoretical interest in the tunneling
spectroscopy of strongly correlated 1D structures away from
equilibrium
\cite{GGM_long2010,jakobs08,gutman08,trushin08,pugnetti09,Ngo,takei10,bena10}.

In the case
of a  LL made of 1D interacting fermions, the Keldysh Green function may be
evaluated theoretically via the non-equilibrium bosonization technique.
Assuming that a long LL conductor is coupled to
two reservoirs (modeled as non-interacting 1D
wires\cite{Maslov,Safi,Ponomarenko}) with
distribution functions $n_R(\epsilon)$ and  $n_L(\epsilon)$ respectively,
one obtains
\cite{GGM_long2010}
\begin{equation}
\label{d3}
G^\gtrless_R(\tau)=\mp \frac{i\Lambda}{2\pi u}
\frac{\overline{\Delta}_R[\delta_R(t)]\overline{\Delta}_L[\delta_L(t)]}
{(1\pm i\Lambda \tau)^{1+\gamma}},
\end{equation}
where $u=v/K$ is the sound velocity,
\begin{equation}
\gamma=(1-K)^2/2K\,,
\end{equation}
and
\begin{equation}
K=(1+g/\pi v)^{-1/2}
\end{equation}
 is the standard LL parameter in the interacting region.
 The phase  $\delta_\eta(t)$ is found to be a
 superposition of rectangular pulses,
\begin{equation}
\label{delta_spinless}
\delta_\eta(t)=\sum_{n=0}^\infty \delta_{\eta,n}w_\tau(t,t_n)\,,
\end{equation}
where
\begin{equation}
t_n=(n+1/2-1/2K)L/u\,
\end{equation}
and
\begin{eqnarray}&&
\label{delta_spinless1}
\delta_{\eta,2m}=\pi t_{-\eta} r_L^mr_R^m(1+\eta K)/\sqrt{K}\,,
\nonumber \\&&
\delta_{\eta,2m+1}=
-\pi t_{-\eta} r_\eta^{m+1} r_{-\eta}^{m} (1-\eta K)/\sqrt{K}\,.
\end{eqnarray}
Here $r_\eta$, $t_\eta$ are reflection and transmission coefficients
of plasmons at the left ($\eta=L\equiv -1$) and right
($\eta=R\equiv +1$) boundaries.
For $\tau \ll L/u$ the coherence of plasmon scattering  may  be
neglected and the result assumes the form of  a product
\begin{equation}
\label{c10}
\overline{\Delta}_\eta[\delta_\eta(t)]\simeq\prod_{n=0}^\infty
\overline{\Delta}_{\eta\tau}(\delta_{\eta,n})
\,.
\end{equation}
The  plasmon scattering causes a fractionalization ({\it cf.}
Refs.~\onlinecite{Safi,lehur,Safi97,Pham00,LeHur08,Berg09,Deshpande10})
of the phase soliton,
splitting it into an infinite series of pulses.
As a result, the Fredholm determinant of a counting operator
takes the form of  an infinite product  of determinants,
each calculated for  a rectangular pulse with a corresponding scattering phase
$\delta_{\eta,n}(t)=\delta_{\eta,n}w_\tau(t,0)$.

In the case of smooth boundaries with the  leads we have $r_\eta \simeq
0$, which implies  that only the first ($n=0$) pulse survives in both $\delta_R$
and $\delta_L$. The corresponding amplitudes are depicted in
Table~\ref{table1}.

The above results correspond to the case where  the tunneling
spectroscopy point is located inside the interacting part of the
wire. The case of tunneling into one of non-interacting leads is
studied in the same way; the results can be found in
Ref.~\onlinecite{GGM_long2010}.

So far we have discussed Green functions at coinciding spatial points
having in mind tunneling spectroscopy experiments. Green functions at
different spatial coordinates are also of interest, in particular, in
the context of Aharonov-Bohm interferometry\cite{lehur,GGM_long2010}.
(A similar problem in the context of chiral edge states has been
considered in Refs.~\onlinecite{Chalker07,Levkivskyi09,Kovrizhin10}.)
Equation (\ref{d3}) expressing the non-equilibrium LL Green function in
terms of Fredholm determinants can be generalized for this case as
well \cite{GGM_long2010}.

\subsubsection{Luttinger liquid: Counting statistics}

In  the problem of counting statistics of non-equilibrium LL one is
interested in the   generating function
$\chi(\lambda)=\sum_{n=-\infty}^\infty p_\tau(n) e^{in\lambda}$, where
$p_\tau(n)$  is  the  probability for $n$ electrons to pass through  a
given  cross-section  during
the time interval $\tau$. On the experimental side, the second moment
(shot noise) has been measured in correlated 1D systems
\cite{Kim07,Wu07}; an experimental analysis of higher moments
and of the full counting statistics (FCS) remains a challenging issue.

For the non-interacting case the FCS
generating function $\chi(\lambda)$
has been calculated in Ref.~\onlinecite{Levitov-noise}
by means of Landauer scattering-state approach.
For an ideal quantum wire  (with no scattering inside the wire) with
distributions $n_\eta(\epsilon)$,  the
generating function of FCS  is given by
\begin{equation}
\label{generating_function}
\chi(\lambda)=\Delta_R[\delta_R(t)]\Delta_L[\delta_L(t)]\,,
\end{equation}
with the phases $\delta_\eta(t) = \lambda\eta w_\tau(t,0)$.
For an interacting wire (LL) the result
\cite{GGM_short2010} retains the form of a product of Fredholm determinants,
Eq.~(\ref{generating_function}), but with the scattering phase
$\delta_\eta(t)$  turning into the  following sequence of pulses:
\begin{equation}
\label{pulses_series}
\delta_\eta(t)=\sum_{n=0}^\infty\delta_{\eta,n}w_\tau(t,t_n)\,,
\end{equation}
with  partial phase shifts
\begin{eqnarray}&&
\label{phase_center}
\delta_{\eta,2n}=\eta\lambda t_{-\eta}\sqrt{K} r_\eta^nr_{-\eta}^n
\equiv \eta\lambda e^*_{\eta,2n} \,, \\&&
\delta_{\eta,2n+1}=\eta\lambda t_{-\eta}\sqrt{K}
r_\eta^{n+1}r_{-\eta}^n \equiv \eta\lambda e^*_{\eta,2n+1} \,.
\end{eqnarray}
The time moment $t_n=(n+1/2-1/2K)L/u$ corresponds to the beginning of
the $n$-th pulse.

The result is non-trivial when the measurement interval $\tau$ is
small compared to the length of the LL conductor, $\tau\ll L/u$. (In the
opposite   limit the pulses overlap and one recovers the results of
the FCS of non-interacting fermions \cite{Levitov-noise}.)
As for the tunneling spectroscopy problem, the determinants then
split into a product of determinants for individual pulses.
The FCS of the LL then becomes a superposition of FCS of
non-interacting electrons with fractional charges $e^*_{\eta,n}$.
For the case of smooth
boundaries we obtain  only one fractional charge, $e^*_{\eta,0}=
\sqrt{K}$ (Table~\ref{table1}).
In the opposite limit of sharp boundaries, we obtain a
sequence of fractional charges of the form $e^*_{\eta,n}=
2K(1-K)^n/(1+K)^{n+1}$.

These results describe current fluctuations in the interacting part of
the wire. The FCS measured in the non-interacting part (keeping the
assumption $\tau \ll L/u$) has a similar structure, but the values of the
fractional charges are different, see Ref.~\onlinecite{GGM_short2010}.

\subsection{Luttinger liquid of bosons: Tonks-Grirardeau gas}
\label{bosonic_problems}

We now consider the  problem of a  non-equilibrium LL formed by bosons
with strong repulsion. Interacting bosons out of equilibrium attract currently a
great deal of attention, in particular, in connection with experiments
on cold atoms \cite{cold_atoms}.

