I'm a YouTuber who has been making daily gaming videos for almost 7 years now. I play all my games completely blind and give my unadulterated reactions and feedback on everything I experience. I also give each games' characters a unique voice and tend to ad lib humorous scenarios whenever I have a chance. YouTube has become my livelihood and my dream job and thanks to it, I've met a number of wonderful people and been privileged enough to garner a loving fanbase, whom I call my "Picky Penguins."
I'll be honest: I never really intended to make a Patreon account. While I've done fundraising events before for things like my dog Bernie and additional capture cards, as well as selling my own line of Picky Penguin plushies, my main source of income has always been YouTube's ad revenue. Over the years, as my channel grew in size, it became possible for me to work full-time on YouTube and make it my sole focus. It was always my hope that I would be able continue to make my living through this system.
However, I've come to realize over the past 6 months that this is no longer possible. My monthly revenue has fallen to the point where making a living has become difficult, with my CPM now being half of what it used to be. It's no secret that YouTube has been making changes to its system in an attempt to appease advertisers. I honestly thought I had avoided the brunt of these changes, but it seems I was mistaken.
So this basically leaves me with two choices: either censor myself on YouTube by playing games that fit their guidelines and avoiding any form of profanity; or instead reach out to you all for help and attempt to break free of this unreliable system of revenue.
I want to continue to be true to you guys just as I always have been and give you all the content that you subscribed for; and it's my hope that this venture will give me the means to bring you guys even higher quality videos than I could before.
If I Support You, What Do I Get?
Let's Play Series: The channel's bread and butter. I pick a game I've never played and play through it blind from beginning to end, all while taking suggestions from my fanbase. Expect a lot of goofy voices, adlibbing, and inside-jokes to happen along the way.
The Council of Voices: My channel's "original" series, pulling characters from a number of different video games and placing them in my own original story. It's easily my most ambitious and difficult-to-make series. By supporting me here, it's my hopes that I can hire an editor or two to help make these videos more consistently and frequently (and without sacrificing a Let's Play).
A Real Moment With NicoB: My vlog-styled videos, which usually involve me unboxing geeky stuff, cooking gaming related foods, talking about important updates, and giving a look behind-the-scenes.
Anime Reaction/Reviews: One part reaction, one part abridged series. I react to different anime while also adlibbing a number of goofy moments. I've only done two at the time of making this, but I would definitely like to do more of these in the future, and with your help I can.
Bernie the Dog: Anything and everything Bernie-related; ie. my female, black French Bulldog who loves cuddling, playing chase-the-toy, and occasionally showing up in a video or two (preferably at the end, see Goals section).
Even if you decide you can't donate or do initially but need to stop after some time, don't feel bad! We all have our own financials to worry about. Regardless, I appreciate all the love and kindness you penguins have shown me over the past six and a half years. And while the current situation may not be the most ideal, I hope that in the end, it can help me to bring you guys even better content than I could before.
Love you, penguins, and stay classy!
There aren't any tiers here. I don't want to hide any of my content behind a paywall. Even if you can't donate, it doesn't make you any less of a Picky Penguin. By supporting me, you are helping me bring you all even better content than I could before with just YouTube's ad revenue. Whether you give a dollar or more, just know that your patronage is greatly appreciated.
With $4,250 per month, I'll hold a small contest every livestream where the winner will get their own choice of Picky Penguin plushie from the store. I tested this before with having people guessing Obscure Video Game Music, and would love to do something along that line again. These contests will be offered to all fans, not just the patrons. This goal just makes these contests possible!


text:
Q: Why the Castelnuovo exact sequence is named after Castelnuovo I have seen variations of the following exact sequence referred throughout the literature as the Castelnuovo sequence:
$$0\longrightarrow \mathscr I_{X:H}(-d)\longrightarrow \mathscr I_X\longrightarrow \mathscr I_{X\cap H,H}\longrightarrow 0$$
where $X\subset\mathbb P^n$ is some scheme and $H$ is a hypersurface of degree $d$.  The proof is straightforward from the definition of ideal quotients.
In what context did it first appear, and why is it named after Castelnuovo?

redpajama_set_name: RedPajamaStackExchange


Hi All-Sorry I haven't been blogging much. November has been a crazy month comprising of Graduation, being Called to the Bar of England and Wales and moving house. Busy busy!
Despite this month being full of changes I have still managed to put some thought towards wedding planning.
As you'll have seen from my venue reviews, I have been struggling to find my dream venue. There always seems to be a compromise- no exclusivity, late licence only til 11.30, venue being too small. It's been tedious but I am determined to get what I want.
I knew what I wanted but because I couldn't really explain what I wanted it's been impossible to find it. Until now.
Armed with my prized photo I've been trawling the internet to find a venue that could match my vision. And I may have found it!
Speaking with other brides, this seems to be the best way forward. Find pictures of what you want: venue, table dressings, flowers, bridesmaid dresses. Once you know this is what you want for your day, stick to it. Do not be swayed. Compromises aren't the end of the world but try not to give in too easily.
That's a beautiful photo, I would love to see what your venue looks like good luck!


Industrial and interaction designer Vinay Venkatraman is the CEO of Leapcraft – a design-driven innovation consultancy based in Copenhagen, Denmark.
In 2013 Vinay Venkatraman established Leapcraft, a new-age global innovation provider working with user-centred design, big data and technology exploration. Prior to this Venkatraman co-founded Copenhagen Institute of Interaction Design (CIID) in 2006.
Venkatraman helps shape the strategy and content for numerous initiatives through consulting, teaching and researching lead initiatives. He is trained as a product and interaction designer in India and Italy. His cross-disciplinary approach to design has in the past spanned design of consumer products, software and film visual effects.
He currently spends his time between creating new education curriculums, shaping policy initiatives for the Danish government and consulting large global companies on innovation around new design strategies and product experiences. He has helped create product strategies for companies like Nokia, Intel, Novo Nordisk, Maersk line, Lufthansa Technik, Philips lighting and more. His passion lies in incubating new technology ideas, finding new models of sustainable socio-economic development using appropriate technologies.
As part of his academic interests, he has taught courses at the Copenhagen Business School, IUAV University in Venice and the IT University in Copenhagen. His current interests include tangible user interfaces, service design and finding new models of sustainable economic development using emerging technologies. As part of this Venkatraman has initiated a global research track for emerging economies called Frugal Digital to help empower small businesses using innovation based on simple and inexpensive technologies.
In 2013 he also initiated the Big Data Visualization academy in collaboration with Danish Design Centre to create new skills and build awareness of how big data can be utilised along with design thinking and innovation strategy.
Venkatraman routinely travels and lectures world wide on platforms like TED, where he speaks on innovation, user-centred methods and design for social change.
Recently he was the recipient of the Grundfos RejseGalat award from the Danish Design Council and has served on numerous jury panels for design awards.


Tenders, Buffalo wings and boneless wings.
Red cabbage, egg, cucumber, romaine, iceberg, olives, tomatoes, onions, radishes and carrots.
Turkey, ham, American cheese, red cabbage, egg, cucumber, romaine, iceberg, olives, tomatoes, onions, radishes and carrots.
Cappicola, ham, salami and provolone cheese. Red cabbage, egg, cucumber, romaine, iceberg, olives, tomatoes, onions, radishes and carrots.
Salad served in a large taco shell with blackened chicken and spicy ranch dressing. Red cabbage, egg, cucumber, romaine, iceberg, olives, tomatoes, onions, radishes and carrots.
Grilled chicken, crumbled bleu cheese, diced eggs, diced tomatoes, red onions and bacon. Red cabbage, egg, cucumber, romaine, iceberg, olives, tomatoes, onions, radishes and carrots.
Pepperoni, sausage, bacon, ham, beef, mushrooms, green peppers and onions.
Spinach, tomato, olives, broccoli, mushrooms, garlic, onions and green peppers.
Pepperoni, feta cheese, mozzarella cheese and pizza sauce.
Tzatziki sauce, gyro meat, topped with diced tomato and onions.
Spicy beef, topped with diced tomatoes, lettuce and sour cream.
Sauce on top of three different cheeses.
French fries, cheddar and mozzarella cheese, bacon and sour cream.
Grilled chicken, hot sauce and crumbled blue cheese.
Ziti pasta, marinara and Parmesan cheese.
Ricotta cheese, mozzarella cheese, garlic and broccoli or spinach.
Lots of fresh ground beef and cheddar topped with ketchup and bacon.
Lettuce, tomato, mayo and lots of bacon.
Grilled chicken, Alfredo sauce, broccoli and mozzarella cheese.
Ham, cappicola, Genoa salami and provolone cheese. Served with lettuce, tomato, onions and extra virgin olive oil on our hearth baked Amoroso's roll.
Served with lettuce, tomato, onions and extra virgin olive oil on our hearth baked Amoroso's roll.
Grilled chicken, romaine and Caesar dressing on our hearth baked Amoroso's roll.
Served with lettuce, tomato and a small side of fries.
Stuffed with mozzarella and sauce.
Stuffed with mozzarella and sauce and your choice of two toppings.
Stuffed with ricotta and mozzarella. Served with marinara on the side.
Stuffed with ricotta and mozzarella and your choice of two toppings. Served with marinara on the side.
Lamb and beef served in pita with tzatziki (cucumber) sauce, onions and tomatoes.
Marinated chicken strips in pita with tzatziki sauce, onions and tomatoes.
Marinated pork tenderloins in pita with tzatziki sauce, onions and tomatoes.
With hard-boiled egg. Served with small side of fries.
With bacon. Served with small side of fries.
Served with small side of fries.
1/2 lb. 100% sliced ribeye on our hearth baked Amoroso's roll.
Sauce and mozzarella. 1/2 lb. 100% sliced ribeye on our hearth baked Amoroso's roll.
Lettuce, tomato and red onions. 1/2 lb. 100% sliced ribeye on our hearth baked Amoroso's roll.
With A-1 sauce. 1/2 lb. 100% sliced ribeye on our hearth baked Amoroso's roll.
100% fresh chicken breast on our hearth baked Amoroso's roll.
Crumbled bleu cheese and hot sauce on our hearth baked Amoroso's roll.
On our hearth baked Amoroso's roll.
100% fresh ground beef served with a small side of fries.
BBQ sauce topped with onion rings, bacon and cheese. 100% fresh ground beef served with a small side of fries.
Marinara sauce and two mozzarella sticks. 100% fresh ground beef served with a small side of fries.
Salsa, sour cream and jalapeno on tortilla. 100% fresh ground beef served with a small side of fries.
A-1 sauce topped with onion rings, bacon and cheese. 100% fresh ground beef served with a small side of fries.
Sweet sausage, green peppers and onions. On our hearth baked Amoroso's roll.
Corned beef, 1000 Island, Swiss cheese and sauerkraut on marbled rye roll. On our hearth baked Amoroso's roll.
With french fries. On our hearth baked Amoroso's roll.
With french fries, lettuce, tomato, honey mustard and bacon. On our hearth baked Amoroso's roll.
Feeds 3-5 style. Served with garlic bread.
With two cheeses, bacon and jalapeno.


