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El Salvador Political System
Short for SV by Abbreviationfinder, El Salvador is a republic with strong presidential power. Since the end of the civil war in 1992, politics has been dominated by the right-wing Arena and the former left-wing guerrilla FMLN. The country is characterized by violence, mainly criminal youth gangs, but the police are also behind. Corruption and impunity mean that confidence in the judiciary is low.
The 1983 Constitution provides that El Salvador should have a state of the art pattern from the United States with an executive, a legislative and a sentencing institution.
Countryaah: Total population and chart of El Salvador for years of 2020, 2021, 2022, 2023 and 2024. Also covers population density, birth rate, death rate and population growth rates.
The executive is exercised by the president, who is elected in general elections for a five-year term. The president may not run for re-election directly, but may return after the absence of a term of office. For victory in the first round of elections, at least half of the votes are required, otherwise a second round will be held between the two candidates who received the most votes. The president is both head of state and government as well as commander-in-chief. For its part, the president has a vice president who, like the government, is appointed and dismissed by the president.
The legislative power has Parliament (asamblea nacional), whose 84 members are elected in general elections, according to a proportional electoral system, for a term of three years.
The president can veto approved bills, but the veto can be revoked if two-thirds of the members of the Assembly so demand. To amend the constitution, a proposal must be approved by Parliament for two consecutive terms of office. The voting age is 18 years.
El Salvador is divided into 14 regions. Each region is governed by a governor appointed by the president for three years at a time. The mayors of the country's 262 municipalities are elected in elections that are held at the same time as the parliamentary elections. Should parliamentary and local elections occur the same year as a presidential election, the parliamentary and local elections are held on a different day than the presidential election. Since 2014, Salvadoran citizens have been allowed to vote abroad in El Salvador elections.
Politics is characterized by a strong polarization between right and left, where two parties have long dominated. In the 2019 presidential election, however, a candidate belonging to a third party (see below) prevailed.
The Left Party The Farabundo Martí for National Liberation Front (Frente Farabundo Martí para la Liberación Nacional, FMLN) was previously a guerrilla movement consisting of five guerrilla groups that joined forces in 1980 to make revolution (see Modern History). With the peace of 1992, the FMLN became a political party. During the period 2000–2005, the party had a majority in parliament, but on the other hand, none of FMLN's three presidential candidates succeeded in the 1994–2004 elections. It was very much because all three had a past in the guerrillas and that the electorate associated them with its hard line during the civil war. Prior to the 2009 election, the party instead appointed a popular TV journalist for its presidential candidate, and he won the election. In the 2014 elections, Vice President and former guerrilla commander Salvador Sánchez Cerén won.
The Republican National Alliance (Alianza Republicana Nacionalista, Arena) was founded in 1981 by Roberto d'Aubuisson, a former major educated in the United States. He and several of the party's early members were behind some of the death patrols that raged during the civil war. Arena had government power in 1989–2009. The party is closely linked to the business community and its association of private entrepreneurs' national association (Asociación Nacional de la Empresa Privada, Anep). The loss in the 2009 presidential election led to major internal conflicts.
A short time later, a number of MPs left the party. They later formed the Grand Alliance for National Unity (Gran Alianza por la Unidad Nacional, Ghana). Gana has been the third largest party in parliament since 2012 and, despite its background in Arena, has collaborated with FMLN in parliament. In the 2019 presidential election, Ghana's candidate Nayib Bukele already won the first round. Bukele has a background in the FMLN but now has to seek cooperation with Arena in Parliament to be able to pursue his politics (see further Current policy).
The arena could long lean towards the National Reconciliation Party (Partido de Conciliación Nacional, PCN), the military's old party from 1961. In the 2000s, however, it appeared that the PCN voted with the left. After a ruling in the Supreme Court in 2011, the party was forced to change its name to the National Consultation Party (Partido de Concertación Nacional, PCN). The conservative Christian Democratic Party (Partido Demócrata Cristiano, PDC) was also forced to change its name but was then able to regain its original name (see Calendar).
Funes on a historic visit to Cuba
President Funes makes a historic state visit to Cuba for three days. He is the first Salvadoran leader in 50 years to visit Cuba. During a meeting with Cuba's leader Raúl Castro, Funes says he "came to correct a historic mistake" and refers to El Salvador's broken diplomatic relations with the country after the 1959 revolution. Funes also criticizes the US trade embargo on Cuba.
Bus strike under gang threat
Following the bus attack in June (see June 2016), a law is adopted that makes it illegal to belong to any of the country's criminal youth gang, Maras. In an attempt to scare President Funes from approving the law, the two largest gangs – Mara 18 and Mara Salvatrucha – force the country's bus drivers to strike for 72 hours. The strike affects half the country's bus traffic.
16 dead after gang attack
At least 16 people are killed when the youth gang Maras 18 shoots and fires on a bus on the outskirts of the capital, San Salvador. The reason for the attack is unclear, but it is part of a growing wave of violent crimes committed by the criminal gangs.
Funes forms a national movement
In order to gather popular support for its policies, Funes forms the Citizens' Movement for Change, a movement for various groupings in society that want to support the government.
Splits between Funes and FMLN
The gap between Funes and FMLN is becoming clearer. Many in the party think that Funes does not pursue a sufficiently radical policy. When the party celebrates the one-year anniversary of its election victory, Funes does not participate.
The government is expanding cooperation with the military
The Government unveils a new security plan with increased cooperation between police and the military to curb the growing crime of violence. Among other things, the police will borrow guns from the military and use its barracks. The police also get better vehicles and IT equipment.


text:
{% extends "base.html" %}
{% load humanize %}
{% block mainbody %}

          <button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">

          </button>

            Tweet

Home

About

Documentation

Pokéapi - The Pokémon RESTful API

                What is this?

                    This website provides a RESTful API interface to {{ site_data.total_items|intcomma }} objects
                    related to Pokémon. We specifically cover the video game franchise, though we'd like to cover the card game too. Using this website you can consume information on Pokémon, their moves, abilities, types, egg groups and much much more.

                What exactly is an API?

                    This is probably worth clearing up very quickly for those who don't know.

                    An API (Application Programming Interface) is a set of interfaces (in this case, url links)
                    that are publicly available, that allow developers to interact with an application.

                    In this instance; the application is a database of {{ site_data.total_items|intcomma }} pokemon-related objects.

                Isn't there 101 other Pokémon websites already?

                    Yes and that's exactly the problem!

                    101 instances of the same website means 101 instances of the same data.

                    We aim to provide a single database that any number of other websites
                    can consume and use.

                    Often, and especially when new Pokémon games or updates are released, the 101+ websites
                    take weeks to update as people have to enter the same information in all those different places.

This solves that problem.

                    If all those sites consumed their data from here, they would have the exact same information that is updated at exactly the same time, with no errors between each website.

                    The overall benefit is a better collaboration and consistency across all the different Pokémon
                    websites and applications. It's good for all!

                How much information is stored here?

                    I'm glad you asked because we've got an impressive amount of data!

                    We currently have {{ site_data.total_items|intcomma }} individual items in our database:

{{ site_data.pokemon }} Pokémon

{{ site_data.moves }} Moves

{{site_data.move_pokes|intcomma }} Pokémon<->move links

{{ site_data.abilities }} Abilities

{{ site_data.types }} Types

{{ site_data.egg_groups }} Egg groups

{{ site_data.descriptions }} Descriptions

{{ site_data.sprites }} Sprites

{{ site_data.games }} Games

The server has processed {{ total|intcomma }} api calls at an average of {{ average_day|intcomma }} calls per day.

                The API is missing stuff!

                    I know! Feel free to contribute to open issues on GitHub.

                So who built this?

                    I'm Paul Hallett, a software engineer obsessed with creating things
                    that benefit people. This was a weekend project of mine that has since grown
                    beyond a single weekend's worth of work.

                    Find out more about me here

                    I gathered the information on this site from various resources:

Veekun had a huge bunch of CSV's that
                        I used to build most of the data on the site.

Bulbapedia has a tonne of extra information that proved useful when designing the data model.

                    I'd also like to thank:

Laven Pillay, who scraped together most of the sprites used on the site.

                What's the technology stack?

                    The website framework is Django,
                    a super awesome framework built around Python.

                    We use a Postgres database to store all our data.

                    We use Django-tastypie to expose our data through a RESTful API.

                    We're hosted on DigitalOcean servers, click the link to help keep the site running!.

{% endblock %}

redpajama_set_name: RedPajamaGithub


Mr. Éric Laflamme is Chairman at Reno de Medici SpA, President & Chief Executive Officer at Natcan Trust Co. and President & Chief Operating Officer at Cascades Boxboard Group, Inc. Mr. Laflamme was previously employed as a Principal by Cascades, Inc. He also served on the board at Cascades SAS. He received his undergraduate degree from the University of Sherbrooke.
No news for RM in the past two years.
All Company Executives Reno de Medici S.p.A.