To make the connection between the fermionic and the
bosonic LL particularly transparent, we will adopt a toy model with
the same setup,  and with  the same behavior of the LL interaction constant
$K(x)$ as the one assumed for the fermionic models considered above.
 Specifically, we will assume that $K(x)$ takes takes the  value 1 in the
reservoirs, and a value $K$ in the central part of the setup. For
a gas of fermions
 $K=1$ implies  the absence of interaction; now, in the present context,
 it corresponds to hard-core bosons (whose many-body wave function
vanishes when the coordinates  of two particles  coincide); this  system is
known as the Tonks-Girardeau gas\cite{Girardeau}. The wave function of
this system is
related to that of non-interacting fermions via the transformation
\begin{equation}
\label{bosons-to-fermions-1}
\psi_B(x_1,\ldots,x_N)= s(x_1,\ldots,x_N) \psi_F(x_1,\ldots,x_N)\,,
\end{equation}
where $s(x_1,\ldots,x_N)$ is a sign factor ($\pm 1$) counting the
parity of the number of permutations of  coordinates,
\begin{equation}
\label{bosons-to-fermions-2}
s(x_1,\ldots,x_N) = \prod_{i>j}^N \sgn(x_i-x_j)\,.
\end{equation}
If the fermionic wave function is real, this simply yields  $\psi_B =
|\psi_F|$.
We will further assume that after this boson-to-fermion
transformation, the fermions in the reservoirs are characterized by
distribution functions $n_\eta(\epsilon)$, as in the above fermionic
models. While very natural in the fermionic language, this requirement
is in general quite artificial for bosons. We do not know whether it
can be realized in an experiment and consider this as a theoretical
toy model. A more realistic situation arises in the case of partial
non-equilibrium, where each of the reservoirs is at equilibrium
but the temperatures of the two reservoirs  are different.

We will analyze the single-particle bosonic Green functions
\begin{eqnarray}&&
G_B^>(x,t)=-i\langle\Psi_B(x,t)\Psi^\dagger_B(0,0)\rangle\, \,\,,  \\&&
G_B^<(x,t)=-i\langle\Psi^\dagger_B(0,0)\Psi_B(x,t)\rangle \,\,\,  .\\&&
\end{eqnarray}
that carry information about spectral properties (density of states
and distribution functions) of the system.
To calculate them, we proceed, in analogy with fermionic systems, via
the non-equilibrium bosonization technique. The term ``bosonization'' here is,
perhaps, not optimal since the original system is
bosonic to begin with. What actually happens is a transformation from the
original bosonic fields $\Psi_B$ to new bosonic fields $\phi, \theta$,
the latter  describing
density fluctuations in the system. The original field operator is
expressed in term of the new fields as
\cite{Haldane}
\begin{equation}
\label{bose_operator}
\Psi^\dagger_B(x)=\sqrt{\rho_0+\Pi(x)}\bigg\{\sum_{m \in {\rm even}
}e^{im\phi(x)}{\bigg\}}e^{-i\theta(x)}\,.
\end{equation}
Here the field $\phi(x)$ is related to the smeared density $\rho(x) = \rho_0 +
\Pi(x)$ (where $\rho_0$ is the average density) via $\rho(x)
=-\partial_x\phi(x)/\pi$.
The  bosonic fields ($\phi, \theta$) satisfy the commutation relation
\begin{equation}
[\phi(x),\theta(x')]=\frac{i\pi}{2}\rm{sgn}(x-x')\,\,.
\end{equation}
The bosonization  prescription (\ref{bose_operator}) may be further
simplified by discarding fast oscillating terms (corresponding to
$m\ne 0$ in Eq.~(\ref{bose_operator})) and neglecting $\Pi(x)$ in
comparison to $\rho_0$ in the preexponential factor. We thus obtain
\begin{equation}
\Psi^\dagger_B(x)\simeq\sqrt{\rho_0}e^{-i\theta(x)}\,.
\end{equation}
The goal of the discussion above was to present the correlators
needed for $G_B^\gtrless(x,t)$ in terms of the bosonic fields
$\phi, \theta$. We next discuss the pertinent action.

Since the boson-to-fermion transformation (\ref{bosons-to-fermions-1})
preserves the density $|\psi|^2$, and in view of our assumption about
the density matrix in the reservoirs, the Keldysh action of the
non-equilibrium Tonks-Girardeau gas has exactly the same form as for
the corresponding problem of free fermions \cite{GGM_long2010},
\begin{equation}
S_0[\rho,\bar{\rho}]=\sum_\eta S_0[\rho_\eta,\bar{\rho}_\eta]\,\,,
\end{equation}
where $\rho$ and $\bar{\rho}$ are the classical and quantum components
in Keldysh representation,
and the action for excitations with a  given chirality is
\begin{equation}
S_0[\rho_\eta,\bar{\rho}_\eta]=-\rho_\eta\Pi_\eta^{a^{-1}}\bar{\rho}_\eta-i\ln
Z_\eta[\bar{\chi}_\eta]\,.
\end{equation}
The information about the non-equilibrium state of the problem is encoded
in the infinite sum of vacuum loops
\begin{equation}
i\ln Z_\eta[\bar{\chi_\eta}]
=\sum_{n=2}^\infty \frac{i^{n+1}}{n!}\bar{\chi}_\eta^nS_{n,\eta}\,,
\end{equation}
representing a partition function of free fermions subject to the
external quantum field
\begin{equation}
\bar{\chi}_\eta=\Pi_\eta^{a^{-1}}\bar{\rho}_\eta\,.
\end{equation}
Here $S_{n,\eta}$ is the $n$-th order density cumulant of free
fermions in the given non-equilibrium state .
The right and left density components are related to the fields $\phi$
and $\theta$ via
\begin{equation}
\rho_\eta(x)=\frac{\eta}{2\pi}\partial_x\phi_\eta\,,
\end{equation}
where
\begin{eqnarray}&&
\phi_R=\theta -\phi\,, \nonumber  \\&&
\phi_L=\theta+\phi \,.
\end{eqnarray}
In order to find the Green functions of the original bosons  one therefore needs
to calculate the  functional integral
\begin{eqnarray}
\label{hard_core_bosons_funct_int}&&
G_B^>(x,t)=-i\rho_0\int {\cal D}\phi e^{iS[\rho,\bar{\rho}]}\nonumber \\&&
\times
e^{(-i/\sqrt{2})[\theta[0,0]-\theta[x,t]+\bar{\theta}(0,0)+\bar{\theta}(x,t)]}\,\,,
\end{eqnarray}
and similarly for $G^<$.
This   functional integral is fully analogous to the one we had to
evaluate while studying the Green functions of free fermions
(see  Ref.~\onlinecite{GGM_long2010} for details).
The only  difference is  in the source part,
 i.e., in  the exponent that contains terms linear in bosonic fields.
This difference has a rather transparent meaning: creation of the
fermion $\psi_\eta$
corresponds to the vertex operator  $\Psi_{F\eta}^\dagger \propto e^{-i\phi_\eta}$
that generates a soliton (a step-like plasmon wave with amplitude
$2\pi$) that propagates in the  direction $\eta$.
By contrast, bosons represented by the  operators $\Psi_B$ do
not have chirality; the corresponding creation operator
$\Psi_B^\dagger
\propto e^{-i\theta} = e^{-{i\over 2}(\phi_R + \phi_L)}$ generates both
right and left moving waves. This results in  two
Fredholm determinants---one corresponding to the left and another to
the right reservoir---both  with  scattering phases  $\pi$
(as opposed to a single determinant with a scattering phase $2\pi$ for
free fermions):
\begin{eqnarray}&&
G^>_B(x,\tau)=-i\rho_0\Delta_{R,\tau-x/v}(\pi)\Delta_{L,\tau+x/v}(\pi)\nonumber
\\&&
\times e^{-i\frac{\pi\tau}{8}[\sgn(\tau+x/v)+\sgn(\tau-x/v)]}\,.
\label{G-Tonks-Girardeau}
\end{eqnarray}
Here the numerical prefactor has been fixed by comparison with the
equilibrium case, see Appendix \ref{Tonks_girardo_equilibrium}.
At zero temperature $\Delta_\tau(\delta) \sim
(1+\Lambda^2\tau^2)^{-{1\over2}(\delta/2\pi)^2}$, which reproduces the
  well-known $x^{-1/2}$ (for $\tau=0$) behavior corresponding to the
  $k^{-1/2}$ momentum distribution of particles in the equilibrium
  $T=0$ Tonks-Girardeau gas.