FAQs | Launch of GoDigitalQld - Queensland Digital Economy Strategy and Action Plan | Building digital skills and capability in Queensland - online engagement space.
What is the purpose of the Queensland Digital Economy Strategy and Action Plan - GoDigitalQld?
What is the Queensland Government's role and what are the implications for other departments and key stakeholders?
How does GoDigitalQld strategy and action plan contribute to achieving the Queensland Government's priorities and values?
The digital economy (sometimes referred to as the internet or information economy) is a relatively new term in government and business circles. Economic and social advancement lie at the heart of developing the digital economy.
This strategy defines the "digital economy" as "The global network of economic and social activities that are enabled by information and communications technologies, such as the internet, mobile and sensor networks." This definition is also used by the Australian Government.
Digital technologies and services are increasingly global, with both production and consumption growing exponentially world-wide. Queensland needs to embrace this global trend, effectively a new industrial revolution, in order to advance our economy, attract investment, build our prosperity and improve Queenslanders' lives and lifestyles.
GoDigitalQld is a roadmap for driving and coordinating digital economy activity that is within the Queensland Government's remit to control directly or in partnership with other entities.
The strategy and action plan provides an effective basis from which the Queensland Government can work closely with other levels of government, business and industry peak bodies, community and human services organisations, and trusted advisors to leverage opportunities, deliver better digital services, and share information that will benefit the Queensland economy, communities and businesses.
Successful implementation of the strategy will allow the Queensland Government to take full advantage of the opportunities presented by the evolving digital economy.
Provide leadership in setting direction on digital economy matters.
Innovatively use digital technologies and channels to revitalise Government service delivery to its customers and improve productivity.
Reduce red tape and regulatory barriers and administrative practices preventing greater take-up of more efficient digital government and community services.
Better communicate to Queenslanders, businesses and industry the importance and relevance of the digital economy so they are enabled to participate in and benefit from the digital economy.
GoDigitalQld manages expectations, and provides clarity for stakeholders and customers on the Queensland Government's direction and responsibilities in the delivery of digital economy activity.
Help boost productivity and ensure that the Queensland Government is well placed to deal with the economic, fiscal and demographic challenges that are facing the state over the coming decades.


What are some good real believable excuses for missing work? It is one thing to come up with an excuse before you miss work, it is another thing to make up one afterwards. If your excuse sounds flimsy, your boss may ask for some proof, so you really need to come up with a believable excuse.
Death of a family member or friend: If someone in your family or your friend's family passed away, you can easily prove this to your boss. If not, just find someone who recently died in your neighborhood and tell your boss that it was your best friend's mom/dad and your friend really needed your support.
Broken/flat tire: If you ever have a flat/broken tire, take a picture of it and you can use it as an excuse as if it happened yesterday.
Pet Illness: If you don't have a pet, pretend that you have one or you are pet sitting your sister's pet.
Medical tests: Health related excuses are always good excuses because your boss won't feel comfortable to ask the details of your illness.
Child Issues: Kids are very difficult to take care, but they are also great sources for excuses for missing work. They can be sick, or they might have problems at school, or you might have problems with your daycare/babysitter.
Jury duty: Nobody will check whether you had jury duty that day. You can just claim that you had to go and wasn't selected for jury duty.
Home emergency: You can have a broken pipe, carbon monoxide leak, or some other home related emergency to deal with. These are also good excuses.
Diarrhea/Food Poisoning: This is my favorite excuse. You don't even have to go to the doctor when you have this excuse. You usually can recover in a day or two, so you can use this excuse for missing work for a couple days.
Please share in the comments if you have better ideas/excuses for missing work.