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Home » Randy lecturers attempted to sleep with me – Bayelsa first-class law graduate
Randy lecturers attempted to sleep with me – Bayelsa first-class law graduate
Ebizi Eradiri, the first female first-class law graduate of the Niger Delta University, Wilberforce Island, Bayelsa State, who was recently made the Face of the Bayelsa Girl Child, has disclosed how some randy lecturers almost scuttled her ambition of making first class.
Eradiri, who also bagged first-class feat at the Nigerian Law School, spoke during a homecoming reception, tagged '#Schoolnobescam' held in her honour by the Sele Eradiri Foundation in collaboration with other non-governmental organisations in Yenagoa on Wednesday.
Governor Douye Diri had on Monday formally received the Bayelsa-born female lawyer in company of her father, and announced the award of automatic scholarship for her master and doctorate degrees in any university in Nigeria or abroad.
Diri equally offered her automatic employment to lecture at the law faculty of the state-owned NDU and also declared her as the New Face of the Bayelsa Girl Child with a view to making her a role model for young girls in the state and the entire Ijaw nation to emulate.
Eradiri, who hails from the Yenagoa Local Government Area, said prayers, hard work and dedication to her studies helped her overcome the frustration by some sex-for-marks lecturers.
She said, "I was very conscious of my dressing, which enabled me to get the best dressed female student in the Faculty of Law, in the year l was graduating. I made sure I didn't wear skimpy things that would expose sensitive parts of my body.
"I felt that was the starting point for me not to even attract the wrong lecturers to myself. I would say it was prayer because there was a time when we had a borrowed course and a particular lecturer was trying to do something funny.
"When I sensed it from that particular lecturer in the first semester, l called home and told them what was going on and we all prayed.
"At some point, l had to escalate the issue to my HoD and told her what the lecturer was doing; she called and warned him. These are some of the challenges the girl child is likely to face, but through prayers and escalating them to the appropriate quarters, l think they can scale through."
Eradiri said the lowest grade she had during her university days was a 'C' which was given to her by a lecturer who insisted on having sexual intercourse with her.
She promised to deploy her appointment as the New Face of the Bayelsa Girl Child as a platform to propagate reading culture among the youth in the state.
The post Randy lecturers attempted to sleep with me – Bayelsa first-class law graduate appeared first on Within Nigeria.
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Forty students are about to experience becoming scientists in the 2018 Climate Science Youth Camp, a project organized annually by the Department of Science and Technology-Science Education Institute (DOST-SEI), which will run this year from April 17 to 22 in the island province.
This year's theme, "Oceans and Climate Towards a Resilient Planet", emphasizes the interaction of oceans and atmosphere and how climate and weather affect our lives.
This is the camp's eighth run and the second time in Siquijor, following last year's classroom-based Bootcamp. For SEI Director Dr. Josette Biyo, the camp's job in Siquijor is yet to be completed.
Students will have the actual "camp experience" this year as they get to spend more time in the ocean with no less than marine scientists from the University of the Philippines-Marine Science Institute (UP MSI) and weather forecasters from the Philippine Atmospheric, Geophysical and Astronomical Services Administration (DOST-PAGASA) as camp facilitators.
"We'd like to continue what we've started in the province. Siquijor is home to marine sanctuaries which we need to preserve especially because of their huge influence on climate change. We hope that through the science camp, we can instill in our participants their role in the changing climate and empower them with basic skills to survive the risks they face in their communities," said Biyo.
Image: UP Marine Science Institute's Mark Tolentino (rightmost) engages the interest of Science Camp participants in plankton sampling activity.


In Excel 2007: Data Validation in Depth, author Dennis Taylor shows how to use the data validation tools in Excel to control how users can input data into workbooks and ensure data is entered consistently and accurately. The course covers creating dropdown lists, preventing duplicate entries, and controlling the format of numeric data, dates and times, and text entered into worksheets. Exercise files are included with the course.
- Hi I'm Dennis Taylor and welcome to Excel 2007 Data Validation In Depth. If you need your data to be accurate, and you want to enter it quickly, then this is the right course for you. I'll be showing you how to limit the types of numbers you can enter, and how to set up error and warning messages. We'll look at drop-down lists as a way to ensure valid data entry, and save a lot of typing effort. And we'll be examining methods for controlling the entry of date time information as well as limiting the length of text entries.
These are quick and easy ways to greatly increase data accuracy. Let's get to it with Excel 2007 Data Validation In Depth.


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Breadcrumb LinksHomeTrine University News2018Top Paralympian shares keys to a life of excellence
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Top Paralympian shares keys to a life of excellence
Tom Davis said there was no small amount of irony in him coming to a college campus to speak about living a life of excellence.
"I pretty much about threw my life away through four years of college, doing just about everything the exact opposite of living a life of excellence," Davis, a Fremont resident who is one of the world's top Paralympians, told a more-than-capacity crowd at Trine University's Fabiani Theater on Sept. 26.
Weaving in humor as well as stories from experiences that included serving in the U.S. Army, being gravely wounded in a roadside bomb attack in Iraq and competing as a handcyclist, Davis shared eight keys to living a life of excellence with Trine students and members of the community in attendance.
1. Do what you love
Sharing about his struggles with alcohol abuse through college and afterward, resulting in a series of dead-end jobs, Davis said he realized he needed to change course or, "I was going to end in prison, or I was going to end up dead."
Davis found the opportunity to do what he loved when he enlisted.
"I loved the Army," he said. "I just wish I didn't have to travel down the road that I did to get there. You guys have that opportunity right now to take positive steps to find what you love and do it.
"Find what you enjoy and what brings you satisfaction, and do that. That's what your job should be."
2. Roll with the punches
A roadside bomb and ambush in Iraq cost Davis his left leg above the knee and resulted in massive loss of blood, a broken left leg, a fractured right knee, fractured arms, a dislocated my elbow, fractured vertebrae, fractured bones in his head, traumatic brain injury and post-traumatic stress disorder.
"I look at all that, but I'm still here," he said, noting that one of his comrades, Spc. Brett Tribble, age 19, did not survive the attack.
In the aftermath, Davis said, "There were two things that saved my life. One, was accepting Jesus Christ as my Savior. After I gave my life to Christ, I lived a life of freedom, joy and satisfaction. The other thing was finding my handcycle and riding it."
3. Learn from others
Noting that his life story contains both examples to follow and avoid, Davis said, "You can learn two things from every single person you meet: what they do well, and what not to do."
4. Set goals that others think are impossible
"When I got out of the hospital and I started my physical therapy I didn't just say, 'I want to get better and I want to walk again.' I said, 'I want to go back on active duty. I want to deploy again. I want to fight again for my country,' " Davis said. "And I worked my butt off to get there. I used to ruck march, I used to weightlift, I used to do everything I could to make me physically strong to be able to be deployed again."
Further problems with his knee and back derailed that dream and left him unable to walk. So instead, Davis set lofty goals for handcycling.
"When I started riding my bike I didn't say, 'Hey, I want to ride my bike and I want to be healthy,' " he said. "No. I wanted to race. I wanted to win. I wanted to be a Paralympian. I set those goals and then said I wanted to be the best."
5. Understand that life is not about you
Quoting I Corinthians 9:24, where the Apostle Paul says to "Run in such a way as to get the prize," Davis said, "He's talking about the race of life. But what if that race is a relay? When you're running a relay at the track, four people have to get a baton all the way around the track. It's not just about one person, it's about all four. It's about passing that on."
People are not meant to be buckets where knowledge merely sits, Davis said. Rather, "You're meant to be a vessel and take your talents and abilities and invest them into others."
6. Surround yourself with people who are willing to give their lives for you
From medics and surgeons to his wife and those who have sponsored his racing, Davis said there are many people who have invested in him. In turn, he has helped train other handcyclists.
"You need those people in your life," he said. "Don't try to do it alone, because you can't. Invest your life into other people, and let them do the same for you."
7. Ignore the idiots
"These are the people who are going to tell you that you can't do it. You're not fast enough, you're not smart enough, you're not good enough," Davis said. "Because of their own self-identity issues, they've got to take out their insecurities on somebody else. Don't listen to them."
8. Define success and excellence
"It took me a long time to understand what success is," Davis said. "Are trying hard and excellence the same thing? No, they're not. Trying hard means you simply put an effort in. Excellence means doing everything that you can to fulfill your potential. It means that everything that you do is done to the best of your ability."
Photo: Tom Davis, left, speaks with Trine University students in Fabiani Hall following his presentation on Sept. 26.
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School Counselors and Student Assistance Counselors are always here to help you during school hours as a safe place to talk. Your mental health and well-being are extremely important to us.
Outside of school hours or during vacation/break periods throughout the school year, if you are in a mental health crisis and need the support of a professional, please remember the following resources below. In any event of an emergency, always call 9-1-1.
Additional resources are available on the SAC webpage, HERE.


text:
Q: Change Terminal Colors without changing vim colors? Is there is a way of changing terminal colors without changing the colors in terminal VIM?

A: You can use the CSApprox package in order to use Vim's color themes on a terminal that supports the xterm 256 color extension. (Of course, the colors are approximated into that 256 color pallette: hence the "Approx".) These colors are not affected (or should not be) by changes in the 16 color ANSI palette.
So for instance you can improve how, say, colorized ls appears without changing how your Vim syntax highlighting appears.
Another package that is useful is ColorSamplerPack which contains a whole bunch of color themes that you can experiment with one you have CSApprox installed.
These packages are found on http://www.vim.org.

A: Not a real solution tough:
I removed the stuff changing my terminals definitions for colors and changed dircolors accordingly.

redpajama_set_name: RedPajamaStackExchange


The 2015 FLUID Diversity Mentoring Programme was launched yesterday (14 April) at RIBA in London, where past and potential future mentors and mentees from across the industry gathered to celebrate and share the successes and stories of the class of 2014, and to look ahead to an even bigger and better programme for the coming year.
FLUID Diversity Mentoring Programme is an innovative scheme developed by RIBA's Architects for Change (AfC) committee and the Construction Industry Council, to address the retention and development of talented practitioners from diverse backgrounds for management and leadership roles in the built environment.
Applications from potential mentors and mentees from every sector of the construction industry and from all career levels, from recent graduates to company Directors and Partners are welcomed. Application forms and guidance notes are available here.
As with previous years the organisers would particularly like to support and encourage applications from women, BME and LGBT professionals, professionals with disabilities and those from socio-economically disadvantaged backgrounds.
The project has been developed in response to evidence gathered on diversity by the Construction Industry Council (CIC), AfC, Commission for Architecture and the Built Environment (CABE), the Government's Fair Access to the Professions Report, the Equality and Human Rights Commission's Race Discrimination in the Construction Industry Inquiry Report in addition to other reports.


Kavanagh Builders are a family run Coventry based building firm specialising in home extensions and renovations.
Established over 40 years we have built up an excellent reputation for high quality workmanship and a friendly service. We understand that any building project large or small, on your property, can be a cause of anxiety. Kavanagh Builders consistently aim to minimise these worries by ensuring that projects are completed on time and within budget. Our professional approach and tidy manner will result in minimal disruption to your normal routine.