Equation (\ref{G-Tonks-Girardeau}) yields the Green function of the
non-equilibrium Tonks-Girardeau gas with a  LL constant $K=1$. We now
assume that the interaction is different in the central part of the
system, so that $K(x)$ there is equal to $K\ne 1$. Performing the
analysis in analogy with the fermionic problem, we find
\begin{equation}
G^>_B(x,\tau)=-i\rho_0\Delta_R[\delta_R(t)]\Delta_L[\delta_L(t)]
e^{-i\frac{\pi\tau}{4}\sgn(\tau)}
\,,
\label{G-Tonks-Girardeau-b}
\end{equation}
where each of the phases $\delta_\eta(t)$ is given by the arithmetic
mean of the corresponding phase for fermionic Green functions $G_{FR}$
and $G_{FL}$. In general we obtain again an infinite sequence of pulses,
as for the fermionic problem. In the case of  smoothly varying $K(x)$
only the first pulse survives  in each of the phases $\delta_\eta(t)$;
its amplitude is equal to $\pi/\sqrt{K}$, as shown in Table~\ref{table1}.

\subsection{Summary}

Let us briefly summarize the results presented
above. All the problems considered (Fermi edge singularity,
tunneling spectroscopy of interacting fermions, their full counting
statistics, and spectral properties of interacting bosons) can be
solved by the non-equilibrium bosonization approach, with  the results
expressed in terms of Fredholm determinants of counting
operators. In these expressions,
all differences between the problems are encoded in the
values of scattering phases $\delta_\eta(t)$.
These scattering phases consist either of one pulse (for the FES
problem and LL problem with smooth boundaries), or of a sequence of
well-separated pulses (for a sufficiently long LL sample with  sharp
boundaries). In the latter case the determinant can be split into  a
product of determinants, each of which corresponding to a single pulse.
Therefore, physical properties of a number of many-body problems are
governed by the behavior of Fredholm determinants with a single phase pulse.
The analysis of this behavior is presented in the next section.

It is worth mentioning that there is a vast literature on the
connection of Fredholm determinants to counting statistics as well as to
quantum and classical integrable models and free-fermion problems; see,
in particular,
Refs.~\onlinecite{Levitov-noise,Klich,Muzykantskii03,Shelankov03
Braunecker06,Schoenhammer07,Avron08,Hassler08,Abanov09,Jimbo80,Izergin98
bettelheim06,Zvonarev,Nazarov,Marquardt}.

\section{Asymptotic properties of Fredholm determinants}
\label{Fredholm_determinant}

\subsection{Ultraviolet regularization and reduction to Toeplitz form}
\label{s:Toeplitz}

We consider a Fredholm determinant of the counting operator for
scattering  phase exhibiting  a single pulse of an amplitude $\delta$
and duration $\tau$,
\begin{equation}
\label{single_pulse}
 \delta(t)=\delta \times w_\tau(t,0)\,.
\end{equation}
In this case the Fredholm determinant (\ref{determinant_definition})
is of the Toeplitz type.
To show this, one  defines a projection operator  $\hat{P}$ that acts on a
function $y(t)$ by restricting it to  the time interval $[0,\tau]$:
\begin{eqnarray}
\hat{P} y(t)=\left\{
\begin{array}{l}
      y(t)\, , \,\,\, {\rm for}\,\,\,  t \in [0,\tau]
      \\ \\
      0 \,, \,\,\,\,\,\,\,\,\,\,\,  {\rm  otherwise}\,.
\end{array}
\right.
\label{projection_operator}
\end{eqnarray}
For  the single-pulse scattering phase (\ref{single_pulse})
Eq.~(\ref{determinant_definition}) can then be rewritten in the form
\begin{equation}
\label{determinant_definition2}
\Delta[\delta(t)]=
{\mathrm{det}}[1 + \hat{P}(e^{-i\delta}-1) \hat{n}]\,\,.
\end{equation}
Since  $\hat{P}^2=\hat{P}$, we can bring  the
determinant (\ref{determinant_definition2})  to the form
\begin{equation}
\label{determinant_Toeplitz}
\Delta[\delta(t)]=
{\mathrm{det}}[1
  + \hat{P}(e^{-i\delta}-1) n \hat{P}]\,\,.
\end{equation}
This determinant still requires an ultraviolet regularization. A
possible way to introduce it is to discretize the coordinate $t$ by
introducing an elementary unit of the size   $\Delta t=\pi/\Lambda$,
such that $t_j=j \Delta t$. This corresponds to restricting the energy
$\epsilon$ variable to the range $[-\Lambda,\Lambda]$.
In the formulations of Szeg\H{o} and Hartwig-Fisher theorems that will be
applied below the function $f(z)$,
that generates the matrix is defined in the complex plane of variable $z$,
and its values on the unit circle $z=e^{i\theta}$
parametrized by the angle $\theta\in [-\pi,\pi]$ are
important. In Eq.~(\ref{determinant_Toeplitz}) this function is
$f(\epsilon) = 1 + n(\epsilon) (e^{-i\delta} -1)$.
The correspondence between  $\epsilon$ and $\theta$ is established by rescaling the energy
$\pi\epsilon/\Lambda = \theta$. Further, we need to eliminate the
jump in $n(\theta)$ at $\theta = \pm \pi$ that results from a hard
cutoff and would generate an additional, unphysical contribution of
the Fermi-edge type. This is done by introducing a phase factor,
\begin{equation}
\label{f_epsilon_periodic}
f(\epsilon) = [1 + n(\epsilon) (e^{-i\delta} -1)] e^{-i{\delta\over
    2}{\epsilon\over \Lambda}}\,,
\end{equation}
that makes $f(\epsilon)$ periodic on $[-\Lambda,\Lambda]$.
Fourier transforming the periodic function  $f(\epsilon)$, we obtain
$f(t_j)$ with $t_j=j \pi/\Lambda$.
Equation
(\ref{determinant_Toeplitz})  then reduces to a determinant
of a large ($N \times N$, where
$N=\tau \Lambda/\pi$) but finite matrix
\begin{equation}
\label{Toeplitz}
\Delta_N[f]={\mathrm{det}}[f(t_j-t_k)]\,, \,\,\,  0\leq j,k \leq N-1\,.
\end{equation}
In the above derivation we assumed $\tau>0$; the result for $\tau<0$
follows from  the property
$\Delta_{-\tau}(\delta)=\Delta_\tau(-\delta)$.

The matrix $\{f(t_j-t_k)\}$ with $0\leq j,k \leq N-1$ is of a Toeplitz
form. Bellow this will allow us to apply  known mathematical results
concerning the asymptotic properties of its determinant $\Delta_N$
in the limit of large $N$.
Physically, this corresponds to the regime of long time
$\tau$, i.e. to infrared asymptotics of correlation functions under
interest. For arbitrary times $\tau$
Eqs.~(\ref{Toeplitz}), (\ref{f_epsilon_periodic}) can be directly used
for numerical evaluation of the determinant $\Delta_N[f]$.