"John Anderson (born 28 November 1932 or 1933) is a former British television personality best known as referee and official trainer on the UK TV show, Gladiators. He has previously worked as a teacher and as a coach for Commonwealth Games and Olympic Games athletes, including Commonwealth Games champion and former World Record Holder David Moorcroft. John was National Coach for the Amateur Athletics Association of England and subsequently the first full time National Coach in Scotland. He was coach to an Olympian at every Olympics from 1964 to 2000 and has coached 5 world record holders and 170 GB Internationals in every event.
As a young man, John wanted to teach and was passionate about all kinds of sport. He represented Scotland as a schoolboy footballer. This was in the 1950's when there was no formal coach education structure available in the country. The only way in to sport as a career was to train as a physical education teacher and there were only two options available to him on that front – Jordanhill College in Scotland or Loughborough in England. Jordanhill College is now of course part of Strathclyde University in Glasgow. John went to Jordanhill and subsequently did a degree at the Open University and went into teaching in Junior Secondary School the east end of Glasgow. Progress as a coach was then down to self study and self motivation – he read voraciously, mainly in the Mitchell Library in Glasgow. He was interested in all sports and went on the FA football coaching course at Loughborough. He did so well that he became the first home Scot to gain the prestigious Full FA Coaching Certificate. It should be noted that at that time only 4 were awarded every year and none had ever been awarded to a 'home Scot.' When he came back home with the qualification, football clubs didn't want to know. There was no desire to use his qualification from those in the sport in Scotland where the clubs all seemed content to do what they had always been doing. He went on teaching and covered such sports as gymnastics and swimming as well as football. He reckons that these helped his future coaching of athletes – all experiences are useful and teach the interested coach, it raised his awareness of the coaching process and taught him how to motivate all kinds of people in different sports, and much more.
He had been a pupil at Queen's Park Secondary School at the same time as Ally MacLeod. They became firm friends and played together for the Scotland Schools team then when John was National Coach, Ally was manager of the Scottish football team. At a personal level, John was best man when Ally was married.
Many in Scottish athletics have stories about John at this time – for instance Helen Donald tells of the time she was running in the WAAA's championships at Crystal Palace and, coming off the last bend in third place was encouraged by John, who was there with his Maryhill athletes, roaring her on and wearing his kilt! Anyway, Maryhill Ladies AC took off and his initial goal of 'best club in Scotland in three years' was achieved – use the link and see how well they did.
Never a man to stand still and let inertia govern his conduct as so many do, he contacted his colleagues in other schools and asked them to send along any talented girls that they had and, while they were at it, to send along their parents as well! They were all used and the parents who were helping with the coaching and training of the girls, used to attend classes that he held at his Mum's house on Sundays He always wanted to know more, and attended a summer school at Loughborough College. In an attempt to test himself, he decided to take all the Senior Coach awards that were available. This was a mammoth undertaking and I cannot imagine any coach doing it today: in fact I have only ever heard of John and Wilf attempting it. He did this – as did Wilf Paish – and then when he heard that new post had been created, that of a peripatetic national coach in England and Wales, he applied. He was given the job and travelled the length and breadth of England and Wales coaching and working with coaches. He even collected some athletes who had no access to coaching or who needed help. This was when there was no national TV, no emails, no mobile phones and communication sometimes took a long time. There was in many clubs no scientific basis for what they were doing – they were doing what their predecessors had done for donkey's years. He didn't like that idea. So he started reading again – back to the Mitchell Library, and he wrote to people and sometimes there was a long time for a reply because he was dependent on the postal service.
Then he discovered Geoff Dyson's book, "The Mechanics Of Athletics" with its scientific approach to the body, information that wouldn't change , that was scientifically and mathematically based. As he says, his coaching went from being hopeful to being scientific. Later he found Tim Noakes and his work was also assimilated into the training process. Already a voracious reader, he continued to be so despite the increasing levels of success that his athletes had. If he was going to coach somebody then he had to have a scientific basis for what he was going to do or he would not do it. That has not changed – all training has to have a scientific underpinning.
It was at this point that he was asked to do some coaching with the Glasgow High Kelvinside RFC by a rugby friend who was also into athletics. John did some work with them but it was mainly sprints and speed development. The sessions are still remembered by some of those who took part – one chap recalls doing pre-season training on the big pitch at Old Anniesland. Rumour hath it that they disagreed over what constituted a warm-up! The sessions were hard work as Kenny Hamilton, now director of rugby at Glasgow Hawks recalls "3!… 2!…. 1! – I remember him well. A fair amount of resistance-running – possibly the first I experienced which used tyres. I seem to remember a conversation about stretching He was very enthusiastic about stretching muscles – a comparatively foreign concept in rugby circles in those days. He was delivering a talk some place and was asked about how long each stretch should be held for ……. "8 seconds he replied" This then became a bit of a standard but he quietly admitted that there was absolutely no science behind it! However, I can confirm that we were all bloody fit that year, except Cammy!" Cammy Little who was a very good rugby player (he was one of Glasgow's first contracted players and also played for the Barbarians) says he missed the sessions as it was summer and he played cricket: an old tactic that worked a treat!! John says he was not really a rugby man but it's funny how these things go around: he is now living near Leicester and since the Chief Exec is a friend he goes along to see the Tigers play and in 2012 even went to Twickenhan to see the Scottish match. He also admits that he has done some work with the Leicester Academy boys and focused on sprinting.
The only thing that he reckons might be queried is whether his interpretation of what their (Dyson and company's) work had been, was fair. In response to that he can only look at the results of his work with various athletes. With 5 world record holders and 170 GB internationals then there can be a fair assumption that his interpretations have been appropriate. He always measures every coach on the basis of their output. Not if they have only ever had one outstanding athlete – anybody might have an outstanding talent simply by chance – but have there been improvements in all of the athletes that they have coached. John always had talented athletes who came to him who were improved further by his insights and methods. Among those in Scotland to benefit from his coaching were Leslie Watson, Moira Kerr, Duncan Middleton, Graeme Grant, Hugh Barrow, Hamish Telfer (a notable coach in his own right), Craig Douglas, Lindy Carruthers, and the sisters Alix and Jinty Jamieson. The set-up in Glasgow at the time was interesting in that coaches co-operated with each other and Tom Williamson and John worked together on some of the same athletes.
No warm down shower; Back on blue train to office. It was there that I first spoke to John – I had gone along to see what this session that was spoken of was about and like everybody else was very impressed.
Hugh, who had been coached for the previous eight years by Johnny Stirling at Victoria Park, switched coaches and began to train with John from 1966. He had been AAA's Junior One Mile champion, and was the world 16 year old mile record holder which was only broken by Jim Ryun and trained as noted with some of the best half-milers the country has produced under John's guidance at Westerlands at lunchtime, as well as at the club. John travelled a lot – unlike some National coaches. I once formulated the theory that one particular national coach's car always broke down at Ingliston – and a lot of his communication was done by letter. An example of this is a letter sent to Hugh in 1970, reproduced below.
The second half with the more personal correspondence is omitted but this does show the detail that he sent the runners, even at that relatively early stage in his career. His first ever GB runner came from this period: it was Hugh Baillie of Bellahouston Harriers who had that distinction when he ran in the 4 x 440 yards relay.
I mentioned earlier that he worked with the Scottish Schools on their squad training days and he brought the very best of coaches with him. For instance to one such day that he was organising at Scotstoun, he had Alex Naylor, Eddie Taylor, Sandy Ewen and professional runner Michael Glen, plus from England and from the ranks of the best athletes, there were Vic Mitchell, Mike Lindsay, Peter Warden and Menzies Campbell with athletes such as Graeme Grant, Hugh Barrow, Sandy Robertson and Don Halliday as 'coaching assistants.' That is by any standards a remarkable line-up. To have it for Schools athletes shows the priority given to appropriate development of young athletes.
John's coaching career was really taking off and when I checked some figures with John he confirmed that he had indeed coached over 170 GB athletes as Wiki had said. A look at some of them would be very informative.
When David started to work on his running with John as coach, John was already coaching another Coventry runner who was very good indeed but whose name seems to have fallen from view. She was Sheila Carey – a top class 800/1500/3000m runner who competed in two Olympics (1968 and 1972 in Munich where she set a new GB record for the 1500m), helped set a world 4 x 400m relay record at the Edinburgh Games in 1970. John had met her at a training camp in Font Romeu when he was there with a GB team. One afternoon he decided to take the men, for whom he was mainly responsible, up higher to a plateau where they could do some training. He saw a woman climbing up with them – she was Sheila Taylor and then, on the way home, she asked John if he would coach her. He was living in Hamilton at the time, she was in Coventry. She was quite clear and determined and so the partnership was formed. She ran in the Edinburgh Commonwealth Games in 1970 where she was one of the fallers at the end of the women's 800m and was unplaced.
The story of the selection for Mexico in 1972 is interesting. The selection for the Olympics was the AAA's Championship. Sheila wasn't well on the day and failed to qualify. The first two were selected and John had a phone call the following week. he was told that there was to be a run-off for the third 800m place between Ann Smith, trained by Gordon Pirie in New Zealand and the third placer in the AAA's. Sheila would be part of rest of the field. John had other plans and on the day of the race he told her that she was going to win and go to the Olympics. Tactics were simple – John would wait at a particular spot on the trackside and when he shouted to her to go, she was to really go for it all the way to the finish. She responded really well, left the other two in her wake and won. She went to Mexico. It is a little known fact that John spent some time coaching blind athletes, and Sheila went on to teach in a school for the blind where she also became involved in coaching blind athletes. Still running as a V65, see her recent profile at http://www.thepowerof10.info/athletes/profile.aspx?athleteid=1967 , Sheila was one of the Olympic torch-bearers in Warwick in 2012.
It was the last time that world record was broken by someone other and African. He also won gold in Brisbane at the Commonwealth Games and set a British and European 3000m record of 7:32.39.
* John Graham trained with him from 1982 to 1987 which included a second in Rotterdam in 1985 in 2:09:58, 2:10:57 when finishing fifth in New York in 1983 and two Commonwealth Games fourth places.
* Judy Simpson won bronze in the 1986 European Games pentathlon and competed in three Olympic Games in 1982, 1986 and 1990, although her top achievement was winning gold in the Commonwealth Games at Edinburgh in 1986..
* Glasgow's Lynne MacDougall ran in the Olympic 1500m Final in Los Angeles 1984 the high spot of a career of top class running including European Indoor Championships in 1984 and 1990, Commonwealth Games in 1986 and 1990, and with a range of personal bests ranging from 2:01.1 for 800m in 1984 right up to 2:36:29 for the marathon in 2002.
* David Jenkins 4 x 400 silver in Olympics in 1972,silver in Europeans in 1974, USA 400m champion in 1975, Commonwealth gold in 1978. His 1971 victory in the European Championships at the age of 19 was quite superb.
* David Wilson: Hurdler and High Jumper who took part in the 1972 Olympics as a sprint hurdler, in the 1970 Commonewealth Games as a high jumper and in the European indoors as a high jumper. He had personal bests of HJ 2:05, LJ 6.90, TJ 13.15, PV 3.30, Discus 36.64, 60mH 7.9, 110H 14.0 but never competed in a decathlon as far as I can discover.
* David Bedford who asked John to coach him. David had just run in the European Championships in Helsinki where, after leading right up to the last lap, he was destroyed by a 54 second last lap by Juha Vaatainen and then finished sixth. Video of the last two laps can be found on youtube at this link – http://www.youtube.com/watch?v=Sfm_lTSOjhI . John had been there with David Jenkins and they met there. The following week John came along to Meadowbank to do his coaching when he saw this tall, thin chap in red socks jogging round the track. Recognising him, he asked what he was doing there and Bedford replied that he was what had brought him – he wanted John to coach him. They reached an agreement and worked together for many years. When he came up to Edinburgh David stayed with one of John's runners, Dave Hislop and the partnership worked both athletically and socially.
With over 170 GB athletes, there were obviously many, many more but you get the quality of the coaching from that sample. Women's heptathlon to men's marathon via sprints, hurdles and high jump. And with hurdler William Sharman he is still in 2013 producing champions! From Maryhill in 1960 to London in 2013 the span is heading to 55 years.If the figure in Wikipedia of 170 GB internationals is correct, it must be more than any other coach ever.
The Mussabini Medal celebrated "the contribution of coaches of UK performers who have achieved outstanding success on the world stage." Along with the Mussabini Medal, there also existed The Dyson Award, for "individuals who have made a sustained and significant contribution to the development and management of coaching and individual coaches in the UK". This award was named after Geoff Dyson, the first chief national athletics coach, who died in 1981.
He was even at one point an agent getting the appropriate races for his athletes. This was at the time when he was coaching Liz McColgan. It was difficult at times getting the appropriate races to fit into their carefully planned programmes, and some of the agents were out for themselves rather than for the athletes, so he offered to act as their agent, free of charge, and find them the appropriate competition. It did work rather well for his charges.
Then there was 'the day job'. After the Heriot Watt Director of Physical Education, he moved to Nuneaton as Deputy Chief Liaison and Recreation Officer where he soon moved up to be Chief Leisure and Recreation Officer before finally ending up as Director of Leisure Services in London with a staff of 600 to supervise.
He was never still. And he thrived on it. Many coaches only ever have one national standard athlete or one Olympian in their charge, many very good coaches never have either but John held down a series of demanding jobs while coaching athletes to the highest honours and performing the many other associated functions noted above.
The two comments below the article read as follows: "Back in the 90′s hey day of Gladiators, I was a working at the Pizza Express in Brindley Place, Birmingham, next door to the NIA where Gladiators was filmed. For several weeks every year, the paths outside were thronged with foam handed punters, and we often saw the Gladiators themselves walking past. Wolf even belied his image and would wave and smile at the kids. But the man himself, John Anderson was a regular customer. He would always come in by himself, and sit at table 13 and order two garlic breads for starters, and then a pizza. He was a really nice guy, and would happily sign autographs for the kids. Probably the nicest minor celebrity I met while working there, although it could be a tie between him and Bob Holness." was the first and the second contrasts this with his on-screen appearance and reputation. It reads "The wimp ref Sky employed was awful. We nicknamed him 'dad ref' because 'Gladiators Ready!?' sounded more like 'dinners ready.' " which clearly indicates that John was just a bit tougher than the US original!
There was even a set of toy gladiators produced with a six inch John Anderson figure: a toy firm called Character Options made and sold sets of the Gladiator characters – and of course there had to be one of John as well. Advertised as Gladiators: John Anderson 6″ Action Figure, it looked like this.
"Who are the Flying Coaches?
A range of coaches have been identified on the basis of their experience and expertise in technical events. The Flying Coach Programme has seen the likes of former Chicago Marathon winner Paul Evans and World Champion coach John Anderson visiting clubs. Coaches interested in becoming 'Flying Coaches' should contact their area Club and Coach Support Officer to register interest.
Wheelchair Racing: An introduction to basic push technique, chair set up and training programmes.
Seated throws: Advice and guidance on seated throws, including throwing frames, tie downs and fixings.
Coaching blind or visually impaired athletes: Advice and guidance on supporting blind or visually impaired athletes, to include guide running and competition pathways.
Coaching deaf or hearing impaired athletes: Advice and guidance on coaching deaf and hearing impaired athletes. To include information on effective communication, technology, Deaf UK Athletics and competition pathways.
Coaching athletes with a learning disability: Advice and guidance on coaching athletes with a learning disability. To include information on Mencap, Special Olympics and competition pathways.
Other impairment specific visits: Advice and guidance on coaching athletes with a specific impairment (Cerebral Palsy, amputees etc). To include information on National Disability Sports Organisations and competition pathways.
So it is not an easy option to follow for the coach – the last section is interesting with our prior knowledge of his work with blind athletes.
– the links are just below the first picture of the three coaches!
As we said above he is still coaching a small number of top class athletes but he is not yet easing himself into retirement as a coach.
Success at the level he has enjoyed didn't alter the fact that he was a coach who worked with athletes of all abilities. With his personality and ability he would have been a success in any walk of life: we are fortunate that he chose athletics.


Community Gardens, market fruits, and flowers, welcoming notes of orange and bergamot, soothing properties of cedarwood. A natural soap bar made with plant-based oils and butters. It's handmade and traditionally air-cured for six weeks.
This scent is inspired by Mount Hood, Woodlot's home turf, with the smells of flowers, market fruits and community gardens. Orange and bergamot welcome while cedarwood soothes and calms, creating a fresh and friendly aroma.