Bring fun to lunchtime with star and fish shaped nuggets as well as sandwich and entrée portions. Fortified with whole grains and soy protein, you can feel good about offering these nutritious oven baked Pollock portions.
frozen fillets on a lightly oiled sheet pan. CONVECTION OVEN: Preheat oven to 400°F and bake for 10-12 minutes. CONVENTIONAL OVEN: Preheat oven to 425°F and bake for about 15 minutes. NOTE: COOK TO AN INTERNAL TEMPERATURE OF 165°F MINIMUM.


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The Sir Terry Pratchett Reading Challenge: The Amazing Maurice and His Educated Rodents
Before I say anything about this fun book, Congrats Ivan William! He's one of my fellow bibliophiles from ACS(I) and he recently bought his first Terry Pratchett. Which, is an event I consider worth celebrating.
Ok, so on to the book. If I remember correctly, The Amazing Maurice and His Educated Rodents is one of the books aimed at children, like the Tiffany Aching series. It actually doesn't matter, because even though it's funny (and the humour is more obvious), it does have a deeper message.
Now, while this book is loosely based on the Pipe Piper of Hamelin (whoops, almost typed Hamlet), it's really about rats (the "Educated Rodents" of the title, finding out what makes a rat a rat (and what about those rats who can't talk or think?), while Maurice (the cat), unwillingly grows a heart. Meanwhile, Keith (the pied piper) meets Malicia (the mayor's daughter) and they try to have an adventure (well, Malicia does. Keith just happened to be there).
The rats are a really lovable bunch. There's Peaches, a rather bossy female rat; Hamnpork, the old leader rat who isn't that enthusiastic about change; Dangerous Beans, the thinker of the group and Darktan, an athletic young rat. There are a bunch of other rats, but these are the main four. Within these four, there are musings on what makes a rat a rat? and a change in the way things are run. This leads to one of those "old vs new" themes that could be old, but is actually really well done (and resolved in a very humorous way).
Of course, Maurice is lovable. In fact, he's the star of the book for me. He's very much like Puss in Boots, although he'd definitely deny the resemblance. But he's sassy (I'm sorry Maurice, I couldn't think of another word) and has a heart of gold despite his mean exterior. I especially love how he's a good negotiator, because look at his effect on people:
"Now he [the mayor] had the slightly hunted expression of anyone who'd been talked at by Maurice for any length of time. It said, "I'm going where I don't want to go, but I don't know how to get off". "
If only I could do that. I could probably get the 2/3 majority needed in a MUN conference. Or you know, get my teachers to give me better marks.
The humans, on the other hand, were a mixed lot. Keith is a sweet kid, but Malicia was so caught up in her story that she was rather insensitive for most of the book (I did not like to write that sentence). But everyone works out to be likable in the end so....
Personally, I don't see much difference between the "kid" and the "adult" Discworld novels. You should just read them all!
Labels: fiction , humour , reading challenge , Terry Pratchett , western
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A murky Mongolian saga
TO THE surprise of many, Bat Khurts, the head of Mongolia's National Security Council, is back at his desk in Ulaanbaatar, and not sitting in a German prison, awaiting trial for his alleged involvement in a kidnapping in 2003. The charges that allowed his detention have been dropped. Among those surprised was the Foreign Office in Britain, apparently, where Mr Khurts was arrested last year in controversial circumstances. He was extradited to Germany in August, and his trial was due to begin on October 24th. Germany's Chancellor, Angela Merkel is due in Mongolia on a planned visit on October 12th.
Besides affecting Mongolia's relations with Britain, which are now tetchy, and with Germany, which is in its good books, the case has cast depressing light on the thuggery of Mongolia's security services. It has also been a constant reminder of a grisly political assassination with long-lasting effects.
Mr Khurts faced charges related to a kidnapping in May 2003 in the French port of Le Havre. Damiran Enkhbat, a Mongolian who had gone into exile after being freed early from a jail sentence for assault, was duped into going to a McDonald's for what was supposed to be a meeting with a compatriot. Instead, he was set upon by four men, drugged, bundled unconscious into a car and driven across Europe for four days, before being put on a Mongolian Airlines flight from Berlin to Ulaanbaatar. Mr Khurts, who at the time ran Mongolia's main spy agency, was accused of being one of Mr Enkhbat's assailants, and the driver of the car.
On return, Mr Enkhbat was detained as a suspect in the brutal murder in 1998 of Sanjasuuren Zorig, who had been the most prominent leader of the country's democratic revolution in 1989-90, and was at that time in government as the infrastructure minister. Some of his supporters believe that, at the age of just 36, he was about to become prime minister, and was assassinated on the order of corrupt politicians who saw their interests threatened. His murder remains unsolved.
Despite alleged torture, Mr Enkhbat never admitted any involvement. Amnesty International, a human-rights lobby, campaigned for him when he was denied access both to a lawyer and to medical care for a life-threatening condition. He died shortly after his release from prison in 2006, as a result, believe his family, of his maltreatment in detention. His children, who are German citizens, brought charges against Mr Khurts.
Mongolian officials do not bother to deny that the kidnapping happened. As if it were an unfortunate but rather trifling oversight, they say they have accepted it was wrong, apologised and everybody should move on. Clearly it did not affect Mr Khurts's climb up the ladder of Mongolia's security establishment. So it was natural that he should be the man designated last year to take part in talks with Britain on closer security co-operation.
He was given a visa, in response to an application accompanied by a diplomatic note verbale, and his trip was discussed in advance by the countries' respective ambassadors and their host governments. But instead of chewing the cud over an important partnership, he found himself locked up: arrested on arrival at Heathrow airport.
Tsogtbaatar Damdin, state secretary at Mongolia's foreign ministry, says Mongolia remains baffled by what he describes as the British "entrapment" of Mr Khurts. Like Germany, he insists that his release is purely the result of a judicial decision, unrelated to political considerations such as Mrs Merkel's imminent visit.
That is still scheduled, though there must be a risk it will be derailed by unrelenting turmoil in the euro zone. But, says Mr Tsogbaatar, Mongolia is "grateful" to the Germans, and most Mongolians seem to take it for granted that the release is a goodwill gesture intended to smooth Mrs Merkel's way. Mr Khurts arrived back, if not quite to a hero's welcome, than at least to the handshake of a deputy foreign minister (who was at the airport by coincidence, says Mr Tsogtbaatar).
A spokesman at the German embassy in Ulaanbaatar says that Mr Khurts was freed after his country's second-highest court (after the constitutional court) ruled that charges of "Verschleppung", a specific form of abduction covered under article 234(a) of Germany's criminal code, should be dropped. This was the count which justified his detention. Charges of "deprivation of freedom" and "causing bodily harm" still stand, but Mr Khurts seems unlikely ever to face them.
The German spokesman says there were contacts with Britain before Mr Khurts arrived back in Mongolia on September 27th. But two days later, a foreign-office spokesman contacted by The Economist was unaware that he was free. Indeed, Germany seems to have managed the release very quietly. Few if any German and British newspapers have mentioned it.
Britain denies Mr Khurts was entrapped, and also emphasises the separation of its judicial and political processes. Indeed, having managed to antagonise Mongolia, a small but booming economy, with what turned out to be a fool's errand of an extradition action, some officials may be wishing they were more co-ordinated than they are. By Banyan for The Economist
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text:
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\begin{document}

\begin{titlepage}

\rightline{UTHET-09-0102}

\begin{centering}
\vspace{1cm}
{\Large {\bf Exact Gravity Dual of a Gapless Superconductor
}}\\

\vspace{1.5cm}

 {\bf George Koutsoumbas $^{\sharp}$}, {\bf Eleftherios Papantonopoulos $^{*}$} \\
 \vspace{.2in}
 Department of Physics, National Technical University of
Athens, \\
Zografou Campus GR 157 73, Athens, Greece \\
\vspace{.2in}
 {\bf George Siopsis $^{\flat}$}
\vspace{.2in}

 Department of Physics and Astronomy, The
University of Tennessee,\\ Knoxville, TN 37996 - 1200, USA
 \\
\vspace{3mm}

\end{centering}
\vspace{2cm}

\begin{abstract}

A model of an exact gravity dual of a gapless superconductor is presented
in which the condensate is provided by a charged scalar field
coupled to a bulk black hole of hyperbolic horizon in asymptotically AdS spacetime.
A critical temperature exists at which the mass of the black hole vanishes and
a scaling symmetry emerges.
 Below the critical point, the black hole acquires its hair through  a  phase transition while   an electromagnetic perturbation of
the background Maxwell field determines the conductivity
of the boundary theory.

\end{abstract}

\vspace{3.5cm}
\begin{flushleft}
$^{\sharp}~~$ e-mail address: kutsubas@central.ntua.gr \\
$^{*} ~~$ e-mail address: lpapa@central.ntua.gr \\
$ ^{\flat}~~$ e-mail address: siopsis@tennessee.edu

\end{flushleft}
\end{titlepage}

\section{Introduction}

The AdS/CFT correspondence has become a powerful tool in studying
strongly coupled phenomena in quantum field theory using results
from a weakly coupled gravity background. According to this
correspondence principle~\cite{Maldacena:1997re}, a string theory
on asymptotically AdS spacetimes can be related to a conformal
field theory on the boundary. In recent years, apart from string
theory, this holographic correspondence, following a more
phenomenological approach, has also been applied to nuclear
physics in order to describe certain aspects such as heavy ion
collisions at RHIC \cite{Mateos:2007ay} and to certain condensed
matter systems. Phenomena such as the Hall effect
\cite{Hartnoll:2007ai} and Nernst effect \cite{Hartnoll:2007ih,
Hartnoll:2007ip, Hartnoll:2008hs} have dual gravitational
descriptions.

Recently the AdS/CFT correspondence has also been applied to
superconductivity~\cite{Hartnoll:2008vx}. The gravity dual of a
superconductor consists of a system with a black hole and a
charged scalar field, in which the black hole admits scalar hair
at temperature smaller than a critical temperature, while there is
no scalar hair at larger temperatures. A condensate of the charged
scalar field is formed through its coupling to a Maxwell field of
the background. Neither field was backreacting on the metric. This
decoupled Abelian-Higgs sector can be obtained from an
Einstein-Maxwell-scalar theory~\cite{Gubser:2008px} through a
scaling limit in which the product of the charge of the black hole
and the charge of the scalar field is held fixed while the latter
is taken to infinity. Considering fluctuations of the vector
potential, the frequency dependent conductivity was calculated,
and it was shown that it develops a gap determined by the
condensate.