The following important point is also worth stressing. The Green functions
of LL tunneling spectroscopy and FES problems require
evaluation of such determinants $\Delta(\delta)$ at phases $\delta$ that are not
small. For example, in the case of relatively weak LL interaction ($K$
close to unity) or small phase shift $\delta_0$ for the scattering on
the core hole in the FES problem, one needs to know the determinant
at $\delta$ close to $2\pi$, see Table~\ref{table1}. For strong LL
interaction or large phase shift $\delta_0$ the value of $\delta$ can
be, in principle, arbitrarily large. As was discussed in our papers
\cite{GGM_long2010} the determinant $\Delta(\delta)$ should be then
understood as analytically continued from the region of small
$\delta$. We emphasize now that the present regularization
(discretization of time and introduction of the phase factor ensuring
periodicity in energy) implements the required analytic continuation.
Indeed,
in the original form of the determinant, Eq.~(\ref{determinant_definition2}),
the information about the integer part of $\delta/2\pi$ was not
explicit, which made the analytic continuation necessary. On the other
hand, in the present regularization the integer part of $\delta/2\pi$ enters
explicitly via the last phase factor in
Eq.~(\ref{f_epsilon_periodic}). As we will demonstrate below, this
allows one to directly compute the determinant at arbitrary large $\delta$.

\subsection{Simplified analysis of asymptotics via Szeg\H{o} formula }
\label{s:Szego}

The long time behavior of determinants of Toeplitz matrices can be
found using  the Szeg\H{o} theorem and its extension known as
Fisher-Hartwig conjecture. The condition of applicability of Szeg\H{o}
theorem requires that $f(z)$ is a sufficiently smooth function. This
condition is not fulfilled in our case. Indeed, already at equilibrium (and at
zero temperature) $f(\epsilon)$ has a jump at the Fermi energy. In
non-equilibrium situations we are interested in $f(\epsilon)$ will have
two (``double-step distribution'') or more such jumps. We will see,
however, that the Szeg\H{o} formula nevertheless yields correctly the
main ingredients of the result (dephasing rate and modified power-law
exponents). A more accurate treatment will be performed below in
Sec.~\ref{s:Fisher-Hartwig} in the framework of Fisher-Hartwig
formula.

Here we assume $|\delta|<\pi$. (The accurate consideration in
Sec.~\ref{s:Fisher-Hartwig} will be performed for arbitrary $\delta$.)
We first consider a simple case  of thermal equilibrium,
when the  determinant (\ref{determinant_Toeplitz}) can be
calculated explicitly
\begin{equation}
\Delta_{\tau}(\delta)\simeq\frac{1}{
\left(1+\Lambda^2\tau^2\right)
^{\frac{1}{2}\left(\frac{\delta}{2\pi}\right)^2}
}
\left(
\frac{\pi T \tau}{\sinh \pi T \tau}
\right)^{\left(\delta/2\pi\right)^2}\,.
\label{det_eq}
\end{equation}
Note that the precise behavior of the functional determinant at the
ultraviolet scale, $\tau \sim \Lambda^{-1}$, depends on the
regularization procedure.
Equation (\ref{det_eq}) corresponds to  a smooth cut-off
$e^{-|\epsilon|/\Lambda}$ in the energy space\cite{GGM_long2010} that
is different from the regularization we use in this work.
We are interested, however, in energy scales much less than
$\Lambda$. i.e. $\tau \gg \Lambda^{-1}$, where the determinant does
not depend on the regularization scheme, up to an overall prefactor
independent on the distribution function $n(\epsilon)$.
At  $T=0$ one readily finds from Eq.~(\ref{det_eq})
\begin{equation}
\label{eq_a1}
\Delta_\tau(\delta) \simeq
(\tau\Lambda)^{-\left(\delta/2\pi\right)^2}\, ,\,\,  \tau \gg
\Lambda^{-1}\,.
\end{equation}

To apply the Szeg\H{o} formula (see Appendix
\ref{Fisher-Hartwig-conjecture}), we have to calculate the Fourier
transform $V(t_j)$ of $\ln f(\epsilon)$,
\begin{eqnarray}&&
\label{eq_d1}
V(t_j)=\int_{-\Lambda}^{\Lambda} \frac{d\epsilon}{2\pi}e^{-i\epsilon  t_j}
\ln f(\epsilon)\,.
\end{eqnarray}
where $f(\epsilon)$ is given by Eq.~(\ref{f_epsilon_periodic}).
For the case of the Fermi-Dirac distribution with $T=0$ one finds
\begin{eqnarray}&&
\label{Veq}
V(t_j)=\frac{\delta}{2\pi} \times
\left\{
\begin{array}{ll}
1/t_j\ , & \qquad t_j \ne 0\ ; \\
-i\Lambda\ , & \qquad t_j = 0\ .
\end{array}
\right.
\end{eqnarray}
According to the (strong) Szeg\H{o} theorem [Eq. (\ref{Szoego})],
the large-$N$ behavior of
the determinant reads, in the present notations
\begin{equation}
\label{szego-result}
\Delta_N \sim \exp \left\{N\, \Delta t\, V(0) + \Delta
t\,\sum_{j=0}^Nt_jV(t_j)V(-t_j)\right\}\,.
\end{equation}
The first term in the exponent $N\, \Delta t\, V(0) = \tau V(0) =
-i\delta\tau\Lambda/2\pi$ is purely imaginary and yields just a phase
factor. Calculating the second term, we find
\begin{eqnarray}&&
\label{eq_b1}
\Delta t \sum_{j=0}^N t_j V(t_j) V(-t_j) \simeq
-\left(\frac{\delta}{2\pi}\right)^2\int_{\Lambda^{-1}}^\tau\frac{dt}{t}=\nonumber
\\&&
=-\left(\frac{\delta}{2\pi}\right)^2\ln (\tau\Lambda)\,.
\end{eqnarray}
Here we assumed that the time is sufficiently long (compared to the
ultraviolet scale),  $\tau\Lambda \gg 1$, which is
exactly the condition of applicability of the Szeg\H{o} theorem ($N\gg
1$).
Exponentiation of Eq.~(\ref{eq_b1}) according to
Eq.~(\ref{szego-result}) reproduces the result
(\ref{eq_a1}).

It is easy to verify that the Szeg\H{o} formula yields the correct
behavior of the determinant also at finite temperature $T$.
(In fact, in the long-time regime $\tau T \gg 1$ the Szeg\H{o} theorem
becomes rigorously applicable.)

We turn now to the non-equilibrium situation and  focus on a double step
distribution function,
\begin{equation}
\label{double-step}
n(\epsilon)=(1-a)n_0(\epsilon-\epsilon_0) + an_0(\epsilon-\epsilon_1)\,.
\end{equation}
Here  $\epsilon_0= -aU$, $\epsilon_1= (1-a)U$, and
$n_0(\epsilon)$ is the zero-temperature Fermi-Dirac function,
$n_0(\epsilon)=\theta(-\epsilon)$.