In the context of the economic promotion initiative Galati 2020 a workshop took place on the 2nd and 3rd of June in Galati. Among the participants were representatives of the Romanian Orthodox Church, the public administration and the economy. The workshop was comprised of two parts, on one hand there was a series of speeches dealing with EU funding, the EU Strategy for the Danube Region and future project activities, and on the other there were three working group phases dealing with the business sectors agriculture, tourism, lifelong learning, logistics as well as building trade and energy efficiency.
The workshop aimed to foster the dialogue of those responsible in the chosen business sectors. In specific working groups the different market systems and their actors were analyzed. Moreover, problems of the sectors and possible solutions were discussed and documented. The moderation of the different working groups was carried out by Mr. Rolf Ackermann from the Department of Advanced Training of the Ministry of Cultural Affairs and Education Baden-Württemberg, Mr. Jürgen Raizner, Head of Steinbeis Danube Center/Competence Center, Hans Füller, former chairman of the Wirtschaftsgilde (an organization occupied with business ethics) and Rainer Bausch, former head of the agricultural office in Herrenberg.
Both the participants and Fairventures Worldwide were satisfied with the outcomes of the workshop. As a result, precise analyses of the sectors were compiled and a first pilot project for the agriculture sector was developed. For the other sectors promising solutions were identified and those responsible for each sector were appointed and a project coordinator was contracted. The persons responsible for the sector will help the project coordinator to make sure that solutions will be put into action. The tasks of the coordinator include the representation of Fairventures in Galati and the application for EU funding. Fairventures Worldwide will support the coordinator with its expertise and will continue to work on the ascertainment and the implementation together with the other members of the steering committee in Germany.
Fairventures would like to thank the Romanian Orthodox Church and the public University of Galati for helping to plan and carry out the workshop and all participants. Special thanks go out to the evangelical Lutheran bishops Dr. Renz, Prof. Dr. Maier and to the regional bishop of Württemberg, Dr. h. c. July whose donations made this workshop possible in the first place.


text:
3 Up, 3 Down: Jornadas 29 and 30 (and some brief news)
By Allen Dodson Mar 27, 2012, 1:28pm CEST
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We haven't had one of these in a while... before I get to the player selections I of course want to give a "big up" to mister Lotina. With the team having another day off it's a bit of a slow news day in Vila-real, and EPM has spoken to Lotina's assistant, José Luis Ribera, to get his comments on Lotina's approach.
Obviously (as the results have shown so far) the big difference has been that the team has tightened up defensively. Ribera notes that he and Lotina "have introduced some new defensive principles" (the clean sheet on Sunday was our first since the Barca game January 28) but also (shock!!) that players perform better when they're played in their natural positions:
No encontrad - Deportes - El Periódico Mediterraneo
And by the way, Villarreal-Real Madrid was the most watched game on TV in La Liga this season!
Speaking of Real Madrid, they take on another yellow team, APOEL, today in the Champions League. Our fellow SBN blog, Managing Madrid, has profiled the Cypriots here (I know, horrible pun in the title, but go with it) and there's also a nice BBC article as well. I believe the game is on Fox Sports in the US. Interesting that not only do they play in yellow, their stadium is about the size of El Madrigal.
Okay, now let's get to the 3 Up. Tough choice this week. I am going to pick 4, and still leave out deserving players....always a sign we've been playing well.
(1) Rubén Cani. We've been critical of the ex-Zargoza man much of the season, but against both Madrid and Rayo he played in a slightly different role, behind the strikers at the top of a midfield diamond, essentially, and performed well. He created our first goal on Sunday, of course, but in both games was busy breaking up plays, creating opportunities, and (for a change) not getting in the referee's face too much! Lotina seems to have asked him to give ~60 really quality minutes a game, and he has responded.
(2) Mario Gaspar. It's been a tale of three seasons for Mario. Coach Garrido used him until Ángel returned, then discarded him; Coach Molina never played him; Coach Lotina has started him twice, with excellent results. Maybe Mario is just well-rested, but he showed a burst of speed against Rayo that had us wondering if it was really Mario out there! And positionally he has been good.
(3) Diego Lopéz. He made a couple of key saves against Rayo, one from a Armenteros header that would have tied the score and another from a Movilla strike in injury time; against Madrid he really didn't have all that much to do, amazingly enough. But quite apart from specific plays, our 'keeper, who only a short time ago was saying he wished the season would be over (the implication being the longer it continued, the lower in the standings we might fall) is playing with confidence. As Madrid lined up to take a last-minute corner, López was winking at his defenders--we've got this. And we did.
(4) Marcos Senna. Do you need to ask why? Game in, game out, he has been strong. And his free kick goal against Madrid will be replayed for years to come--and may have just been the spark this team needed to save this season.
3 Down:
(1) Joan Oriol. Yeah, he won the free kick that Senna converted, but against Rayo in the second half Lass Bangoura pretty much destroyed him. Oriol couldn't stay close to him, in fact he looked like he couldn't even find him most of the time. However, Oriol at least avoided committing silly fouls and giving away dangerous free kicks, so credit to him for that. Jaume Costa showed some promise in the couple of games he played, but realistically Oriol is going to remain at left back. But step it up,please, Joan!
(2) Gonzalo Rodriguez. It's been a tough season for Gonzalo. He was slow to recover from his horrific leg-break, and while he's never been a pacy defender, he seems to have lost a step. He had been a constant starter under Molina, but Coach Lotina seems to have decided his best center-back pairing is Mateo Musacchio and Cristián Zapata, and so far he appears to be right; they have worked well together. I've always thought Gonzalo's commitment enabled him to cover up some of his partner's mistakes in the center of our defense, but that commitment also has led to rash challenges and positional errors.
(3) Gonzalo Castellani. Molina put him on the promotion fast-track and made him his first-choice midfielder off the bench, but under Lotina, Jonathan deGuzmán appears to have taken his place in the team. Castellani has looked okay in limited action without wowing anyone, sure, but I don't expect to see him getting a lot of playing time in the remaining nine games.
Nine "finals" remain. Endavant Villarreal!!

redpajama_set_name: RedPajamaCommonCrawl


text:
Ricardo Enrique Puelma Laval (Copiapó, 2 de julio de 1878 - 1935, Santiago) fue un médico cirujano y político chileno, miembro del Partido Radical (PR). En 1930 ejerció brevemente como diputado de la República por la Circunscripción Departamental de Tarapacá, al haber sido nombrado en septiembre de ese año por el presidente Carlos Ibáñez del Campo como ministro de Bienestar Social, desempeñó el cargo hasta julio de 1931.

Biografía

Nació en Copiapó, el 10 de julio de 1878.

Los estudios los realizó en el Liceo de Copiapó, para después estudiar medicina en la Universidad de Chile. Se recibió como médico cirujano el 29 de diciembre de 1902, con una tesis titulada: Defensas e inmunidad de las enfermedades infecciosas. Hizo cursos de posgrado y obtuvo diplomas en Sanidad Militar en Italia, España, Suiza y especialmente en Francia, en 1919.

Se trasladó a Iquique, por tres años, donde desempeñó el cargo de médico interno del Hospital de Iquique desde 1902 a 1905.

Posteriormente, fue designado médico del Regimiento de caballería Granaderos desde 1905 a 1923, donde lcanzó el grado de Teniente coronel de Sanidad, el que tenía cuando jubiló, como jefe y médico cirujano de la I División. Durante muchos años fue médico jefe ad honorem del Policlínico de Enfermedades de Trascendencia Social de la comuna de Iquique.

En el curso del año 1919, fue comisionado al extranjero, en un viaje de estudios.

Entre otras actividades, se dedicó también a escribir y publicó diversas obras de carácter científico y sociológico.

Trayectoria política

Durante su carrera política militó en el Partido Radical (PR).

Durante el gobierno del presidente Carlos Ibáñez del Campo, fue nombrado ministro de Bienestar Social, cargo que ejerció entre el 5 de septiembre de 1930 y el 13 de julio de 1931.

En las elecciones parlamentarias de 1930 (Congreso Termal), resultó elegido diputado, por la 1ª Circunscripción Departamental de Pisagua y Tarapacá, para el período 1930-1934. Integró la Comisión Permanente de Guerra y Marina; y de la de Higiene y Asistencia Pública. Sin embargo, al aceptar el cargo de ministro de Salud, incompatible con el de diputado, se incorporó en su reemplazo, Serafín Elguín Morales, el 9 de diciembre de 1930. Este último tampoco pudo completarlo debido a la disolución del Congreso Nacional en junio de 1932.

Falleció en Santiago en 1935.

Obras

 Alma Rusa (ensayo)
 Mundo Interior (1929)
 Biología Celular y Mecanismo de la Vida
 Defensa e Inmunidad de las Enfermedades Infecciosas
 Arenas del Mapocho

Referencias

Enlaces externos

Nacidos en Copiapó
Fallecidos en Santiago de Chile
Diputados del XXXVI Período Legislativo del Congreso Nacional de Chile
Políticos de Chile
Radicales de Chile
Cirujanos de Chile
Alumnado de la Universidad de Chile
Ministros de Salud de Chile
Ministros de Estado de Carlos Ibáñez del Campo

redpajama_set_name: RedPajamaWikipedia


text:
Home News Altcoins ConstitutionDAO fails to win Sotheby's auction
ConstitutionDAO fails to win Sotheby's auction
The online group, ConstitutionDAO, has failed in its bid to purchase the last privately owned, 1st edition print copy of the U.S. Constitution at public auction at Sotheby's on Thursday.
"The 'Official Edition' of The United States Constitution" was instead won by an unknown bidder for $41M (or $43.2 million after auction fees), meaning the DAO failed in its historic attempt to put it "in the hands of The People."
The news broke in an announcement on the official Discord. "While this was not the outcome we hoped for we still made history tonight," the post read.
This specific copy is one of just thirteen copies of the Official Edition of the Constitution from the Constitutional Convention. It was first purchased from Sotheby's by the late real estate developer S. Howard Goldman in 1988 for $165,000. His widow Dorothy Goldman put it up for sale this year and decided that the proceeds will go to the Dorothy Tapper Goldman Foundation.
Project participants began to band together just a week ago as a decentralized autonomous organization, or DAO, to pool funds for the auction. In the hours leading up to the sale, ConstitutionDAO had raised over $49 million in Ethereum donations collected via Juicebox, a platform for community-owned Ethereum-based projects.
The auction was streamed live.
In exchange for donations, the 17,437 backers were issued governance tokens called PEOPLE. These do not provide fractionalized ownership, rather give token owners the ability to vote on proposals around structure, governance and operational direction.
Participants will now be able to get a refund of their contribution via Juicebox.
ConstitutionDAO
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I've learnt from the errors of others when it comes to investing. : altcoin
Andreessen Horowitz aims to raise $4.5 billion to invest in crypto funds