The model of the gravitational dual to the superconductor
in~\cite{Hartnoll:2008vx} was further studied beyond the probe
limit~\cite{Hartnoll:2008kx}. Away from the large charge limit, the
backreaction of the scalar field to the spacetime metric has to be
taken into consideration. It was found that all the essential
characteristics of the dual superconductor were persisting.
Moreover, even for very small charge the superconductivity was
maintained. These models however are phenomenological models. The
classical fields and their interactions are chosen by hand. It would
have also been desirable that these models emerge from a consistent
string theory~\cite{Ammon:2008fc}.

In this work we propose a model of a gravity dual of a gapless
superconductor in which a charged scalar field provides
the scalar hair of an exact black hole
solution~\cite{Martinez:2004nb,Martinez:2005di}. It has been shown
in~\cite{Koutsoumbas:2006xj} that, below a critical temperature,
this black hole solution undergoes a spontaneous dressing up with
the scalar hair, while above that critical temperature the dressed
black hole
  decays into the bare black hole. At the critical point, the mass of the
  black hole vanishes and a scaling symmetry emerges, because the metric becomes purely AdS.
  We will show that, if the scalar field coupled to gravity in the bulk is charged, a condensate forms, while
  an electromagnetic perturbation  of the background
determines the conductivity and therefore the superfluid density of the
boundary theory. There is evidence that these black hole solutions can be
obtained from eleven-dimensional supergravity
theory~\cite{Papadimitriou:2006dr}.

The paper is organized as follows.
In section \ref{sec2} we discuss an exact black hole
solution with scalar hair and in
 section \ref{sec3} we explain how the black hole
acquires its hair through a third order phase transition. In section
\ref{secst} we outline a stability analysis of hairy black holes. In
section \ref{sec4} we discuss the dual superconductor on the
boundary of the exact hairy black hole solution and calculate its
conductivity and superfluid density analytically. In section
\ref{sec5} we support our analytical results of section \ref{sec4}
with a numerical investigation and present evidence showing that the
superconductor is gapless. Finally, section \ref{sec6} contains our
concluding remarks.

\section{Black Hole with Scalar Hair}
\label{sec2}

To obtain a black hole with scalar hair, we start with the four-dimensional action
\begin{equation}\label{holaction1}
I = I_{gr} + I_{\mathrm{matter}}
\end{equation}
consisting of the Einstein-Hilbert action with a negative cosmological constant $\Lambda = - \frac{3}{l^2}$,
\begin{equation}
I_{gr} = \frac{1}{16\pi G} \int d^4x\sqrt{-g}\left[ R+ \frac{6}{l^2} \right] \end{equation}
where $G$ is Newton's constant, $R$ is the Ricci scalar, $l$ is the AdS radius and a charged scalar together with a Maxwell field (matter fields)
\begin{equation}
I_{\mathrm{matter}} = \int d^4x\sqrt{-g}\left[ g^{\mu\nu} D_\mu\phi (D_\nu\phi)^{*}
-\frac{1}{6}R\phi^*\phi
-\lambda (\phi^* \phi)^{2}\right]
-\frac{1}{4 }\int d^{4}x\sqrt{-g}F^{\mu
\nu }F_{\mu \nu }~,
\end{equation}
where
\begin{equation} D_\mu \phi \equiv \partial_\mu\phi + iqA_\mu \phi \end{equation}
and $\lambda$ is an arbitrary coupling constant. The
corresponding field equations are
\begin{eqnarray}
G_{\mu\nu} -\frac{3}{l^2} g_{\mu\nu}&=&8\pi G T_{\mu\nu}^{\mathrm{matter}}~, \nonumber\\
D_\mu D^\mu \phi&=&\frac{1}{6}R\phi+\lambda\phi |\phi|^2 ~, \nonumber\\
\frac{1}{\sqrt{-g}} \partial _{\nu }(\sqrt{-g}F^{\mu \nu }) &=& J^\mu~,
\end{eqnarray}
where the energy-momentum tensor is given by
\begin{equation}
\label{Tuvfield}T^{\mu\nu}_{\mathrm{matter}}= \frac{1}{\sqrt{-g}} \frac{\delta I_{\mathrm{matter}} }{\delta g_{\mu\nu}}~,
\end{equation}
and the electric current is
\begin{equation}
\label{Tuvem}J_\mu = iq (\phi^* D_\mu \phi - \mathrm{c.c.})
~.
\end{equation}
The presence of
a negative cosmological constant allows the existence of black holes
with topology $\mathbb{R}^{2}\times\Sigma$, where $\Sigma$ is a
two-dimensional manifold of constant negative curvature. These
black holes are known as topological black holes
(TBHs)~\cite{topological, Vanzo:1997gw}. The simplest solution reads
\begin{equation}\label{linel}
ds^{2}=-f_{TBH}(\rho)dt^{2}+\frac{1}{f_{TBH}(\rho)}d\rho^{2}+\rho^{2}d\sigma ^{2}\quad
,\quad f_{TBH}(\rho)=\frac{\rho^{2}}{l^2} -1-\frac{\rho_0 }{\rho}~,
\end{equation}
with $\phi = 0$, $A_\mu = 0$.
$\rho_0$ is a
constant which is proportional to the mass and is bounded from
below ($\rho_0\geq-\frac{2}{3\sqrt{3}} l$).
$d\sigma^{2}$ is the line
element of the two-dimensional manifold $\Sigma$, which is locally
isomorphic to the hyperbolic manifold $H^{2}$ and of the form
\begin{equation}\label{eqSigma}
\Sigma=H^{2}/\Gamma \quad \textrm{,\quad  $\Gamma\subset
O(2,1)$}~,
\end{equation}
where $\Gamma$ is a freely acting discrete subgroup (i.e., without
fixed points) of isometries. The line element $d\sigma^{2}$ of
$\Sigma$ can be written as
\begin{equation}
d\sigma^{2}=d\theta^{2}+\sinh^{2}\theta d\varphi{^2}~,
\end{equation}
with $\theta\ge0$ and $0\le\phi<2\pi$ being the coordinates of the
hyperbolic space $H^{2}$ or pseudosphere, which is a non-compact
two-dimensional space of constant negative curvature. This space
becomes a compact space of constant negative curvature with genus
$\mathrm{g}\ge2$ by identifying, according to the connection rules of
the discrete subgroup $\Gamma$, the opposite edges of a
$4\mathrm{g}$-sided polygon whose sides are geodesics and is centered at
the origin $\theta=\varphi=0$ of the
pseudosphere~\cite{topological, Vanzo:1997gw, Balazs:1986uj}. An
octagon is the simplest such polygon, yielding a compact surface
of genus $\mathrm{g}=2$ under these identifications. Thus, the
two-dimensional manifold $\Sigma$ is a compact Riemann 2-surface
of genus $\mathrm{g}\geq2$.  The configuration (\ref{linel}) is an
asymptotically locally AdS spacetime. The horizon structure of
(\ref{linel}) is determined by the roots of the metric function
$f_{TBH}(\rho)$, that is
\begin{equation}
f_{TBH}(\rho)=\frac{\rho^{2}}{l^2}-1-\frac{\rho_0}{\rho}=0~.
\end{equation}
For $-\frac{2}{3\sqrt{3}} l <\rho_0<0$, this equation has two distinct
non-degenerate solutions, corresponding to an inner and an outer
horizon $\rho_{-}$ and $\rho_{+}$ respectively. For $\rho_0\geq0$, $f_{TBH}(\rho)$
has just one non-degenerate root and so the black hole
(\ref{linel}) has one horizon $\rho_{+}$. The horizons for both cases
of $\rho_0$ have the non-trivial topology of the manifold $\Sigma$.
We note that for $\rho_0=-\frac{2}{3\sqrt{3}} l$, $f_{TBH}(\rho)$ has a
degenerate root, but this horizon does not have an interpretation
as black hole horizon~\cite{topological}.

The boundary has metric
\begin{equation}\label{eqnew} ds_\partial^2 = -dt^2 + l^2 d\sigma^2 \end{equation}
so spatially it is a hyperbolic manifold of radius $l$ (and of curvature $-1/l$).

The temperature, entropy and mass of the black hole are,
respectively, \begin{equation} T=\frac{3}{4 \pi l} \left( \frac{\rho_{+}}{l} - \frac{l}{3\rho_+} \right)~, \quad
S_{TBH}=\frac{\sigma \rho^{2}_{+}}{4G}~,\quad
M_{TBH}=\frac{\sigma\rho_{+}}{8 \pi
G} \left( \frac{\rho_+^2}{l^2} - 1 \right)~.\label{relations2} \end{equation} obeying the law of thermodynamics
$dM=TdS$.

A static black hole solution with topology $\mathbb{R}^{2}\times
\Sigma $ and scalar hair, is given by
 (MTZ black hole)~\cite{Martinez:2004nb}
\begin{equation}\label{MTZconf}
d{s}^{2}=-f_{MTZ} (r) dt^{2}+
\frac{dr^{2}}{f_{MTZ} (r)} +r^{2}d\sigma^{2} \quad, \quad f_{MTZ} = \frac{r^{2}}{l^2}-\biggl(1+\frac{r_0}{r}\biggr)^{2}~,
\end{equation}
with
\begin{equation}\label{Psiconf}
\phi(r)= \frac{1}{\sqrt 2}\Psi(r)~~,~~~~ A_\mu = 0 ~.
\end{equation}
where \begin{equation}\label{Psiconf1} \Psi (r) \equiv -\sqrt{\frac{3}{4\pi
G}}\frac{r_0}{r+r_0} \end{equation} is the form of the scalar hair found in the
case of a {\it real} scalar
field~\cite{Martinez:2004nb,Martinez:2005di}. Our normalization is
slightly different due to the fact that we have a {\it complex}
scalar field.  Also, we have chosen a negative sign in
(\ref{Psiconf1}) so that the condensates take on positive values.