The function $f(\epsilon)$ has now the form
\begin{eqnarray}
\label{eq_a2}
f(\epsilon)&=& e^{-i{\delta\over 2} {\epsilon \over \Lambda}}
\nonumber \\
& \times & \left\{
\begin{array}{ll}
      e^{-i\delta} \,, & \ \   -\Lambda < \epsilon < \epsilon_0
      \\
      1+\left(e^{-i\delta}-1\right)a  \,, & \ \ \epsilon_0 < \epsilon
      < \epsilon_1
\\
1 \,, & \ \ \epsilon_1 < \epsilon
      < \Lambda\,.
\end{array}
\right.
\end{eqnarray}
The Fourier transform of $\ln f$, Eq.~(\ref{eq_d1}), reads
\begin{equation}
V(t_j)= \left\{
\begin{array}{ll}
-\frac{1}{t_j}\left(\beta_0e^{-i\epsilon_0t}+\beta_1e^{-i\epsilon_1t}\right)
\,, & \ \ t_j\ne 0 \\[0.3cm]
-i{\delta\Lambda\over 2\pi} + iU\left(a{\delta\over 2\pi} +
  \beta_1\right)\,, & \ \ t_j=0\,,
\label{v_t_double_step}
\end{array}
\right.
\end{equation}
where we defined
\begin{eqnarray}&&
\label{eq_a4}
\beta_1=-\frac{i}{2\pi}\ln\bigg[1+\left(e^{-i\delta}-1\right)a\bigg] \,,
\nonumber \\&&
\beta_0=-\frac{\delta}{2\pi}-\beta_1\,.
\end{eqnarray}
Now we apply the Szeg\H{o} theorem. The leading, linear-in-$t$, term in the
asymptotics of $\ln \Delta$ is governed by $V(0)$ given by the second
line in Eq.~(\ref{v_t_double_step}). Particularly important is the real
part of $V(0)$ that leads to the exponential decay of the determinat
with time, $\Delta \propto \exp( - \tau/2\tau_\phi)$. The
corresponding decay rate is given by
\begin{equation}
\label{dephasing1}
\tau_\phi^{-1} =2{\rm Re}\: V(0)=
-\frac{U}{2\pi}\ln\bigg[1-4a(1-a)\sin^2\frac{ \delta}{2}\bigg]\,.
\end{equation}
To find the subleading term in the Szeg\H{o} formula (\ref{szego-result}),
we have to evaluate the sum $\Delta t\sum_{k=1}^N  t_k V(t_k)
V(-t_k)$. We get
\begin{eqnarray}
&&
\Delta t\sum_{k=1}^N  t_k V(t_k) V(-t_k) \\ \nonumber
&& \simeq
-\int_{\Lambda^{-1}}^\tau {dt\over t} (\beta_0^2 + \beta_1^2 + 2
\beta_0\beta_1\cos Ut) \\ \nonumber
&&
\simeq \left\{
\begin{array}{ll}
-\left({\delta\over2\pi}\right)^2
\ln \Lambda \tau\ , & \ \ \tau \ll U^{-1}\\[0.3cm]
-\left({\delta\over2\pi}\right)^2  \ln {\Lambda\over U} - (\beta_0^2 +
\beta_1^2)\ln U\tau
\ , & \ \ \tau \gg U^{-1}\,.
\end{array}
\right.  \nonumber \\
&&
\label{szego-subleading-double-step}
\end{eqnarray}
In the short-time regime, $U\tau\ll 1$, we simply reproduce the
equilibrium result. On the other hand, for long times,  $U\tau\gg 1$,
a different behavior emerges,
\begin{equation}
\label{eq_a9}
\Delta_\tau(\delta) \sim e^{-\tau/2\tau_\phi}
(\Lambda/U)^{-(\delta/2\pi)^2}(U\tau)^{-(\beta_0^2+\beta_1^2)}\,,
\end{equation}
where  $\beta_0, \beta_1$ are given by Eq.(\ref{eq_a4}) and $\tau_\phi$
by Eq.~(\ref{dephasing1}).

As has been already mentioned, the present problem goes, strictly
speaking, beyond the range of applicability of the Szeg\H{o} theorem,
since  the function $f(\epsilon)$ has discontinuities. This
results in the (correct) $\ln N$ behavior of the second term in the exponent of
(\ref{szego-result}), while it should have a constant
limit as $N\to \infty$ under the conditions of applicability
of the Szeg\H{o} theorem. It turns out, however, that the key results
obtained above---dephasing rate and modified power-law exponents---are
correct. This will be shown in Sec.~\ref{s:Fisher-Hartwig} by using
recent mathematical results on Fisher-Hartwig conjecture which treats
Toeplitz determinants of exactly the type we have encountered.
The application of the Fisher-Hartwig formalism will allow us
not just to confirm the above results but also to go considerably
further. First, we will calculate the asymptotics of the determinants
exactly, including prefactors $\sim N^0$. Second, we will
obtain results for an arbitrary phase $\delta$. As we have already
emphasized, this is important for the analysis of the many-body problems
considered above. Third, we will obtain  not only the leading contribution
but also subleading terms. As we show below, various contributions
have very transparent physical meaning in the problems of FES and
tunneling spectroscopy, corresponding to power-law behavior at
multiple Fermi edges.

\subsection{Accurate analysis of asymptotics via Fisher-Hartwig conjecture}
\label{s:Fisher-Hartwig}

It is instructive to begin again by considering the zero-temperature
equilibrium case, $n(\epsilon) = \theta(-\epsilon)$.
In the case of a single singular point, the Fisher-Hartwig
generating function $f(z)$ has the form
\begin{equation}
\label{a5}
f(z)=e^{V(z)}|z-z_0|^{\alpha_0}
\left(\frac{z}{z_0}\right)^{\beta_0}g_{z_0,\beta_0}(z)\,,
\end{equation}
where $g_{z_0,\beta_0}(z)$ is a ``jump function'',
Eq.~(\ref{jump-function}).
Comparing Eq.~(\ref{a5}) with  Eq.~(\ref{f_epsilon_periodic})
(where we set  $\theta = \pi \epsilon/\Lambda$ and $z=e^{i\theta}$),
we identify the parameters:
$z_0=1$, $\alpha_0=0$, $\beta_0=-\delta/2\pi$, and $V(z) = - i\delta/2$.
Using the Fisher-Hartwig formula (\ref{fisher-hartwig}), we obtain the
asymptotics
\begin{equation}
\label{fh-equilibrium}
\Delta_N(\delta) =
e^{-i{\delta N\over 2}} N^{-(\delta/2\pi)^2}
G\left(1-{\delta\over2\pi}\right)G\left(1+{\delta\over2\pi}\right)\,,
\end{equation}
where $G(z)$ is the Barnes $G$-function.
In physical notations $N=\tau\Lambda/\pi$.
It is now easy to see that the Fisher-Hartwig formula (\ref{fisher-hartwig})
reproduces correctly the power-law behavior (\ref{eq_a1}) of the
determinant.

The result (\ref{fh-equilibrium}) is valid for arbitrary
$\delta$. Consider an important case of $\delta$ in the
vicinity of $2\pi$, $\delta=2\pi+\delta'$ with $|\delta'|\ll 1$,
that is relevant to the FES problem with small
scattering phase and to tunneling spectroscopy of LL with weak
interaction. Using $G(1) = 1$ and $G(z) \simeq z$ for small $z$, we get
\begin{equation}
\label{fh-equilibrium-near-2pi}
\Delta_\tau(\delta) \simeq - {\delta'\over 2\pi}
e^{-i\tau\Lambda(1+\delta'/2\pi)}
\left({\tau\Lambda\over\pi}\right)^{-(1+\delta'/2\pi)^2}\,.
\end{equation}
It was shown earlier \cite{GGM_long2010} that
$\Delta_\tau(\delta)$ at $\delta\to 2\pi$ should yield, up to a
proportionality factor,
the free fermion Green function $G_0(\tau)$, see Eq.~(\ref{a1}).
As we see from
Eq.~(\ref{fh-equilibrium}), the exact correspondence in
the present ultraviolet regularization of the determinant is
\begin{equation}
\label{fh-equilibrium-free-fermions}
G_0^\gtrless(\tau) = e^{i\tau\Lambda}{\Lambda\over \pi v}
{1\over 1\mp i/\Lambda\tau} \: \lim_{\delta'\to 0}
{1\over \delta'} \Delta_\tau(2\pi+\delta')\,.
\end{equation}
We will demonstrate below how this general formula works for the case
of a multiple-step distribution.