I think he was thinking, "Look at all of the pretty colors"!
Mullock Creek Marina in Fort Myers, Florida is one of those places only the locals know about. My friend who lives in Fort Myers hooked us up and we had a wonderful afternoon kayaking through an estuary (for those of you who don't know exactly what that means…"An estuary is a partly enclosed coastal body of brackish water with one or more rivers or streams flowing into it, and with a free connection to the open sea"). It was a steal at $25 for an all day rental. Partly cloudy skies and light winds made for a perfect afternoon.
My two girlfriends (who are sisters) and I drove the 16 hours from Ohio to Cape Coral, Florida in two days and arrived on Monday afternoon. Back in the day, we would've driven straight through. To take advantage of the remaining sunshine, we changed into our bathing suits and headed to the pool. A friend who is like a relative very generously allows me to stay at her condo which is near Ft. Myers. There is a small stretch of beach with a fun restaurant bar called Cape Coral Yacht Club about five minutes from the condo. After relaxing for a bit at the pool, we headed there for a casual dinner and to watch the sunset.
Yesterday, April and I had a great day at the Fort Myers Beach! While I was taking a dip in the ocean, I looked up at April and she looked as big as the buildings. It reminded me of the movie that Darrel Hannah was in where she was a giant. It also got me to thinking of how that applies to life and people–how everyone's perspective is unique to them–shaped by events and people in their lives.
While taking a walk along the beach (which is on my left), I thought this scene of houses and a bit of inlet water was quite pretty.
I love how the water sparkles like diamonds when the sun hits it, so I asked April to make some magic….
There is magic all around us if we open our eyes!
My friends — April and Wayne — were such fun when I asked them to dance and shake the maracas before we went out for dinner! April is in her early 40's…don't you think she's "hot"? She's very athletic…in fact she's out jogging right now as I do this post. She rides a Harley, runs in charity events, bought a boat recently (so she skis)…practices yoga and is a certified holistic health coach (or something like that)!
Of course, Wayne, the guy — has to take it to the next level — juggling with them! And he does it quite well! Isn't he cute! Wayne is also quite amazing! He's won awards in his age group (which is still the Fabulous 50's) for swimming. He swam 12 miles around Key West last year!! He turned me on to the Yoga place here in Fort Myers. He's also almost single!
Stay tuned for the next installment of fun!
I think some of the best Yoga I've experienced is right here in Fort Myers at Fort Myers Fitness 24/7 and it's only $5.00 (what a deal). I usually do "Hot" Yoga (where the room is 100 degrees) in Cincinnati. I've been a few times during the three weeks I've been visiting here from Cincinnati and LOVE the instructor. He has a calm presence and voice and explains every move in a fluid fashion and you know you're working your body and becoming more aware of everything!
This is after class…just posin' for all of you!
If you haven't given Yoga a try or its been a long time…I strongly urge you to go. It's one of the best forms of exercise and will help keep you looking and feeling younger for the rest of your life! There was a lady in the class that was at least 100 lbs. over weight…so it doesn't matter what shape you start out in! I've run a half-marathon, hike, and a multitude of other activities and feel that this gives the best return—both physically and mentally!


text:
\section{Introduction}
Isolated quantum systems described by time-dependent Hamiltonians, due to explicit violation of the energy conservation, manifest various phenomena that are inaccessible by their stationary counterparts. To capture their properties accurately one needs to understand their dynamical response to the external driving. This is particularly crucial in the case of state-of-the-art atomic physics experiments where extremely precise coherent control of strongly correlated quantum systems is tremendously rigorous and is treated as the specific dream come true \cite{1993WarrenScience}.

One of the typical directions considered for coherent manipulation of atomic systems is related to periodic driving \cite{2017EckardtRMP}. On different levels, it has been demonstrated that such forcing can be used as a powerful tool for precise controlling of quantum dynamics and it gave a ride to a plethora of fundamentally important and beautiful results. To mention only several examples: the dynamical control of the superfluid-Mott insulator transition \cite{Zenesini}, the AC-induced coherent resonant tunneling \cite{Ivanov, Sias}, expansion dynamics of Bose-Einstein condensates through periodic driving \cite{Lignier}, creation of artificial gauge fields \cite{Aidelsburger1, Aidelsburger2}, the realization of topological insulators via time-periodic potentials \cite{Jotzu, Aidelsburger3}, the coherent coupling between different energy bands \cite{Gemelke, Ha}, or frustrated magnetism \cite{2011StruckScience}. On the theoretical side, the underlying concept which gives an adequate description of a periodically driven quantum system is the Floquet theory \cite{Shirley, Sambe, Grifoni} which gives a nice tool for an appropriate description of the system stroboscopically, {\it i.e.}, after each period of the driving.

External driving is a commonly used concept in atomic physics problems (see \cite{2017EckardtRMP,2011PolkovnikovRMP} for reviews) and recently it was also exploited in the limit of a small but well-determined number of particles \cite{2016VolosnievPRB,2016EbertAnnPhys,2016YinPRA,2016GharashiPRA,2020MukherjeePRA}. However, still, it is not fully clear how different correlations of such systems are dynamically generated during such a process. One of the natural questions is on collectiveness of different properties, {\it i.e.}, how different few-body results start to resemble their many-body counterparts when the number of particles is successively increased. In our work, we make another step in this direction and we focus on transmutations of the system's properties enforced during a single period of external driving. First, we start with an interacting ground state of a system of a few interacting fermions confined in an external static trap. Then the system is non-adiabatically affected by a moving external potential barrier that crosses the system back and forth between the edges of the trap. In this way we investigate how the system dynamically transits between the two well-explored stationary cases, {\it i.e.}, confined in a pure harmonic oscillator \cite{2013AstrakharchikPRA,2013SowinskiPRA,2013GharashiPRL,2014LindgrenNJP,2014DeuretzbacherPRA,2014HarshmanPRA,2014DAmicoJPhysB} and in a double-well \cite{2016SowinskiEPL,2017TylutkiPRA,2017HarshmanPRA,2018ErdmannPRA,2018BurchiantiPRL,2019ErdmannPRA}. Depending on the rapidity of the barrier we observe how the state of the system is pulled away from the temporal ground state. By quantifying this distortion with a well-defined temporal fidelity, we capture the non-trivial interplay between external forcing, quantum statistics, number of particles, and interaction strength. The sweeping barrier protocol proposed here can be viewed as a few-body counterpart of the scenario recently realized experimentally in the many-particle limit with $^6$Li atoms \cite{2020KwonScience}. It gave a route to the beautiful observation of the DC Josephson supercurrent as previously predicted theoretically \cite{2019ZaccantiPRA}.

Since our purely theoretical work is motivated by seminal experiments with two-component mixtures of few fermionic $^6$Li atoms confined in quasi-one-dimensional external traps \cite{Serwane, Zurn, Wenz} we focus on equal-mass components. However, generalization to different-mass atoms (as also conceivable experimentally \cite{2010TieckePRL,2011NaikEPJD,2015CetinaPRL,cetina2016ultrafast,Grimm2018DyK}) is straightforward. Since perfect control and manipulation of these systems were convincingly demonstrated we believe that our findings may have importance for further experimental and theoretical progress (for general reviews see \cite{2016OnofrioReview,2016ZinnerRev,2019SowinskiRPP}).

\section{The Model}
In the present study we focus on a few two-component ultra-cold fermionic atoms that interact through short-range delta-like potential initially confined in a harmonic trap. In addition to the harmonic potential we introduce a gaussian potential barrier which periodically moves across the system. We aim to study a resistivity of the system properties to this disturbance depending on its rapidity. This specific situation can be modeled by the following many-body Hamiltonian
\begin{eqnarray} \label{Hamiltonian}
 \hat{\mathcal{H}}(x_0) = \sum_{\sigma} \int\!\!\mathrm{d}x\,\hat{\Psi}^{\dagger}_{\sigma}(x) \left[H_{0} + U(x_0)\right] \hat{\Psi}_{\sigma}(x)
+ g \int \mathrm{d}x\,\hat{\Psi}^{\dagger}_{\uparrow}(x) \hat{\Psi}^{\dagger}_{\downarrow}(x) \hat{\Psi}_{\downarrow}(x)
 \hat{\Psi}_{\uparrow}(x),
\end{eqnarray}
where the single-particle part of the Hamiltonian contains two parts $H_0$ and $U(x_0)$. The first represents the static harmonic oscillator part of the standard form
\begin{equation}
H_0 = -\frac{\hbar^2}{2m}\frac{\mathrm{d}^2}{\mathrm{d}x^2}+\frac{m \Omega^2}{2}x^2.
\end{equation}
The second describes the additional gaussian barrier of the width $\beta$ and height $U_0$ centered around (in principle time-dependent) position $x_0$. It can be written as
\begin{equation}
U(x_0)= \frac{U_0}{\sqrt{\pi}\beta} \mathrm{e}^{-(x-x_0)^2/\beta^2}.
\end{equation}
From now, we will use the natural units of the harmonic oscillator which means that energies, lengths, and momenta have units of $\hbar\Omega$, $\sqrt{\hbar/m\Omega}$, and $\sqrt{\hbar m \Omega}$, respectively. In our work we focus on the case of relatively narrow and quite high barrier, {\it i.e.}, in these units we set $U_0=4$ and $\beta=0.2$, respectively. However, generalization to other barriers is straightforward.

In the Hamiltonian (\ref{Hamiltonian}), the fermionic field operators $\hat{\Psi}_{\sigma}(x)$ annihilate fermion of component $\sigma\in\{\downarrow,\uparrow\}$ at position $x$, while $g$ is an effective interaction coupling between fermions belonging to opposite components. The field operators obey standard anti-commutation relations $\{\hat{\Psi}_\sigma(x),\hat{\Psi}_{\sigma'}^\dagger(x')\}=\delta_{\sigma\sigma'}\delta(x-x')$ and $\{\hat{\Psi}_\sigma(x),\hat{\Psi}_{\sigma'}(x')\}=0$. It is clear that independently on the position of the barrier $x_0$ and its motion the Hamiltonian (\ref{Hamiltonian}) commutes with operators of the number of particles in individual components, $\hat N_\sigma=\int\!\mathrm{d}x\,\hat{\Psi}^{\dagger}_{\sigma}(x)\hat{\Psi}_{\sigma}(x)$. Therefore in the following, we analyze properties of the system in the eigensubspaces of fixed $\hat{N}_\downarrow$ and $\hat{N}_\uparrow$.