The above hairy black hole solution is obtained for the special value of the coupling constant
\begin{equation} \lambda = \frac{8\pi G}{3l^2}~. \end{equation}
Other solutions (charged black holes) also exist for values of
$\lambda$ below the above  critical value in the case of a {\it
real} scalar field~\cite{Martinez:2005di}. It would be interesting
to extend those solutions to the case of a {\it complex} scalar
field $\phi$ as well.

The conformally coupled scalar field $|\phi|$ can be turned into a
minimally coupled field through the field redefinition \begin{equation} \hat
g_{\mu\nu} = \left( 1 - \frac{8\pi G}{3} |\phi|^2 \right)
g_{\mu\nu} \ \ , \ \ \ \ \hat\phi = \sqrt{\frac{3}{8\pi G}}
\tanh^{-1} \sqrt{\frac{8\pi G}{3}} |\phi|~. \end{equation} The action
involving the real scalar field $\hat\phi$ is \begin{equation}\label{eqxI} I_{\hat\phi} =
\int d^4 x \sqrt{-\hat g} \left[ \frac{1}{2} \hat
g^{\mu\nu}\partial_\mu \hat\phi \partial_\nu \hat\phi -
V(\hat\phi)
+ \dots \right] \end{equation} where
\begin{equation}\label{eqxV}
V(\hat\phi)=-\frac{3}{4 \pi Gl^2}\sinh^{2}\sqrt{\frac{4 \pi G}{3}}\hat\phi~.
\end{equation}
and the dots
represent interaction terms involving other fields, showing that the mass of the scalar
field is $m^2 = -2/l^2$. This mass satisfies the
Breitenlohner-Friedman (BF) bound ensuring the perturbative
stability of AdS spacetime~\cite{Breitenlohner:1982jf,M-T}.
However, the BF bound does not guarantee
the nonlinear stability of
hairy black holes
under general
boundary conditions and potentials.
Therefore, a careful treatment of the stability
issue is needed. In section \ref{secst} we give the main results of the
stability analysis while more details can be found
in~\cite{future}.

The temperature, entropy and mass of the black hole are given
respectively by~\cite{Martinez:2004nb} \begin{equation} T=\frac{1}{
\pi} \left( \frac{r_+}{l} - \frac{1}{2} \right)~,\quad S_{MTZ}=\frac{\sigma l^2}{4G} \left( 2\frac{r_{+}}{l}-1 \right)~,\quad
M_{MTZ}=\frac{\sigma r_{+}}{4 \pi
G} \left( \frac{r_+}{l} - 1 \right)~.\label{relations1} \end{equation}  It is easy to show that the law of
thermodynamics $dM=TdS$ holds.

For non-negative mass, $M_{MTZ} \geq{0}$, this black hole possesses only
one event horizon at
\begin{equation}
r_{+}=\frac{l}{2}\left(1+\sqrt{1+4\frac{r_0}{l}}\right)~,
\end{equation}
and $\phi$ is regular everywhere. For negative masses,
$-l/4<r_0<0$, the metric (\ref{MTZconf}) develops three horizons,
two of which are event horizons located at $r_{--}$ and at $r_{+}$
 \begin{eqnarray}
r_{--}&=&\frac{l}{2}\left(-1+\sqrt{1-4\frac{r_0}{l}}\right)~,
\nonumber \\
 r_{-}&=&\frac{l}{2}\left(1-\sqrt{1+4\frac{r_0}{l}}\right)~,
 \nonumber \\
r_{+}&=&\frac{l}{2}\left(1+\sqrt{1+4\frac{r_0}{l}}\right)~,\label{horizon}
 \end{eqnarray}
 \\
which satisfy $0<r_{--}<-r_0<r_{-}<l/2<r_{+}$. The scalar field
$\phi$ is singular at $r=-r_0$.

Note that if
$\rho_0=0$, $r_0=0$, then both the MTZ  black hole (\ref{MTZconf}) and the TBH
black hole (\ref{linel}) go to
\begin{equation}
ds_{\mathrm{AdS}}^{2}=-\left[ \frac{r^{2}}{l^2} -1\right] dt^{2}+\left[ \frac{r^{2}}{l^2}-1\right]
^{-1}dr ^{2}+r ^{2}d\sigma ^{2}\;, \label{muzero}\end{equation}
which is a
manifold of negative constant curvature possessing an event
horizon at $r=l$. The
MTZ and TBH black holes match continuously at the critical temperature
\begin{equation}\label{eqTcr} T_0 = \frac{1}{2\pi l} \end{equation}
which corresponds to $M_{TBH} = M_{MTZ} = 0$, with
(\ref{muzero}) being a transient configuration.
Evidently, at the critical point (\ref{eqTcr}) a scaling symmetry emerges owing to the fact that the metric becomes pure AdS.

\section{Phase Transition}
\label{sec3}

In this section we will review the results discussed
in~\cite{Koutsoumbas:2006xj} of a phase transition of a vacuum TBH
to MTZ below the critical temperature (\ref{eqTcr}).

Defining the free energy as
$F=M-TS$ and using relations (\ref{relations1}), we obtain \begin{equation}
F_{MTZ}=-\frac{\sigma l}{8\pi G}\left( \frac{2r^{2}_{+}}{l^2}-\frac{2r_{+}}{l}+1 \right)~.
\label{free-energy}\end{equation} The free energy~(\ref{free-energy}) can be
written in terms of the temperature as \begin{equation} F_{MTZ}=-\frac{\sigma l}{8\pi
G}\Big{(}1+2\pi l (T-T_{0}) +2\pi^2 l^2 (T-T_{0})^{2}
\Big{)}~,\label{mtzexpan}\end{equation} where $T_{0}\approx 0.160/l$ is
the critical temperature (\ref{eqTcr}).

On the other hand, the free energy of the TBH, using relations
(\ref{relations2}), is \begin{equation} F_{TBH}=-\frac{\sigma \rho_+}{16\pi G}
\left( \frac{\rho^{2}_{+}}{l^2}+ 1 \right)~, \label{FETBH} \end{equation} which
can be expanded around the critical temperature $T_{0}$ as \begin{equation}
F_{TBH}=-\frac{\sigma l}{8\pi G}\Big{(}1+2\pi l (T-T_{0}) +2\pi^2
l^2 (T-T_{0})^{2} + \pi^3 l^3 (T-T_{0})^{3}+\dots
\Big{)}~.\label{tbhexpan}\end{equation} Using (\ref{mtzexpan}) and
(\ref{tbhexpan}), we can calculate the difference between the  TBH
and MTZ  free energies. We obtain \begin{equation} \Delta F=
F_{TBH}-F_{MTZ}=-\frac{\sigma l}{8\pi G}\ \pi^3 l^3
(T-T_{0})^{3}+\dots~,\label{difference} \end{equation} indicating a third order
phase transition between MTZ and TBH at the critical temperature
$T_0$. Matching the temperatures of the MTZ black hole and the TBH
we obtain \begin{equation}   \frac{r_+}{l} = \frac{3 \rho_+}{4l}-\frac{l}{4
\rho_+}+\frac{1}{2}~.\label{rhor} \end{equation} It is easily seen that $r_+
\le \rho_+,$ and the inequality is saturated for $r_+ = \rho_+=l.$
We remark that the temperature $T$ should be non-negative, so $r_+
\ge \frac{l}{2}$ for the MTZ black hole and $\rho_+ \ge
\frac{l}{\sqrt{3}}$ for the TBH.

Thermodynamically we can understand this phase transition as
follows. Using relations (\ref{relations1}), (\ref{relations2})
and (\ref{rhor}), we find that $S_{TBH}>S_{MTZ}$ and
$M_{TBH}>M_{MTZ}$ for the relevant ranges of the horizons $r_+$ or
$\rho_+.$ If $r_{+}>l$~ (i.e., the radius of the horizon exceeds the radius of the boundary and $T>T_{0}$), both black holes have
positive mass. As $T>T_0$ implies $F_{TBH} \le F_{MTZ},$ the MTZ
black hole dressed with the scalar field will decay into the bare
black hole. In the decay process, the scalar black hole absorbs
energy from the thermal bath, increasing its horizon radius (from
$r_+$ to $\rho_+>r_+$) and consequently its entropy. Therefore, in
a sense the scalar field is absorbed by the black hole.

If $r_{+}<l$~ (i.e., the radius of the boundary exceeds the radius of the horizon and $T<T_{0}$), both black holes have negative mass,
but now $F_{TBH} > F_{MTZ},$ which means that the MTZ
configuration with nonzero scalar field is favorable.  As a
consequence, below the critical temperature, the bare black hole
undergoes a spontaneous ``dressing up'' with the scalar field. In
the process, the mass and entropy of the black hole decrease and
the differences in energy and entropy are transferred to the heat
bath.

At the critical temperature, the thermodynamic functions of the two
phases match continuously, hence the phase transition is not of
first order. The order parameter that characterizes the transition
can be defined in terms of the value of the scalar field at the
horizon; using the solution for the scalar field (\ref{Psiconf}) we
obtain for $T<T_0$, \begin{equation}\lambda_{\phi} =\left| \tanh \sqrt{\frac{8\pi
G}{3}}\phi (r_{+})\right|~= \left|\frac{r_{+}-l}{r_{+}}\right| =
\frac{T_{0}-T}{T_{0}+T} \ \ . \end{equation} For $T>T_0,$ $\lambda_\phi$
vanishes. Therefore the order parameter $\lambda_\phi (T)$ is
continuous at the  critical temperature but its first derivative
jumps from $-\frac{1}{2T_0}$ to $0$ as we cross the critical point.

The pure AdS space of (\ref{muzero}) has free energy
$F_{AdS}=-\frac{\sigma l}{8\pi G}$ as can be easily seen using relations
(\ref{free-energy}) or (\ref{FETBH}) with $r_{+}=l$. Then observe
that $F_{AdS}$ is the constant term of both $F_{MTZ}$ in
(\ref{mtzexpan}) and $F_{TBH}$ in (\ref{tbhexpan}). Hence  the
difference of free energies of TBH or MTZ black holes  with the
free energy of pure AdS space indicates that the configuration
(\ref{muzero}) is transient between the MTZ and TBH phase
transition.
At the critical point the mass of the black hole vanishes and a scaling symmetry emerges.