We now turn to the case of a double-step distribution
(\ref{double-step}). The singular points are
$z_j=e^{i\pi\epsilon_j/\Lambda}$ ($j=0,1$), where $\epsilon_0 = -aU$,
$\epsilon_1 = \epsilon_0 + U$. We consider first the case of
$|\delta|<\pi$.
It is easy to see that Eq.~(\ref{eq_a2}) is of Fisher-Hartwig form of
generating function with two jump-type singularities,
\begin{equation}
\label{eq_a3}
f(z)=e^{V(z)}\left(\frac{z}{z_0}\right)^{\beta_0}
\left(\frac{z}{z_1}\right)^{\beta_1}
g_{z_0,\beta_0}(z)g_{z_1,\beta_1}(z)\,,
\end{equation}
with $\beta_j$ ($j=0,1$) given by Eq.~(\ref{eq_a4}) and
\begin{equation}
\label{V_FH_double_step}
V(z) = {\rm const} = {-i\delta\over 2} + i {U\pi\over\Lambda}\left({a\delta\over
    2\pi} + \beta_1\right)\,.
\end{equation}
The logarithm in Eq.~(\ref{eq_a4}) and in analogous formulas for
$\beta_j'$ below is understood in the sense of its main
branch (with imaginary part between $-\pi$ and $\pi$).
We further note that under the condition
$U \ll \Lambda$ we can approximate $|z_1-z_0| \simeq
\pi U/\Lambda$. Applying Eq.~(\ref{fisher-hartwig}), we thus get
\begin{eqnarray}
\label{fh4}
\Delta_\tau(\delta) &\simeq & \exp\{- {i\delta\over 2\pi}\tau\Lambda
-i\tau\mu - \tau/2\tau_\phi \} \nonumber \\
& \times & \left( {\tau\Lambda\over\pi}\right)^{-\beta_0^2-\beta_1^2}
\left( {\Lambda\over\pi U}\right)^{-2\beta_0\beta_1} \nonumber \\
& \times &
G(1+\beta_0)G(1-\beta_0)G(1+\beta_1)G(1-\beta_1)\,, \nonumber \\
&&
\end{eqnarray}
 where  $1/\tau_\phi$ is the exponential decay (dephasing) rate,
 Eq.~(\ref{dephasing1}),
and $\mu = -U({\rm Re} \beta_1 + a\delta/2\pi)$.
This confirms the  long-time ($U\tau\gg 1$) behavior of the
determinant obtained above from the Szeg\H{o} formula,
Eq.~(\ref{eq_a9}), and yields the exact value of the corresponding
prefactor.

Consider now the more general situation, when $\delta$ is not small:
$\delta = 2\pi M + \delta'$ with some integer $M$ and
$|\delta'|<\pi$.
The exponents $\beta_0$ and $\beta_1$ can be now chosen to be
\begin{eqnarray}
\beta_1 &=& - {i\over 2\pi} \ln(1-a+a e^{-i\delta}) \equiv \beta_1'\,,
\label{fh1} \\
\beta_0 &=& - {\delta\over 2\pi} - \beta_1 = -M - {\delta'\over 2\pi}
- \beta_1' \equiv - M  + \beta_0'\,.
\label{fh2}
\end{eqnarray}
We have introduced here $\beta_0'$ and $\beta_1'$ satisfying
$|{\rm Re} \beta_j'|<1/2$, $\beta_0'+\beta_1' = -\delta'/2\pi$.  The exponents
$\beta_j$ (that may differ from $\beta'_j$ by an integer only) satisfy
$\beta_0+\beta_1 = -\delta/2\pi \equiv -M -\delta'/2\pi$. Equations
(\ref{fh1}), (\ref{fh2}) represent
one possible choice; the final result will not depend
on a particular choice in view of the summation over integers $n_j$ in
Eq.~(\ref{fisher-hartwig-general}).
We obtain from Eq.~(\ref{fisher-hartwig-general}):
\begin{eqnarray}
\label{fh5}
\Delta_\tau(\delta) &\simeq & \exp\{- {i\delta\over 2\pi}\tau\Lambda
-i\tau\mu' -iM\epsilon_0\tau - \tau/2\tau_\phi \} \nonumber \\
& \times & \sum_{n=-\infty}^\infty
\left( {\tau\Lambda\over\pi}\right)^{-(\beta'_0-M+n)^2-(\beta'_1-n)^2} \nonumber\\
&\times&
\left( {\Lambda\over\pi U}\right)^{-2(\beta_0'-M+n)(\beta_1'-n)} \nonumber \\
& \times & e^{-inU\tau}
G(1+\beta_0'-M+n)G(1-\beta_0'+M-n)\nonumber\\
&\times& G(1+\beta_1'-n)G(1-\beta_1'+n)\,, \nonumber \\
&&
\end{eqnarray}
where  $\mu' = -U({\rm Re}\: \beta'_1 + a\delta'/2\pi)$. When $M=0$,
the dominant term (that is characterized by the smallest power-law exponent
${\rm Re}[(\beta'_0-M+n)^2+(\beta'_1-n)^2]$) is the one with $n=0$,
reproducing Eq.~(\ref{fh4}).

In the
particularly interesting case of $M=1$, when $\delta$ is in the
vicinity of $2\pi$, the two leading terms are those with $n=0$ and
$n=1$. Retaining only these terms, we find
\begin{eqnarray}
\label{fh6}
\Delta_\tau(\delta) &\simeq & \exp\{- {i\delta\over 2\pi}\tau\Lambda
-i\tau\mu' - \tau/2\tau_\phi \} \nonumber \\
& \times &
\left( {\tau\Lambda\over\pi}\right)^{-(\beta'_0)^2-(\beta'_1)^2}
\left( {\Lambda\over\pi U}\right)^{-2\beta_0'\beta_1'}
\left(-{\delta'\over 2\pi}\right)\nonumber \\
& \times & \left[ (1-a)e^{iaU\tau}\left( {\tau\Lambda\over\pi}\right)^{2\beta_0'}
\left( {\Lambda\over\pi U}\right)^{2\beta_1'} \right. \nonumber \\
&+& \left. a e^{i(a-1)U\tau}\left( {\tau\Lambda\over\pi}\right)^{2\beta_1'}
\left( {\Lambda\over\pi U}\right)^{2\beta_0'}\right]\,.
\end{eqnarray}

In the limit $\delta'\to 0$, substituting Eq.~(\ref{fh6}) into
Eq.~(\ref{fh-equilibrium-free-fermions}), we correctly reproduce the
free-electron Green function for the double-step distribution,
$G^\gtrless_0(\tau)= [(1-a)e^{iaU\tau} + a
e^{(1-a)U\tau}]G^\gtrless_{0,T=0}(\tau)$, where
$G^\gtrless_{0,T=0}(\tau)$ is the equilibrium, $T=0$ value of
$G^\gtrless_0(\tau)$.