In the following, a whole analysis will be carried out numerically in the static, barrier-independent single-particle basis $\{\phi_i(x)\}$ being the eigenbasis of the pure harmonic oscillator Hamiltonian $H_0$. Therefore, after decomposing field operators in this basis as following
\begin{eqnarray}
 \hat{\Psi}_{\downarrow}(x) = \sum_i \phi_{i}(x) \hat{a}_{i}, \ \
 \hat{\Psi}_{\uparrow}(x) = \sum_i \phi_{i}(x)\hat{b}_{i},
\end{eqnarray}
where $\hat{a}_i$ and $\hat{b}_i$ are annihilation operators for the $\downarrow$ and $\uparrow$ fermions at state $\phi_i(x)$, one rewrites the many-body Hamiltonian (\ref{Hamiltonian}) to the form
\begin{eqnarray} \label{Hamiltonian2}
\hat{\mathcal{H}}(x_0) &= \sum_i \left(i+\frac{1}{2}\right)\left(\hat{a}^{\dagger}_{i}\hat{a}_{i} + \hat{b}^{\dagger}_{i}\hat{b}_{i}\right)
+ \sum_{ij} U_{ij}(x_0) \left[\hat{a}^{\dagger}_{i}\hat{a}_{j} + \hat{b}^{\dagger}_{i}\hat{b}_{j} + h.c.\right] \nonumber \\
&+ g\sum_{ijkl} I_{ijkl} \hat{b}^{\dagger}_i\hat{a}^{\dagger}_j \hat{a}_k\hat{b}_l.
\label{Ham}
\end{eqnarray}
where $U_{ij}(x_0) = \int\!\mathrm{d}x\,\phi^*_{i}(x) U(x_0) \phi_{j}(x)$ are matrix elements of the barrier potential in the chosen single-particle basis, while the coefficients $I_{ijkl}$ are determined by the interaction part of the Hamiltonian and they are given by $I_{ijkl} = \int\!\mathrm{d}x \phi^*_i(x)\phi^*_j(x) \phi_k(x) \phi_l(x)$. Due to the mirror left-right symmetry of the harmonic oscillator eigenstates these integrals are nonzero only when corresponding sums of the indices $(i + j + k + l)$ are even.

Since the single-particle basis is independent of the position of the barrier, the whole static (but barrier-dependent) Hamiltonian (\ref{Hamiltonian}) can be simply converted to the time-dependent one by varying the position of the barrier $x_0$ in time. We will consider the simplest scenario of a periodic motion of the barrier, $x_0(t) = A\cos(\omega t)$, and we will discuss properties of the system for different frequencies $\omega$ after one period $T=2\pi/\omega$. To make sure that initially the system is not influenced by the barrier we set $A=4$. In this case, the ground-state of the system with the barrier in its initial position is in fact the same as the ground-state of the system in a pure harmonic oscillator. Taking all these initial conditions into account, we investigate properties of the system by solving the time-dependent Schr\"odinger equation, $i\frac{d}{dt}|\psi(t) \rangle = \hat{\mathcal{H}}(x_0(t)) |\psi(t) \rangle$, with the initial condition $|\psi(t = 0) \rangle = |\mathtt{G}_0\rangle$, where $|\mathtt{G}_0\rangle$ is a ground-state of the interacting system confined in a pure harmonic oscillator.

The computational scheme used for solving the time-dependent many-body Schr\"odinger equation is based on representing the Hamiltonian (\ref{Hamiltonian2}) as a matrix in the Hilbert space spanned by Fock states with the lowest single-particle excitations. In our case, the Fock basis is time-independent and it is built from $M$ the lowest single-particle eigenstates of a pure harmonic oscillator. For the cases studied here we set $M=20$ and $18$ for $(N_\uparrow,N_\downarrow)=(1,1)$ and $(2,1)$, respectively, and $M=15$ for $(N_\uparrow,N_\downarrow)=(3,1)$, and $(2,2)$. It means that the dimension of the Fock space in these cases is respectively $D=400, 2754, 6825$, and $11025$. The cut-off $M$ is selected in such a way that, for interactions and other parameters of the problem considered, the final results do not change noticeably when $M$ is increased albeit numerical calculations are still feasible in a reasonable computational time and with reasonable computational resources. After determining all matrix elements of the Hamiltonian in this basis (some of them are time-dependent due to the moving barrier), the time-dependent Schr\"odinger equation is solved numerically by the fourth-order Runge-Kutta method with a time step $\delta t=0.004$ in chosen units of the harmonic oscillator. We also checked that the final results do not change if the time step is decreased to $\delta t = 0.002$ and $\delta t =0.001$. To get a better understanding of the system properties we also calculate the many-body spectra of a given system. For this purpose, we use the same matrix representation of the Hamiltonian as used for time-dependent calculations. For fixed barrier positions $x_0$ we numerically diagonalize the corresponding matrix via the Implicitly Restarted Arnoldi Method \cite{ArnoldiBook}. In this way, we find the lowest eigenenergies as functions of barrier position (with the barrier's position step $\delta x_0=0.01$) and we visualize the temporal spectrum of the system.

The main aim of the present study is to understand the response of a few interacting systems to a potential barrier moving across a harmonic trap. It is clear that in the case of adiabatic motion of the barrier ($\omega\rightarrow 0$), at any moment the system remains in its temporal ground state $|\mathtt{G}(x_0(t))\rangle$, {\it i.e.}, in the many-body ground state of the Hamiltonian $\hat{\cal H}(x_0(t))$. It means that after a whole period, $T=2\pi/\omega\rightarrow \infty$, the system finally returns to the initial ground state $|\mathtt{G}_0\rangle$ and thus the final fidelity ${\cal F} = |\langle\psi(t=T)|\psi(t=0) \rangle|^2$ is exactly equal to unity. Surely, the situation is different when the barrier makes a loop in a finite period of $T$ since then the system can be partially excited to other many-body states. To capture this possibility we introduce the temporal fidelity
\begin{equation}
{\cal F}_\omega(t) = |\langle\psi(t)|\mathtt{G}(x_0(t))\rangle|^2,
\end{equation}
which quantifies the overlap of the transient state of the system $|\psi(t)\rangle$ with the ground state $|\mathtt{G}(x_0)\rangle$ of the temporal Hamiltonian $\hat{\cal H}(x_0(t))$. In this way, we can quite precisely determine moments when the system becomes excited to higher many-body states and associate these excitations with specific properties of the Hamiltonian's spectrum. We suspect that in the adiabatic limit, $\omega\rightarrow 0$, the temporal fidelity ${\cal F}_\omega(t)\rightarrow 1$ for any moment $t$.

At this point, we emphasize that the temporal fidelity ${\cal F}_\omega(t)$ is not the quantity that can be measured directly in state-of-the-art experiments. It is rather a theoretical concept giving the most natural way to quantify the distance in the Hilbert space between different many-body states. However, after appropriate repetition of high-precision measurements, theoretical methods of the quantum state tomography \cite{2003ArianoREVIEW,2017LanyonNatPhys} very often give a route to deduce a form of the considered many-body state. Thus, in principle, the temporal fidelity can be obtained indirectly. In the case of confined systems, it can be done by measuring different probabilities of finding particles occupying different single-particle orbitals and comparing them with corresponding probabilities describing the ground state of the system. In experimental realizations with few interacting particles confined in one-dimensional traps, such measurements are currently accessible \cite{Serwane}.

\begin{figure}
\centering
\includegraphics{_Fig1.pdf}
\caption{ {\bf (top row)} The many-body spectrum of the Hamiltonian $\hat{\cal H}(x_0)$ for $N_{\uparrow} = N_{\downarrow} = 1$ particles as a function of barrier position $x_0$ and different interaction strengths. For the barrier being far away from the center ($x_0=\pm 4$) the spectrum resembles the corresponding spectrum of a pure harmonically trapped system. When the barrier is close to the center, a quasi-degeneracy between many-body states, characteristic for double-well confinement, is visible. Note, that for stronger interactions the energy gap at $x_0=0$ becomes significantly reduced. {\bf (bottom row)} Energy gaps between the lowest three excited states and the temporal ground-state of the Hamiltonian $\hat{\cal H}(x_0)$. It is clear that along with increasing interactions (repulsive as well as attractive) energy gaps closes. Note however that in the case of repulsive forces the lowest excited state, due to inappropriate exchange symmetry, is not dynamically coupled and does not contribute to the dynamics (see main text for detailed explanation). Thus, an effective gap to the lowest relevant excited state grows with increasing repulsions.}
\label{Fig1}
\end{figure}
\section{Two-particle system}
To make our analysis as clear as possible let us start from the simplest system of $N_\uparrow=N_\downarrow=1$ particles. In Fig.~\ref{Fig1} we display the temporal spectrum of the many-body Hamiltonian $\hat{\cal H}(x_0)$ as a function of the barrier's position for different inter-particle interaction strengths. It is clear that whenever the barrier is far from the center of the trap ($x_0=\pm 4$) the spectrum resembles a well-known spectrum of two particles confined in the harmonic confinement \cite{1998BuschFoundPhys} and the ground state is well-isolated from other many-body eigenstates. When the barrier approaches the center of the trap ($x_0\approx 0$), a characteristic quasi-degeneracy of the spectrum is formed. This is a natural consequence of a quasi-degeneracy of the single-particle spectrum in a double-well potential \cite{2016SowinskiEPL,Nandy_2020}. It is important to note that along with increasing interactions, the energy gap at $x_0=0$ between the ground-state and excited many-body states becomes smaller. Since this gap has fundamental significance for excitations when a finite-time transition of the barrier is considered, one can suspect that for sufficiently strong interactions keeping adiabaticity (understood as remaining of the state of the system in the temporal ground state) may be very challenging.