Further evidence of this phase transition was provided
in~\cite{Koutsoumbas:2006xj}. The QNMs of the electromagnetic
perturbations of the MTZ black hole and its charged generalization
were calculated both analytically and numerically and compared
 with the corresponding QNMs of the vacuum TBH. It was found that there is a change in the slope of the
QNMs as we decrease the value of the horizon radius below a
critical value, and it has been argued that this change signals a
phase transition of a vacuum topological black hole towards the
MTZ black hole with scalar hair.

\section{Stability Analysis}
\label{secst}

To perform the stability analysis of the MTZ black hole it is more convenient to work in the Einstein frame (eqs.~(\ref{eqxI}) and (\ref{eqxV})).
Henceforth, we shall work in units in which the radius of the boundary is $l=1$.

The MTZ black hole metric can be written in the form
\begin{equation}
ds^{2}=-\frac{f}{h^{2}}dt^{2}+\frac{dr^{2}}{f}+r^{2}d\sigma^{2}~,
\end{equation}
where
\begin{eqnarray} f &=& f_0(r) = \left[ r^2 - \left( 1 + \frac{r_0}{r} \right)^2 \right] \left( 1 + \frac{r_0^2}{(r + 2r_0)(r+r_0)} \right)^2~, \nonumber\\
h&=& h_0(r) = \left( 1 + \frac{r_0^2}{(r + 2r_0)(r+r_0)} \right)
\frac{r+r_0}{\sqrt{r(r+2r_0)}}~, \end{eqnarray} and the scalar field solution
reads \begin{equation} \hat\phi = \phi_0 (r) = \pm \sqrt{\frac{3}{4\pi G}}
\tanh^{-1} \frac{r_0}{r+r_0}~. \end{equation} Since the potential (\ref{eqxV})
is an even function, the sign of $\phi_0$ is arbitrary; we shall
choose it so that the leading coefficient in the large $r$ expansion
is positive. Thus, for large $r$, we obtain \begin{equation}\label{baound}
\hat\phi (r) = \frac{\alpha}{r} + \frac{c\alpha^2}{r^2} + \dots \end{equation}
where \begin{equation}\label{eqxc} \alpha =\alpha_0 = \sqrt{\frac{3}{4\pi G}}
|r_{0}| \ \ , \ \ \ \ c = - \sqrt{\frac{4\pi G}{3}} \mathrm{sign}
(r_{0})~. \end{equation} Solutions to the Einstein equations with boundary
conditions (\ref{eqxc}) have been found in the case of spherical
horizons and shown to be unstable \cite{Hertog:2004bb}. In that
case, for $\alpha >0$, it was shown that $c<0$ always and the hairy
black hole had positive mass. In our case, we also have $c<0$ when
the black hole has positive mass. However, we obtain $c>0$ when the
black hole has negative mass, which is never the case with spherical
horizons.

We shall now show that in the former case the black hole is unstable
(losing its hair to turn into a TBH) whereas in the latter, it is
stable, as expected from thermodynamic considerations (see section
\ref{sec3}).

To this end,
we apply
the perturbation~\cite{Hertog:2004bb}
\begin{equation}
f(r,t)=f_{0}(r)+f_{1}(r)e^{\mu t} ,\,\,\,\,\, h(r,t)=h_{0}(r)+h_{1}(r)e^{\mu t},\,\,\,\,\,
\phi(r,t)=\phi_{0}(r)+\frac{\phi_{1}(r)}{r} e^{\mu t}~.\,\,\label{perts}
\end{equation}
with $\mu >0$ for an instability to develop.

The field equations give a Schr\"odinger-like wave equation for the scalar perturbation,
\begin{equation}
-\frac{d^{2}\phi_{1}}{dr^{2}_{*}}+\mathcal{V}\phi_{1}=-\mu^{2}\phi_{1}~, \label{scal1}
\end{equation}
where we defined the tortoise coordinate \begin{equation}
\frac{dr_{*}}{dr}=\frac{h_{0}}{f_{0}} \end{equation} and the effective
potential is given by \begin{equation} \mathcal{V} = \frac{f_0}{h_0^2} \left[ -
\frac{1}{2} (1+r^2 {\phi_0'}^2) {\phi_0'}^2 f_0 + (1-r^2
{\phi_0'}^2 ) \frac{f_0'}{r} + 2r\phi_0' V'(\phi_0) + V''(\phi_0)
\right]~, \end{equation}
as in the case of a spherical horizon \cite{Hertog:2004bb}.

Regularity
of the scalar field at the horizon of the MTZ black hole ($r\to r_+$) requires  the boundary
conditions \cite{Hertog:2004bb} \begin{equation} \phi_1 = 0 \ \ , \ \ \ \ (r-r_+) \phi_1' =
\kappa\mu \phi_1\ \ , \ \ \ \ \kappa > 0 ~. \end{equation} For a given $\mu >0$, they uniquely
determine the wavefunction.

At the boundary, the wave equation is approximated by \begin{equation} -
\frac{d^2\phi_1}{dr_*^2} + 5r_0^2 \phi_1 = -\mu^2 \phi_1~, \end{equation} with
solutions \begin{equation} \phi_1 = e^{\pm E r_*} \ \ , \ \ \ E = \sqrt{\mu^2 + 5
r_{0}^2}~, \end{equation} where $ r_* =  - \frac{1}{r} + \dots $~. Therefore,
for large $r$, \begin{equation} \phi_1 = A + \frac{B}{r} + \dots \label{fitAB}\end{equation}
To match the boundary conditions (\ref{baound}) with $c$ given by
(\ref{eqxc}) and $\phi$ expanded as in (\ref{perts}), we need
\begin{equation}\label{eqx33} \frac{B}{A} =- 2 r_{0}~. \end{equation} Since the wavefunction
has already been determined by the boundary conditions at the
horizon and therefore also the ratio $B/A$, this is a constraint on
$\mu$. If (\ref{eqx33}) has a solution, then the black hole is
unstable. If it does not, then there is no instability of this type
(however, one should be careful  with non-perturbative
instabilities, see \cite{bibxxx}). In figure \ref{BA} we give sample
results for both negative and positive values of $r_0.$ If one fits
these functions as in (\ref{fitAB}), it is obvious that
$\frac{B}{A}$ will be negative in both cases. If $r_0$ is positive,
equation (\ref{eqx33}) may have a solution for some value of $\mu,$
so there is an instability. On the contrary, if $r_0$ is negative,
then $- 2 r_{0}>0$ and equation (\ref{eqx33}) has clearly no
solution, so the black hole is stable.

\begin{figure}[!t]
\centering
\includegraphics[scale=0.3,angle=-90]{sample_negmu.ps}
\includegraphics[scale=0.3,angle=-90]{sample_posmu.ps}
\caption{The perturbation $\phi_1$ versus $r$ for $\mu=0.02$
and negative ($r_0=-0.01,$ left graph) or positive ($r_0=-0.01,$
right graph) value for $r_0.$} \label{BA}
\end{figure}

\section{The Dual Superconductor}
\label{sec4}

Using the results of previous sections we will discuss the dual superconductor on the boundary of the exact
supergravity solution.
Recall that for $T<T_0$, a condensate
forms ($\phi\ne 0$), the field equations have as a solution the MTZ black
hole (\ref{MTZconf}) and the scalar field is given by (\ref{Psiconf}).
For $T>T_0$, $\phi= 0$, no
condensate forms and the field equations have as a solution
the TBH of (\ref{linel}).

The metric on the boundary is given by (\ref{eqnew}) and its curvature is $-1/l$ (hyperbolic manifold).
As in the previous section, we shall keep working in units in which the radius of the boundary is $l=1$.

It should be noted that the mechanism of condensation of the scalar
field here is different than the mechanism of condensation of the
dual superconductor in the case of a black hole of flat
horizon~\cite{Hartnoll:2008vx}. In the latter case the scalar field
condenses because an Abelian-Higgs mechanism was in operation. In
our case, the condensation of the scalar field has a geometrical
origin and is due entirely to its coupling to gravity.

The energy of the superconductor which is dual to the hairy black hole solution is (eq.~(\ref{relations1}))
\begin{equation} E_s(T) = M_{MTZ} =
-\frac{\pi\sigma }{4 G} \left(  T_0^2 - T^2 \right) ~, \end{equation} which is
negative for temperatures below the critical point $T_0$. However,
notice that the negative contribution is entirely due to the
Casimir energy. If we subtract the energy at $T=0$, we obtain \begin{equation}
E_s(T) - E_s(0) = \frac{\pi\sigma }{4 G}\ T^2, \end{equation} which is a
positive quantity at all temperatures.

Moreover, the heat capacities in the normal and superconducting
phases, dual to the TBH and MTZ solutions, respectively, are \begin{equation} C_n
= T \frac{\partial S_{TBH}}{\partial T} \ \ , \ \ \ \ C_s = T
\frac{\partial S_{MTZ}}{\partial T}~. \end{equation} Using the explicit form of
the entropy (eqs.~(\ref{relations2}) and (\ref{relations1})), near
zero temperature we have \begin{equation}\label{eqheatc} C_n \approx
\frac{\pi\sigma }{3\sqrt 3 G}\ T \ \ , \ \ \ \ C_s \approx
\frac{\pi\sigma }{2G}\ T \ , \end{equation} therefore both heat capacities
vanish linearly with temperature as $T\to 0$. Such a power law
dependence was also observed in the case of charged holographic
superconductors in flat space \cite{Hartnoll:2008kx}, although the
numerical value of the power could not be determined in that case.
This departure from the typical behaviour of $s$-wave
superconductors  (exponential suppression of the heat capacity as
$T\to 0$) may be due to the presence of a Goldstone mode
\cite{Hartnoll:2008kx}.