These results can be generalized to a multi-step
distribution, Fig.~\ref{figure1}.
Consider a distribution function of the form
\begin{equation}
\label{multistep-distribution}
n(\epsilon) = \left\{
\begin{array}{ll}
1 \equiv a_0 \,, & \qquad \epsilon < \epsilon_0 \\
a_1\,, & \qquad \epsilon_0 < \epsilon <\epsilon_1 \\
\ldots &  \\
 a_m\,, & \qquad \epsilon_{m-1} < \epsilon <\epsilon_m \\
0 \equiv a_{m+1}\,, & \qquad \epsilon_m < \epsilon\,.
\end{array}
\right.
\end{equation}
Here all $a_j$ with $j=1,\ldots,m$ satisfy $0\le a_j \le 1$ without any further
restrictions. In particular, no requirement of monotonicity is
imposed: the distribution  $n(\epsilon)$ can describe inversion of
population in some regions of energy, with $a_{j+1} > a_j$.
Using Eq.~(\ref{fisher-hartwig-general}), we obtain for $\delta = 2\pi
M +\delta'$ where, as before, $M$ is the integer closest to $\delta/2\pi$:
\begin{eqnarray}
\label{fh7}
\Delta_\tau(\delta) &\simeq & \exp\{- {i\delta\over 2\pi}\tau\Lambda
-i\tau\mu' - \tau/2\tau_\phi \} \nonumber \\
& \times & \sum_{n_0+\ldots+n_m=-M} \exp\{i\tau\sum_jn_j\epsilon_j\}
\left( {\tau\Lambda\over\pi}\right)^{-\sum_j\beta_j^2} \nonumber\\
&\times&
\prod_{j<k}\left( {\Lambda\over\pi U_{jk}}\right)^{-2\beta_j\beta_k} \nonumber \\
& \times & \left. \prod_j
G(1+\beta_j)G(1-\beta_j)\right|_{\beta_j = \beta_j'+ n_j}\,.
\end{eqnarray}
Here the exponents $\beta_j'$ (satisfying $|{\rm Re} \beta_j'|<1/2$) are
\begin{equation}
\label{fh8}
\beta_i' = -{i\over 2\pi}\left[\ln(1-a_i+a_ie^{-i\delta}) -
\ln(1-a_{i+1}+a_{i+1}e^{-i\delta})\right]\,,
\end{equation}
the dephasing rate reads
\begin{eqnarray}
\label{fh9}
{1\over \tau_\phi} &=& 2{\rm Im}\sum_j \beta_j'\epsilon_j
\nonumber \\ &=& - {1\over
  2\pi} \sum_{j=1}^m (\epsilon_j-\epsilon_{j-1})\ln [1 - 4 a_j
  (1-a_j)\sin^2{\delta\over 2}]\,,  \nonumber \\
&&
\end{eqnarray}
$U_{jk} = |\epsilon_j-\epsilon_k|$,
and $\mu' = - {\rm Re} \sum_j\beta'_j\epsilon_j$.

The remarkable periodicity in the dependence of the dephasing rate for a
multi-step
distribution, as a function on the phase $\delta$, should be emphasized.
When applied to LL spectroscopy, this results in periodic dependence
of $1/\tau_\phi$ on the interaction
strength\cite{GGM_long2010}. The dephasing rate manifests itself in
a broadening of the singularities in the energy space (see
Sec.~\ref{s:energy_representation}), as well as in an exponential
damping of Aharonov-Bohm oscillations in out-of-equilibrium
interferometry\cite{GGM_long2010}.

While the above results are obtained in time representation, the
experimental measurements of Green functions describing the FES,
Eq.~(\ref{b1}) and the  LL tunneling spectroscopy, Eq.~(\ref{d3}), are
normally performed in energy space. It is thus important to see what
the implications of the above findings in the energy representation are.

\subsection{Singularities in energy representation}
\label{s:energy_representation}

After Fourier transforming  from time into  energy space,
Eq.~(\ref{fh7}) yields multiple power-law singularities of the type
$|\epsilon + \sum_j n_j\epsilon_j-\mu'|^{-1+\sum_j\beta_j^2}$, where
$\beta_j = \beta'_j+n_j$.
Positions of the singularities are given by linear combinations of
the singular points $\epsilon_j$ of the distribution function, with a
small overall shift $\mu'$. All singularities are broadened by the
dephasing rate $1/2\tau_{\phi}$.

As an important example, consider the case $M=1$, where $\delta$ is
close to $2\pi$. The leading singularities then correspond to all
$n_j$ being equal to zero except for one, $n_k= -1$. The position of
each such singularity  is close to $\epsilon = \epsilon_k$ and the exponent is
$\sum_j \beta_j^2 = 1 - 2\beta_k' + \sum_j (\beta_j')^2$. There is such
a singularity for each of the singular points of the original
distribution function (i.e. for each $k=0,1,\ldots,m$) as
expected. Further singularities are much weaker. The next ones correspond
to all $n_j$ being zero except for $n_k=n_l=-1$ and $n_p=1$. Such a
singularity is located at $\epsilon = \epsilon_k + \epsilon_l -
\epsilon_p$, with
an exponent $\sum_j \beta_j^2 = 3 - 2\beta_k'- 2\beta_l'+ 2\beta_p'
+ \sum_j (\beta_j')^2$. The next ones are generated by $n_k=-2$, $n_l=1$,
located at $\epsilon = 2\epsilon_k - \epsilon_l$ and are characterized
by exponents   $\sum_j \beta_j^2 = 5 - 4\beta_k'+ 2\beta_l'+ \sum_j
(\beta_j')^2$, and so on. These subleading singularities can be
understood as resulting from inelastic processes. For example, the
edge $\epsilon = \epsilon_k + \epsilon_l - \epsilon_p$ results from a
creation  of an electron near $\epsilon_k$ accompanied by creation of
a particle-hole pair with energies near $\epsilon_l$ and $\epsilon_p$,
respectively.

Let us present results for dominant singularities for the FES
Green function (\ref{b1}) in the energy space in an explicit form.
(The LL tunneling spectroscopy Green function is analyzed in the same way.)
The behavior of the Green functions $G^\gtrless(\epsilon)$
for energies close to singular points $\epsilon_k+\mu'$
is given by (up to an additive contribution that can be considered as
constant near  $\epsilon_k+\mu'$)
\begin{eqnarray}
\label{fh10}
G^\gtrless(\epsilon) &\simeq& \pm\frac{i}{2v}\prod_{j\neq k}
\left(\frac{\Lambda}{\pi U_{jk}}\right)^{2\beta_j'}
\prod_{j<l}
\left(\frac{\Lambda}{\pi U_{jl}}\right)^{-2\beta_j'\beta_l'}
\nonumber \\
&\times&
(\epsilon-\epsilon_k-\mu'-i/2\tau_\phi)^{\gamma_k}
\nonumber \\
&\times& \left\{
\begin{array}{ll}
1\mp (a_k-a_{k+1}) \,, & \qquad \epsilon < \epsilon_k+\mu' \\
1\pm (a_k-a_{k+1})\,, & \qquad \epsilon_k+\mu' < \epsilon\,,
\end{array}
\right.
\end{eqnarray}
where the exponents $\gamma_k$ are given by
$\gamma_k  = - 2\beta_k' + \sum_j(\beta_j')^2$.

Let us assume for simplicity that all distances between consecutive
singular points are of the same order, $U_{j,j-1} \sim U$. The region
of validity of the behavior (\ref{fh10}) is then
$|\epsilon-\epsilon_k-\mu'|\lesssim U$. Let us emphasize that the
power-law singularity in Eq.~(\ref{fh10}) is smeared by the dephasing
$1/2\tau_\phi$. In a generic situation, when
the phase $\delta' = \delta-2\pi$ is of order $\pi$ (i.e. not small),
the dephasing rate is of order $U$. Then the smearing is strong, and
the power law essentially does not have room to develop.
On the other hand, when the phase $\delta = 2\pi + \delta'$
is close to $2\pi$ (which
corresponds to a weak interaction in LL or to small phase shift
for scattering on core hole in the FES problem), the
dephasing rate is small as $1/2\tau_\phi \sim (\delta')^2U$, which
yields a parametrically broad interval for the power-law behavior,
$(\delta')^2U \lesssim |\epsilon-\epsilon_k-\mu'|\lesssim U$. Note,
though, that the power-law exponents $\gamma_i$ in this situation are
also small, $\gamma_i \sim \delta'$, so that the power law essentially
reduces to a logarithmic correction.

When applied to the problem of split FES, see Eq.~(\ref{b1}), our result agrees
with that obtained by Abanin and Levitov \cite{Abanin}
for a double-step distribution. It should be
emphasized that our approach is different from the one used in
Ref.~\onlinecite{Abanin}. While we work in the non-equilibrium
bosonization framework and present the Green function in terms
of a single determinant $\Delta(\delta)$ at the phase $\delta=
2\pi-2\delta_0$, Abanin and Levitov  used the fermionic FES theory
and obtained the result in the form
of a product of a determinant $\Delta(-2\delta_0)$ and a Green
function, and then analyzed both terms by an approximate solution of the
corresponding Riemann-Hilbert problem.