\begin{figure}
\centering
\includegraphics{_Fig2.pdf}
\caption{Time evolution of the temporal fidelity ${\cal F}_\omega$ for different interactions $g$ and different frequencies $\omega$ for the system of $N_{\uparrow} = N_{\downarrow} = 1$. For better comparison, time is expressed in units of the driving period $T$. Note rapid changes of the fidelity when the barrier crosses the center of the trap. To avoid any misunderstandings, note that the same colors correspond to {\it different} frequencies for attractive and repulsive interactions. } \label{Fig2}
\end{figure}
To get a better and quantitative understanding of the dynamical response of the system depending on the barrier frequency $\omega$, we calculate the temporal fidelity ${\cal F}_\omega(t)$ at different time-frames. These results are shown in Fig.~\ref{Fig2} for some chosen values of interactions and different driving frequencies. For convenience, we compare results for different frequencies $\omega$ by plotting fidelities as functions of time $t$ rescaled with respect to the driving period $T$. It is clear that in the first stage of the dynamics, {\it i.e.}, before the barrier transits through the area occupied by particles, the system remains unaffected by the barrier position. Therefore, in the initial stage, the system is completely described by the ground state of the time-independent Hamiltonian with pure harmonic oscillator and thus the fidelity is close to unity irrespective of the sign of interactions and the frequency $\omega$. Then, when the barrier is in the vicinity of the center of the trap, the fidelity rapidly decreases for both, repulsive and attractive, interactions. Of course in the adiabatic limit (very small frequency $\omega$) the fidelity does not change significantly signaling that the system remains in the temporal ground state. Note however that the magnitude of a fidelity's drop depends on the sign of interactions and it is much deeper in the attractive case. This observation can be directly related to the properties of the many-body spectrum. As clearly seen in Fig.~\ref{Fig1}, the energy gap between the many-body ground state and other excited states closes much differently in the case of attractive interactions and it is more sensitive to the strength $g$. Moreover, it turns out that for repulsive interactions the lowest excited state does not contribute to the dynamics of the system. This is directly related to the fact that this excited state, in contrast to the initial state $|\mathtt{G}_0\rangle$, is anti-symmetric with respect to the exchange of particles' position. Since the Hamiltonian of the balanced system of two particles commutes with this particular symmetry, the states having different symmetry properties are not coupled during the evolution independently on the frequency of the driving. Consequently, an effective gap to the first contributing many-body state is essentially larger. Therefore, to get a significant fidelity drop caused by the first transition of the barrier, one needs to consider scenarios being much further from the adiabatic limit (larger frequencies $\omega$). The situation is reversed in the case of attractive forces. In this case, the first excited state is symmetric under the exchange of particles. Therefore, if the energy gap is small enough, it is easily coupled to the temporal state of the system. It means that the repulsively interacting system is much more robust to the driving than its attractively interacting counterpart.
\begin{figure}
\centering
\includegraphics{_Fig3.pdf}
\caption{The temporal fidelity ${\cal F}_\omega$ (top row) and the inter-component entanglement entropy $S$ (bottom row) calculated for the system of $N_\uparrow=N_\downarrow=1$ particles at time $t=T/2$ (left column) and $t=T$ (right column) as a function of interaction strength and driving frequency $\omega$. Chaotic behavior of the fidelity at the final instant $t=T$ is clearly visible. It indicates unpredictability of the dynamics after the second transition of the barrier through the trap. In contrast, after the first transition ($t=T/2$) the dynamics is much more regular and predictable. In both cases, departure from the adiabatic limit is much more intensive for attractive forces. }
\label{Fig3}
\end{figure}

After the barrier fully transits through the system we observe again that the fidelity does not change in time until returning transition. This occurs for all frequencies, irrespectively on the sign of interactions. Again, this behavior can be explained by a closer inspection of the many-body spectrum. After the transition, decomposition amplitudes of the temporal state of the system to the temporal many-body eigenstates almost do not change since gaps between individual states are much larger than the energy scale defined by the frequency $\omega$. In consequence, an overlap of the temporal state with the temporal ground state of the system remains almost constant.

In Fig. \ref{Fig3}, we present snapshots of the temporal fidelity at $T/2$ and $T$ as a function of driving frequency and the interaction strength. These plots compare the response of the system to single and double transition of the moving barrier. Of course, in both cases, in the adiabatic limit ($\omega\rightarrow 0$) the fidelity remains equal to $1$. Nevertheless, for attractive interactions achieving adiabaticity requires much smaller frequencies. As can be seen, after the first transition of the barrier ($t=T/2$), the fidelity is rather a smooth function of interactions and frequency. In contrast, at the final moment ($t=T$) the dependence on these parameters is highly non-trivial and in practice unpredictable. Random behavior of the fidelity at time $t=T$ is related to non-obvious relative dynamics between the internal motion of the system and the motion of the barrier. Namely, after the first transition of the barrier, the system evolves almost independently on the barrier's position. Depending on frequency $\omega$ the second transition effectively happens at quite randomly chosen moment of this evolution. This is particularly the case when after the first transition the system becomes essentially excited (far from the adiabatic limit) and its evolution is highly non-trivial.

It is very instructive to notice that the situation is substantially different when, instead of the fidelity, one considers quantum correlations induced by the moving barrier. For example, let us focus on the inter-component entanglement entropy defined as
\begin{equation}
S(t) = -\mathrm{Tr}_\uparrow \left[\hat\rho_\downarrow(t) \ln\hat \rho_\downarrow(t)\right]=-\mathrm{Tr}_\downarrow \left[\hat\rho_\uparrow(t) \ln\hat \rho_\uparrow(t)\right],
\end{equation}
where the temporal reduced density matrix of a chosen component $\hat{\rho}_\sigma(t)$ can be calculated straightforwardly by tracing out remaining component $\sigma'$ as $\hat\rho_\sigma(t)=\mathrm{Tr}_{\sigma'} \left[|\Phi(t)\rangle\langle\Phi(t)|\right]$. Analogously as we did for the fidelity, in the bottom row of Fig.~\ref{Fig3} we display the entropy $S(t)$ as a function of the interaction strengths and driving frequencies at two different moments $t=T/2$ and $t=T$. It is clear that for both cases the inter-component correlations are built in the system quite smoothly and nearly symmetrically on both sides of the non-interacting limit. For increasing frequencies, {\it i.e.}, when the system rides away from the adiabatic limit, correlations are almost monotonically enhanced. This regularity of the entanglement entropy can be viewed as a direct consequence of the fact that inter-component quantum correlations are related to period and strength of interactions rather than to a particular decomposition and specific evolution of the quantum state.

 It is clear that a direct experimental access to the entanglement entropy, although in principle possible (for particular examples see \cite{2012AbaninPRL,2015IslamNature}), is not straightforward. In the case of the inter-component entanglement considered here the situation is slightly simpler since experimental filtering out of a selected component can be viewed as the counterpart of a theoretical concept of tracing out of the remaining component, {\it i.e.}, the first step of the analysis. Then, by precise determination of occupation probabilities (similarly as in the case of the ground-state fidelity) and by measuring inter-particle correlations between positions of particles (possible due to very precise single-site resolution microscopes) one can try to reconstruct a reduced density matrix. In this way, entanglement entropy between components may be estimated. Nonetheless, still this is not the quantity that can be easily measured.
\begin{figure}
\centering
\includegraphics[width =\linewidth]{_Fig4.pdf}
\caption{ The single-particle density profile $\rho_\sigma(x)$ for the system of $N_{\uparrow} = N_{\downarrow} = 1$ particles calculated after the first transition of the barrier, $t=T/2$. Different colours correspond to different driving frequencies $\omega$ (compare with Fig.~\ref{Fig2}). For comparison, the density profile calculated for the many-body ground-state (adiabatic limit $\omega\rightarrow 0$) is plotted with dashed line. Along with increasing frequency and/or interactions, the system's density profile departures from the ground-state profile signaling decreasing fidelity. }
\label{Fig4}
\end{figure}
To overcome this experimental difficulty with measuring inter-component entanglement entropy, one can consider the temporal single-particle density profile defined as $\rho_\sigma(x,t) = \langle \psi(t)|\hat\Psi^\dagger_\sigma(x)\hat\Psi_\sigma(x)|\psi(t)\rangle$. This is one of the simplest and directly measurable quantities capturing substantial deviation of the system's state $|\psi(t)\rangle$ from the temporal ground state $|\mathtt{G}(x_0(t))\rangle$. In the case of balanced system it is exactly the same for both components. In Fig.~\ref{Fig4} we plot these densities for the instant $t=T/2$ (after the first transition) and the same parameters of the driving as in Fig.~\ref{Fig2}. It is clear that whenever the fidelity becomes closer to $0$ (stronger interactions and/or larger frequencies), the density profile $\rho_\sigma(x,t)$ becomes significantly different from corresponding density obtained for a temporal ground state (black dashed line).

\section{Spin-balanced system of four particles}
\begin{figure}
\centering
\includegraphics[width =\linewidth]{_Fig5.pdf}
\caption{ {\bf (top row)} The many-body spectrum of the Hamiltonian $\hat{\cal H}(x_0)$ for $N_{\uparrow} = N_{\downarrow} = 2$ particles as a function of barrier position $x_0$ and different interaction strengths. Note the substantial difference when compared to the system of two particles in Fig.~\ref{Fig1}. Here, the spectrum becomes quasi-degenerated for two distant positions of the barrier. The difference significantly changes the dynamical properties of the system. See the main text for details. {\bf (bottom row)} Energy gaps between the lowest three excited states and the temporal ground-state of the Hamiltonian $\hat{\cal H}(x_0)$. Again, when interactions are increased (repulsive as well as attractive) energy gaps become smaller.}
\label{Fig5}
\end{figure}

\begin{figure}
\centering
\includegraphics{_Fig6.pdf}
\caption{The temporal fidelity ${\cal F}_\omega$ (top row) and the inter-component entanglement entropy $S$ (bottom row) calculated for the system of $N_\uparrow=N_\downarrow=2$ particles at time $t=T/2$ (left column) and $t=T$ (right column) as a function of interaction strength and driving frequency $\omega$. In contrast to the two particle case (Fig.~\ref{Fig3}) chaotic behavior of the fidelity is present at the final instant ($t=T$) as well as after the first transition of the barrier ($t=T/2$).}
\label{Fig6}
\end{figure}

\begin{figure}
\centering
\includegraphics{_Fig7.pdf}
\caption{The temporal fidelity ${\cal F}_\omega$ and the inter-component entanglement entropy $S$ calculated for the system of $N_\uparrow=N_\downarrow=2$ particles when the barrier is at the center of the trap ($t=T/4$). As explained in the main text, in this case, the quasi-degeneracy of the spectrum is reached only once and therefore the dynamical response of the system is much more regular.}
\label{Fig7}
\end{figure}