To the exact gravity backgrounds we shall now apply an
electromagnetic perturbation. In the case without a condensate (TBH) the
wave equation for perturbing the vector potential
reads~\cite{Koutsoumbas:2006xj} \begin{equation}
f_{TBH}(f_{TBH}A')'+\left(\omega^{2}-\frac{\xi^{2}+1/4}{r^{2}}f_{TBH}\right)A=0~,\label{weqtbh}\end{equation}
where $A$ is an appropriately defined component of the vector potential.

The wavefunction of the lowest harmonic corresponds to the lowest eigenvalue in
the compact hyperbolic space $\Sigma$ (eq.~(\ref{eqSigma})) given by \begin{equation}
\xi^{2}+\frac{1}{4}=0~.\label{eigenvalue}\end{equation} Defining the tortoise
coordinate
$$r_{*}=-\int^{\infty}_{r}\frac{dr'}{f_{TBH}(r')}~,$$ eq.~(\ref{weqtbh}) is solved to give (with arbitrary normalization)
\begin{equation}\label{eqBC} A(r)=e^{-i\omega r_{*}} \end{equation} which obeys the
correct conditions at the horizon. For large $r$ we have
$r_{*}=-1/r+\mathcal{O}(r^{-3})$ therefore the vector potential at
large radius behaves asymptotically as \begin{equation} A = A^{(0)} +
\frac{A^{(1)}}{r} + \dots \label{expan}\end{equation} According to the
AdS/CFT correspondence, the dual source and the expectation value
for the current in the same direction are given respectively by
\begin{equation} A = A^{(0)} \,, \qquad \langle J \rangle = A^{(1)} \,. \end{equation}
Then the conductivity is \begin{equation}\label{eq:conductivity} \sigma(\omega)
= \frac{\langle J \rangle}{E} = - \frac{ \langle J \rangle}{\dot
A} = -\frac{ \langle J \rangle}{i\omega A} =
\frac{A^{(1)}}{i\omega A^{(0)}} \,. \end{equation} We have $A^{(0)}=1$,
$A^{(1)}=i\omega$ and therefore the conductivity
(\ref{eq:conductivity}) reads \begin{equation}
\sigma(\omega)=\frac{A^{(1)}}{i\omega
A^{(0)}}=1~.\label{conduct}\end{equation} According to the discussion in the
previous section, if the temperature is above the critical
temperature $T_{0}= \frac{1}{2\pi }$ (eq.~(\ref{eqTcr}) setting the radius $l=1$), the most probable configuration is the
vacuum TBH. Then relation~(\ref{conduct}) tell us that  the
boundary conducting theory is in the normal phase, as expected.

If the temperature is below the critical temperature, the
vacuum TBH acquires hair and a condensate forms.
 In this
case, (\ref{Psiconf1}) can be expanded as \begin{equation}
\Psi=\frac{\Psi^{(1)}}{r}+ \frac{\Psi^{(2)}}{r^{2}}+\dots ~, \end{equation} where
\begin{equation} \Psi^{(1)}=-\sqrt{\frac{3}{4 \pi G}}\, r_0\,,\,\,\,\,
\Psi^{(2)}=\sqrt{\frac{3}{4 \pi G}}\, r_0^{2}~.\end{equation}
The two non-vanishing leading coefficients lead to condensates of two dual scalar operators $\mathcal{O}_i$ ($i=1,2$), respectively,
\begin{equation}\label{eqO1} \langle \mathcal{O}_i \rangle = \sqrt 2 \Psi^{(i)} ~,\quad i=1,2~. \end{equation}
Unlike in the case of a flat horizon~\cite{Hartnoll:2008vx}, the existence of two condensates does not imply an instability, as was shown in section \ref{secst}.

The two condensates (\ref{eqO1}) are, respectively,
\begin{equation}\label{eqO} \langle
\mathcal{O}_{1}\rangle=\sqrt{\frac{3\pi^3}{2 G}}\, (T_0^2 -T^2)
\,,\,\,\,\,\,\langle \mathcal{O}_{2}\rangle=\sqrt{\frac{3\pi^7}{2
 G}}\,(T_0^2 -T^2)^{2}~, \end{equation} where we used
(\ref{relations1}) and (\ref{horizon}) to express the condensates as
functions of temperature.  Near the critical temperature $T_{0}$ the
condensates behave respectively as \begin{equation} \langle
\mathcal{O}_{1}\rangle \simeq \sqrt{\frac{3}{8\pi G}}\,\left( 1-
\frac{T}{T_{0}} \right) \,,\,\,\,\,\,\langle
\mathcal{O}_{2}\rangle\simeq \sqrt{\frac{3}{32 \pi G}}\,\left( 1-
\frac{T}{T_{0}} \right)^{2}~. \end{equation} The two condensates are plotted as
functions of temperature in figure~\ref{figO}. Observe that the
condensates $\langle\mathcal{O}_{1}\rangle,\,
\langle\mathcal{O}_{2}\rangle$  have a different temperature
dependence than the corresponding operators in the dual
superconductor of a black hole with flat
horizon~\cite{Hartnoll:2008vx}. This behaviour of the condensates is
reminiscent of materials containing impurities \cite{Skalski}.
\begin{figure}[!t]
\centering
\includegraphics[scale=0.8,angle=0]{O.eps}
\caption{The condensates $\sqrt G \langle\mathcal{O}_1\rangle$ (upper curve) and $\sqrt G \langle\mathcal{O}_2\rangle$ (lower curve) as functions of $T/T_0$ (eq.~(\ref{eqO})).}
\label{figO}
\end{figure}

Applying the electromagnetic perturbations to this background, the
wave equation for the vector potential reads \begin{equation}
f_{MTZ}\left(f_{MTZ}A'\right)'+\left(\omega^{2}-\frac{\xi^{2}
+1/4}{r^{2}}f_{MTZ}-q^{2}\Psi^{2}f_{MTZ}\right)A=0~.\label{weqmtz}\end{equation}
If we use the lowest angular eigenvalue (\ref{eigenvalue}), this
simplifies to \begin{equation}
f_{MTZ}\left(f_{MTZ}A'\right)'+\left(\omega^{2}-q^{2}\Psi^{2}f_{MTZ}\right)A=0~.\label{simpleweqmtz}\end{equation}
Eq.~(\ref{simpleweqmtz}) can not be solved analytically in general. However, we
can solve this equation for weak coupling $q^{2}$ using
perturbation theory. Also, a numerical analysis of
(\ref{simpleweqmtz}) will be presented in the next section. For
$q=0$ the solutions are $e^{\pm i\omega r_{*}}$ where
$$r_{*}=-\int^{\infty}_{r}\frac{dr'}{f_{MTZ}(r')}~.$$ The
acceptable solution is $e^{- i\omega r_{*}}$. Using first-order
perturbation theory, we obtain the solution \begin{equation} A=e^{- i\omega
r_{*}}+\frac{q^{2}}{2i\omega}e^{ i\omega
r_{*}}\int^{r}_{r_{+}}dr'\Psi^{2}(r')e^{-2 i\omega r_{*}}
-\frac{q^{2}}{2i\omega}e^{- i\omega
r_{*}}\int^{r}_{r_{+}}dr'\Psi^{2}(r')~.\end{equation} The lowest limit of the
integration has been chosen at $r_{+}$ to ensure correct behaviour
at the horizon. Expanding $A$ in the large $r$ limit (equation
(\ref{expan})), we get \begin{equation} A^{(0)}=\left. A \right|_{r\rightarrow
\infty}=1+\frac{q^{2}}{2i\omega}\int^{\infty}_{r_{+}}dr\Psi^{2}(r)\left[
e^{-2 i\omega r_{*}}-1\right]~, \end{equation} \begin{equation}
A^{(1)}= \left. -r^{2}\frac{dA}{dr} \right|_{r\rightarrow
\infty}=i\omega-\frac{q^{2}}{2}\int^{\infty}_{r_{+}}dr\Psi^{2}(r)\left[
e^{-2 i\omega r_{*}}+1\right]~.\end{equation} Then, the conductivity to
first-order in $q^{2}$ is \begin{equation}
\sigma(\omega)=\frac{A^{(1)}}{i\omega
A^{(0)}}=1-\frac{q^{2}}{i\omega}\int^{\infty}_{r_{+}}dr\Psi^{2}(r)
e^{-2 i\omega r_{*}}~.\label{conductivitymtz}\end{equation}
The superfluid
density is the coefficient of the delta function of the real part
of the conductivity \begin{equation} \Re[\sigma(\omega)] \sim \pi n_s
\delta(\omega) \,, \end{equation} which is also the coefficient of the pole
in the imaginary part
\begin{equation}\label{eqimomega} \Im[\sigma(\omega)] \sim \frac{n_s}{\omega} ~,\quad
\omega \to 0~. \end{equation}
Therefore using
(\ref{conductivitymtz}) we obtain for the superfluid density \begin{equation}
n_{s}=q^{2}\int^{\infty}_{r_{+}}dr\Psi^{2}(r)=\frac{3q^{2}}{4\pi
G}\, \frac{r_0^{2} }{r_{+}+r_0 }~, \end{equation} or in terms of the temperature, \begin{equation}\label{eqalpha} n_{s} (T) = \alpha\left(T_{0}-T\right)^{2} ~,\quad \alpha = \frac{3\pi
q^{2}}{4G}~. \end{equation}
Notice that near $T=0$,
\begin{equation}\label{eqnsa} n_s(0) - n_s(T) \approx \frac{\alpha}{\pi} T \end{equation}
matching the low temperature behaviour of the heat capacity (\ref{eqheatc}).
Such power law behaviour was also observed in charged holographic superconductors in flat space \cite{Hartnoll:2008kx}. Once again, we see an indication that a Goldstone mode is in play.