Applying these results to the LL tunneling spectroscopy, see
Eq.~(\ref{d3}),  we obtain
split power-law singularities, with modified (compared to the
equilibrium regime) exponents and with broadening
by the non-equilibrium dephasing rate $1/2\tau_\phi$. This is
illustrated in Fig.~\ref{figure2} where we show the behavior of
the tunneling density of states (TDOS), $\nu(\epsilon)=
[G^<(\epsilon)-G^>(\epsilon)]/2\pi i$.
As discussed above, for a weak interaction the
non-equilibrium power laws reduce to logarithmic corrections and are
weakly smeared (by small $1/\tau_\phi$). For an arbitrary strength of
interaction the scale for smearing of singularities becomes comparable
to the distance between the singular points. The profile of TDOS in a
general situation can be obtained by numerical evaluation of the
Toeplitz determinant.

It is worth mentioning some further recent works that addressed the
non-equilibrium LL spectroscopy.  Influence of
non-equilibrium conditions on exponents was also found within the
functional renormalization group approach (by using approximations justified
for weak interaction) in Ref.~\onlinecite{jakobs08};
dephasing was discarded there. Qualitatively similar results (modification of
exponents and oscillatory dependence of dephasing rate on the
interaction strength) were also obtained in Ref.~\onlinecite{Ngo}. The
difference is due to the fact that the non-equilibrium setup  of
Ref.~\onlinecite{Ngo} (a biased quantum wire with an impurity inside the
interacting region)
is different from that of our work, where the non-equilibrium
distribution is assumed to be formed by scattering outside of the interacting
LL region.

\begin{figure}
\includegraphics[width=1\columnwidth,angle=0]{triple_steps2.eps}
\caption{
Distribution functions with multiple edges. Two
examples of three-step distributions are shown:
(A) with monotonously decreasing occupation;
(B) with population inversion.}
\label{figure1}
\end{figure}

\begin{figure}
\includegraphics[width=0.8\columnwidth,angle=0]{triple_step_density_of_states_down.eps}

\vspace*{0.85cm}
\includegraphics[width=0.8\columnwidth,angle=0]{triple_step_density_of_states_down_up_down.eps}
\caption{Schematic results  for TDOS in a LL with not-too-strong
  interaction and with multiple-step
  distributions. The distributions of electrons from both reservoirs are
  assumed to be equal and of the type  shown in Fig.~\ref{figure1}A
  (upper pane) or Fig.~\ref{figure1}B (lower panel). The exponents $\gamma_i$
  characterizing ZBA at multiple edges are indicated. All
  singularities are broadened by the non-equilibrium dephasing rate
  $1/2\tau_\phi$. }
\label{figure2}
\end{figure}

If the phase $\delta$ is close to $4\pi$, $M=2$, the leading
singularities are given by $n_k = n_l =-1$, located at $\epsilon =
\epsilon_k + \epsilon_l$, with an exponent
$\sum_j \beta_j^2 = 2 - 2\beta_k'- 2\beta_l'+ \sum_j (\beta_j')^2$.
The next singularities are produced by $n_k=-2$, located at
at $\epsilon = 2\epsilon_k$, with an exponent
$\sum_j \beta_j^2 = 4 - 4\beta_k'+ \sum_j (\beta_j')^2$, etc.
For the case of a double-step distribution and $\delta = 4\pi$ this
agrees with the exact result for $\Delta_\tau$ obtained in
Ref.~\onlinecite{GGM_long2010}.

\section{ Conclusion and Acknowledgments}

To conclude, we have considered  several  many-body  problems out of
equilibrium, including the FES, the counting statistics, and
the tunneling spectroscopy in LL of fermions
as well as of bosons with hard-core repulsion.
We have shown that the correlation function in all these problems
may be  expressed  in terms of  Fredholm determinants of counting
operators. The operators are controlled by the (non-equilibrium)
distribution function, as well as by the value of the scattering
phase depending on the interaction strength.
Our non-equilibrium bosonization approach
allows to solve these problems and to establish connections
among them.

We have performed an analysis of the long-time asymptotics  of
the relevant Fredholm determinants (which are of Toeplitz form). In the
interesting case of double-step (or, more generally, multiple-step)
distribution functions the corresponding generating functions possess
Fisher-Hartwig singularities induced by Fermi edges.
When transformed from time into energy representation,
the results reveal power-law behavior,
associated with multi-particle processes at various
discontinuities of distribution function (edges).
The power laws thus obtained differ  from equilibrium one;
in addition, the singular behavior is broadened by non-equilibrium
dephasing rate.

This work was supported by GIF, DFG Center for Functional Nanostructures,
Einstein Minerva Center, US-Israel
BSF, ISF, Minerva Foundation, DFG SPP 1285, EU GEOMDISS, and Rosnauka
02.740.11.5072.

redpajama_set_name: RedPajamaArXiv


text:
Blog Tour: The Isolation Door
By Sarah A. - February 17, 2014
Thanks to TLC Book Tours, we're pleased to present a review for The Isolation Door, a new contemporary novel by Anish Majumdar. Make sure to check out the rest of the tour stops to see other reviews!
The Isolation Door
By Anish Majumdar
Published on February 4th 2014
Published by: Ravana Press
Source: Publisher/blog tour
Neil Kapoor, 23, is desperate to create a life beyond the shadow of his mother's schizophrenia. Years of successive relapses and rehabilitations have forced his father into the role of caretaker and Neil into that of silent witness. But there is no light within this joyless ritual, and any hope for the future rests on finding an exit.
Amidst her latest breakdown, Neil attends drama school in pursuit of a role that might better express the truth of who he is. What started as a desperate gambit becomes the fragile threads of a new life. A relationship blooms with Emily, and each finds strength – and demons - in the other. New friendships with Quincy and Tim grow close and complex. But the emotional remove needed to keep these two lives separate destabilizes the family. Neil's father, the one constant in the chaos, buckles under the pressure. Enlisting the aid of an Aunt with means and questionable motives, Neil plies ever-greater deceptions to keep the darkness at bay. But this time there will be no going back. As his mother falls to terrifying depths a decision must be made: family or freedom?
In this powerful fiction debut, acclaimed journalist Anish Majumdar shines a much-needed light into the journey of those coping with serious mental disorders and the loved ones who walk alongside them. Incisive and filled with moments of strange beauty, it marks the arrival of a unique voice in American letters.
For the longest time, Neil's life has centered around his mother and his illness, and he views his chance to go to drama school as a way to start a new life. This only sort of works, as the new friends Neil takes up with bring new complications to his life. Neil's life seems like it was very isolated before school, so he is learning to be his own person and to navigate new relationships at the same time. Inserting himself into the cohort of Emily, Quincy, and Tim can't be the easiest way to do this, as they all come with some significant baggage of their own.
The most compelling parts of this book for me were the glimpses of Priya's life, her feelings, her illness, etc., either through Neil's eyes or through her own. The author has personal experience with mental illness, as his mother has schizophrenia, and so these sections are sometimes the most poignant, poetic passages in the book. The author's writing is very sparse at times, but still rich with emotion, and you are really drawn into Neil's life.
This book raises some interesting questions as Neil finds himself frequently having to choose between taking care of his family, or having his own life, and I can only imagine how difficult that sort of decision would really be. Additionally, I found this book fascinating because of the different cultural attitudes and experiences of mental illness, and you wonder how different things would be for a different family instead of the Kapoors. Overall, this was a fascinating, heartfelt read and I look forward to seeing more from this author.