After detailed studies of the simplest case of two distinguishable particles, it is worth considering slightly larger systems and check roles played by the quantum statistics and particle imbalance. To make it systematic, let us first focus on the balanced system with $N_\uparrow=N_\downarrow=2$. A corresponding many-body spectrum of the Hamiltonian as a function of the barrier's position and different interactions is presented in Fig.~\ref{Fig5}. It is clear that the spectrum has substantially different properties than the corresponding spectrum for a two-particle system (Fig.~\ref{Fig1}). The most prominent difference is related to the existence of two barrier positions at which the quasi-degeneracy of the many-body states is present. It may suggest that the dynamical behavior of the system may be significantly different already after the first transition of the barrier. Indeed, as clearly seen in Fig.~\ref{Fig6}, the temporal fidelity is unpredictable not only at the final moment $t=T$ but also after the first transition $t=T/2$. The phenomenological explanation of this behavior is exactly the same as previously. After the stage the first quasi-degeneracy of the many-body spectrum is present, the dynamics becomes almost independent of the barrier position. However, it remains significantly affected by particular decomposition (which in fact depends on frequency $\omega$) to different excited states. Therefore, depending on the frequency $\omega$, a moment when the stage of the second quasi-degeneracy of the spectrum is activated is highly unpredictable and leads to a very irregular pattern of the fidelity. To make sure that this general picture is correct and argumentation is valid we also check the results for the moment just after the first quasi-degeneracy is deactivated, {\it i.e.}, when the barrier is exactly at the center ($x_0=0, t=T/4$). Corresponding results are displayed in Fig.~\ref{Fig7}. It is clear, that at this instant the temporal fidelity is a very smooth function of frequency and interactions. It resembles corresponding results for $N_\uparrow=N_\downarrow=1$ at $t=T/2$ (see Fig.~\ref{Fig3}). For completeness and better comparison, in Fig.~\ref{Fig6} and Fig.~\ref{Fig7}, we also present entanglement entropy $S(t)$. In this case, similarly as in the case of two particles, quantum correlations are built in the system much more regularly and depend mostly on interaction strength and interaction period. Additionally, we checked that the response of the single-particle density profiles $\rho_\sigma(x,t)$ behaves analogously to the simpler case of two particles, {\it i.e.}, higher deviations from the temporal ground state of the system are signaled by larger disturbances of the densities.

\section{Spin-imbalanced systems}
\begin{figure}
\centering
\includegraphics{_Fig8.pdf}
\caption{The many-body spectrum of the Hamiltonian $\hat{\cal H}(x_0)$ as a function of barrier position $x_0$for imbalanced systems with $N_{\downarrow} = 1$ and $N_{\uparrow} = 2$ or $3$ particles and different interaction strengths. Note the qualitative difference of these spectra when compared to balanced cases (Fig.~\ref{Fig1} and Fig.~\ref{Fig5}). Here, independently on the interaction strength, the many-body ground-state is always well-isolated from excited states. This causes much better resistivity of the system to the external driving (see Fig.~\ref{Fig9}).}
\label{Fig8}
\end{figure}
\begin{figure}
\centering
\includegraphics{_Fig9.pdf}
\caption{{\bf (top row)} The temporal fidelity ${\cal F}_\omega$ for the imbalanced system of $N_\uparrow=2$ and $N_\downarrow=1$ particles at time $t=T/2$ and $t=T$ (left and right column, respectively) as a function of interaction strength and driving frequency $\omega$. It is clear that in both cases, independently of interactions, the adiabatic limit is easily reached for not too high frequencies. It means that the dynamical resistivity of the system is enhanced. {\bf (bottom row)} Energy gaps between the lowest three excited states and the temporal ground-state of the Hamiltonian $\hat{\cal H}(x_0)$ for two chosen interaction strengths in the system of $N_\uparrow=2$ and $N_\downarrow=1$ particles. In contrast to balanced systems the ground state is well-isolated also for attractive forces. This leads to mentioned resistivity of the system.}
\label{Fig9}
\end{figure}

Finally, let us discuss the dynamical response of the system having components with an unequal number of particles. These kinds of systems may have substantially different properties since, by the construction, they break the symmetry between components. The difference is visible already at the initial moment -- individual components have different density distributions and different spatial sizes. It means that during the evolution they become affected by the barrier at different moments and with different intensities. It should be noted, however, that although the smaller component becomes directly influenced by the barrier at later instants, it is indirectly affected earlier due to mediating interactions with the larger component being already poked by the barrier. Thus naively one can suspect that the dynamics of imbalanced systems, as being influenced by a larger number of different parameters, should be more unpredictable. In fact, this phenomenological reasoning is not fully justified. To make it clear let us first analyze the many-body spectra of these systems and their dependence on interactions and the barrier's position. We show them in Fig.~\ref{Fig8} for two systems with a total number of three and four particles. Although their general appearance is analogous to the eigenspectra of the balanced counterparts, one should note a fundamental qualitative difference -- independently of the interaction strength and the barrier position the many-body ground state is always well-isolated from the excited ones. This finite gap leads directly to  relatively high resistivity of the initial state $|\mathtt{G}_0\rangle$ to the driving, provided that the frequency $\omega$ is not too high. The system remains willingly in its temporal ground state $|\mathtt{G}(x_0(t))\rangle$ during the evolution and thus reaching the adiabatic limit is much easier. This effect is well-captured by the temporal fidelity which remains close to unity for a finite range of small frequencies independently on interactions (see Fig.~\ref{Fig9} for the system with $N_\uparrow=2$ and $N_\downarrow=1$ particles). Of course, for high enough frequencies the system becomes excited to other many-body eigenstates and the fidelity rapidly drops to 0. This drop is however rather smooth and only little irregular deviations (mainly for relatively strong interactions) are visible. Counterintuitively, it means that the imbalanced systems subjected to the external driving are much more resistive and predictable than their balanced counterparts. We checked that this fact is also well-reflected in shapes of the single-particle density profiles $\rho_\sigma(x,t)$ which for small enough frequencies resemble density profiles obtained for the temporal ground state.

\begin{figure}
\centering
\includegraphics{_Fig10.pdf}
\caption{Time evolution of the decomposition number $\kappa_\omega(t)$ for the balanced system of $N_\uparrow=N_\downarrow=1$ particles (left) and the imbalanced system of $N_\uparrow=2$ and $N_\downarrow=1$ particles (right). Depending on the character of mutual interactions (repulsive and attractive forces on top and bottom row, respectively) and frequency of the external driving different number of many-body eigenstates become occupied during the dynamics. Rapid changes of $\kappa_\omega$ occur close to the moments when quasi-degeneracies of the many-body spectrum are forced by moving barrier.}
\label{Fig10}
\end{figure}
To get better understanding of mentioned excitations to higher many-body states, let us also consider some generalisation of the concept of the temporal ground-state fidelity ${\cal F}_\omega(t)$ to fidelities with other many-body eigenstates of the system $|\mathtt{E}_k\rangle$. It can be done straightforwardly by introducing the excited-state fidelities ${\cal F}_\omega^{(k)}(t) = |\langle\psi(t)|\mathtt{E}_k(x_0(t))\rangle|^2$ (by definition, ${\cal F}_\omega^{(0)}(t)$ is equivalent to the ground-state fidelity ${\cal F}_\omega(t)$). With these quantities one can easily follow occupations of different many-body eigenstates during the evolution. However, when rapid drivings are considered, number of contributing many-body states becomes significant and precise analysis is difficult. Therefore, based on these fidelities, we introduce single quantity characterising global properties of the state's decomposition. Namely, we use the decomposition number $\kappa_\omega(t)$ defined as
\begin{equation}
\kappa_\omega(t) = \frac{1}{\sum_k \left[{\cal F}_\omega^{(k)}(t)\right]^2}.
\end{equation}
The quantity has a very natural phenomenological interpretation. If the state is decomposed equally among $K$ different many-body states then $\kappa_\omega$ is equal to $K$. Therefore, $\kappa_\omega$ can be understood as an effective number of many-body states contributing to the many-body state. In Fig.~\ref{Fig10} we show the time-evolution of the decomposition number $\kappa_\omega(t)$ in the case of the archetypal balanced and imbalanced system (two and three particles) for two different interaction strength $g$ and different driving frequencies $\omega$. It is clear that along with increasing frequencies (more diabatic processes) larger number of temporal eigenstates become occupied. Note also that rapid changes of $\kappa_\omega$ occur at moments when the barrier's position leads to the quasi-degeneracy of the many-body spectra. These two facts are in full agreement with results for the ground-state fidelity ${\cal F}_\omega(t)$ (for example, compare with Fig.~\ref{Fig2}). In fact, the ground-state fidelity defines the upper bound for the decomposition number, $\kappa_\omega(t)\leq [{\cal F}_\omega(t)]^{-2}$.

\section{Conclusions}
In this work, we studied the dynamical resistivity of strongly correlated few-fermion systems to the driving by an external potential barrier. Assuming that the system is initially prepared in its interacting many-body ground state and by solving exactly the time-dependent many-body Schr\"odinger equation we examine how the system drives away from the temporal many-body ground state. It turned out that the dynamics of the system is always regular up to the instant when a quasi-degeneracy of the many-body spectrum is achieved. For later moments, due to a quite tangled relation between ballistic motion of the system, correlations induced by interactions, barrier position and speed, and corresponding changes of the many-body spectra the dynamics become highly unpredictable and very sensitive to different parameters. Importantly, moments in which the quasi-degeneracy of the spectrum is established highly depend on the number of particles and may occur more than once during the barrier transition. Moreover, we found that systems with an imbalanced number of particles have a non-vanishing energy gap between the ground and excited states for any interaction and any barrier's position. Therefore, imbalanced systems are much more resistant to the external driving.

Our findings presented in this work may have importance for suspected experimental accuracy of time-dependent protocols designed for coherent manipulations of strongly correlated few-body systems. It turns out that, even for such tiny systems of a well-defined number of particles, initially prepared almost perfectly in their isolated ground-state, small and almost adiabatic external driving may lead to unpredictable dynamics and move the system far away from the desired state. The clue for solving this ambiguity is mostly encoded in changes of the temporal many-body spectrum.

\section{Acknowledgments}
This work was supported by the (Polish) National Science Center Grant No. 2016/22/E/ST2/00555. Numerical calculations were partially carried out in the Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw (ICM), under Computational Grant No. G75-6.

\section{References}
\bibliographystyle{iopart-num}

redpajama_set_name: RedPajamaArXiv


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