The normal, non-superconducting,
component of the DC conductivity is given by
\begin{equation} n_n = \lim_{\omega \to 0} \Re
[\sigma(\omega)] \,. \label{normalConductivity}\end{equation}
We obtain
\begin{equation}
\ln n_{n}=2q^{2}\int^{\infty}_{r_{+}}dr\Psi^{2}(r)r_{*}~. \end{equation}
Integrating by parts, we obtain \begin{equation} \ln n_{n} = \frac{3 q^{2}}{2\pi
G} r_0^{2}h(r_{+})~,\label{normalcond1}\end{equation} where \begin{equation}
h(r_{+})=-\frac{1}{r_0^{2}}\ln(r_{+}+r_0)-\frac{1}{(r_{+}+r_0)}\,\sum^{3}_{i=1}
\frac{(r_{+}-r_{i})\ln(r_{+}-r_{i})}{f'_{MTZ}(r_{i})(r_{i}+r_0)}\label{hfunction}\end{equation}
and $r_{i}$ are the three horizons of MTZ black hole given in
(\ref{horizon}). At low temperatures we have $r_0\rightarrow
-\frac{1}{4}$ and the function $h(r_{+})$ (\ref{hfunction}) is
approximated by \begin{equation}   h(r_{+})\simeq -\frac{1}{(r_{+}+r_0)}\,
\frac{(r_{+}-r_{-})\ln(r_{+}-r_{-})}{f'_{MTZ}(r_{-})(r_{-}+r_0)}\simeq
8 \ln T~.\end{equation} Then the normal component of the DC conductivity
(\ref{normalcond1}) becomes \begin{equation} \ln n_{n}\simeq \frac{3q^{2}}{4 \pi
G}\ln T~.\label{loggap} \end{equation}
leading to the low temperature behaviour \begin{equation} n_{n}\sim
T^{\gamma}\,, \,\,\,\,\, \gamma=\frac{3q^{2}}{4\pi
G}~.\label{polygap} \end{equation} The approximation of the  normal component
of the DC conductivity (\ref{polygap}) has a milder behaviour than
the dual superconductor in the case of a black hole of flat
horizon~\cite{Hartnoll:2008vx} in which $n_{n}$ exhibits a clear
gap behaviour. The  behaviour we observe here of the boundary
conducting theory can be found in materials with paramagnetic
impurities \cite{Skalski} and in unconventional superconductors
like the chiral p-wave superconductor \cite{Furusaki}.

These analytical results are supported by a numerical investigation of equation (\ref{simpleweqmtz}) which  will be discussed in the next section.

\section{Numerical Results}
\label{sec5}

In this section we discuss the numerical solution of the wave equation (\ref{simpleweqmtz}) in the interval
$r\in [r_+, \infty)$ and compare it with the analytical results obtained above using perturbation theory.
We shall be working in units in which the radius of the hyperbolic space is $l=1$, so that, e.g., distances will be given in units of $l$ and frequencies and temperatures will be in units of $1/l$.

The boundary condition at the horizon ($r=r_+$) is given by eq.~(\ref{eqBC})
which implies
\begin{equation}\label{eqBC1} A^\prime(r) = -\frac{i \omega}{f_{MTZ}(r)}A(r)~.\end{equation}
Since, by definition, $f_{MTZ}(r_+)=0,$ we applied the boundary
condition (\ref{eqBC1}) at $r=r_++\epsilon,$ where $\epsilon$ is a
small positive quantity. In the following calculations the value
$\epsilon=\frac{r_+}{10000}$ has been used. We integrated up to
$r=R\equiv 5000 r_+$. We solved the wave equation for $r_+ \le 1$
($T\le T_0$) since we know that in this temperature range the
topological black hole acquires hair, while  for $r_+ > 1$ the
vacuum TBH is energetically favorable.

By curve fitting the solution of the wave equation, we calculated
the coefficients $A^{(0)}$ and $A^{(1)}$ defined through
(\ref{expan}). We then deduced the conductivity $\sigma$ using
(\ref{eq:conductivity}). In the limit $\omega\to 0$, the
conductivity yields the densities of the superfluid and normal
components via (\ref{eqimomega}) and (\ref{normalConductivity}),
respectively. We chose $\omega=0.001$ for our numerical
calculations.

\begin{figure}[!t]
\centering
\includegraphics[scale=0.3,angle=-90]{q=0.5_om=0.001_nn.ps}
\includegraphics[scale=0.3,angle=-90]{q=5.0_om=0.001_nn.ps}
\caption{The logarithm of the normal fluid density as a function
of the logarithm of the temperature for $q/\sqrt G=0.5$ (left) and
$q/\sqrt G=5.0$ (right). The solid lines represent the fits
$\ln n_n =0.0538 \ln T +0.149$ (left) and $\ln n_n=2.45 \ln T
+5.3$ (right).} \label{q=0.5_nn}
\end{figure}

\begin{figure}[!b]
\centering
\includegraphics[scale=0.5,angle=-90]{comp_nn.ps}
\caption{The logarithm of the real part of the conductivity as a
function of the logarithm of the temperature for $q/\sqrt G=0.1$ (crosses,
the uppermost symbols),$\, 0.2,0.5,1.0,2.0.$ } \label{comp_nn}
\end{figure}

On the basis of the analytic results in section \ref{sec4} we
expect that at low temperature, the normal fluid density can be
expanded as \begin{equation}\label{eqfitn} \ln n_n = \gamma \ln T + \delta +
\dots \end{equation} whereas near the critical temperature, the superfluid
density is expanded as
\begin{equation}\label{eqfits} n_s = \alpha (T-T_0)^2+ \dots \end{equation} We therefore
fit the data accordingly. The results for $\ln n_n$ at $q/\sqrt
G=0.5$ and $q/\sqrt G=5.0$ are shown in figure \ref{q=0.5_nn}. The
fit (\ref{eqfitn}) has taken into account only the points below
$\ln T = -5$. This is why the data points at higher temperatures
($\ln T > -5$) lie below the fit.

Figure \ref{comp_nn} contains data for various values of the
charge $q$. We observe that the asymptotic slope of the curve as $T\to 0$
increases with the charge.
Table \ref{table1} contains numerical values of the slope
obtained through the fit (\ref{eqfitn}) and compares them
with their analytical counterparts (\ref{polygap}).

We present our results for the superfluid density $n_s$ {\it vs}
temperature in figure \ref{q=0.5_ns} for $q/\sqrt G =0.5, 5.0$.
The fit has been done in the region of temperatures
$(T-T_0)^2<0.005,$ so it does not represent accurately the data at
temperatures away from this region. Again, table \ref{table1}
contains numerical values of the slope obtained through the fit
(\ref{eqfits}) and compares them with their analytical
counterparts (\ref{eqalpha}). The agreement is better for $n_s$
than for $n_n.$

\begin{figure}[!t]
\centering
\includegraphics[scale=0.3,angle=-90]{q=0.5_om=0.001_ns.ps}
\includegraphics[scale=0.3,angle=-90]{q=5.0_om=0.001_ns.ps}
\caption{Superfluid density as a function of $(T-T_0)^2$ for
$q/\sqrt G=0.5$ (left) and $q/\sqrt G=5.0$ (right). The solid lines
represent the fits $n_s=0.552 (T-T_0)^2$ (left) and
$n_s=52.9 (T-T_0)^2$ (right).} \label{q=0.5_ns}
\end{figure}

\begin{table}
\begin{center}

\begin{tabular}{||c|c|c|c|c||}

\hline

$q/\sqrt G$ & $\gamma_{\mathrm{numerical}}$ & $\gamma_{\mathrm{analytical}}$&
$\alpha_{\mathrm{numerical}}$ & $\alpha_{\mathrm{analytical}}$ \\

\hline

0.1 & 0.0020 &  0.0024 & 0.0225 & 0.024 \\

0.5 & 0.0538 &  0.0597 & 0.552 & 0.589 \\

1.0 & 0.187 &  0.239 & 2.196 & 2.356 \\

2.0 & 0.684 &  0.955 & 8.678 & 9.425 \\

3.0 & 1.325 &  2.15 & 20.35 & 21.21 \\

5.0 & 2.522 &  5.97 & 52.90 & 58.90 \\

\hline

\end{tabular}

\end{center}
\caption{Numerical {\it vs}~analytical results for the normal and
superfluid densities for various values of the charge. The numerical
parameters are obtained through the fits (\ref{eqfitn}) and
(\ref{eqfits}), respectively.  Their analytical counterparts are
given by (\ref{polygap}) and (\ref{eqalpha}),
respectively.}\label{table1}
\end{table}

At low temperatures, the superfluid density $n_s$ approaches a
constant. After subtracting this constant, we obtain the behaviour
\begin{equation}\label{eqnsT} n_s(0) - n_s(T) \sim T^\delta \end{equation} where $\delta
\approx 1$ for small charges $q$, in agreement with our earlier
analytic result (\ref{eqnsa}). Sample values of the exponent
$\delta$ are shown in table \ref{table2}. $\delta$ increases as $q$
increases. Similar temperature dependence of $n_s$ was observed in
charged holographic superconductors in flat  space
\cite{Hartnoll:2008kx} indicating the presence of a Goldstone mode.

\begin{table}
\begin{center}

\begin{tabular}{||c||c|c|c||}

\hline

$q/\sqrt G$ & $1$ & $3$&
$5$ \\

\hline

$\delta$ & $1.025\pm 0.007$ &  $1.52\pm 0.03$ & $1.78\pm 0.03$ \\

\hline

\end{tabular}

\end{center}
\caption{The exponent $\delta$ characterizing the low temperature dependence of the superfluid density $n_s$ (eq.~(\ref{eqnsT}))
for various values of the charge.
}\label{table2}
\end{table}

The results of table \ref{table1} are depicted in figure \ref{slopes}. It is
clear that the agreement between numerical and analytical results
is quite satisfactory for the superfluid density, while serious
discrepancies arise for the normal density as $q$ increases.

\begin{figure}[!b]
\centering
\includegraphics[scale=0.3,angle=-90]{slopeR_versus_q.ps}
\includegraphics[scale=0.3,angle=-90]{slopeI_versus_q.ps}
\caption{Numerical and analytical results for the normal (left) and
superfluid (right) densities {\it vs}~$q^2$.  Numerical data are
fitted by $0.176 q^2 - 0.0030 q^4$ (left) and $2.29 q^2 - 0.007 q^4$
(right).} \label{slopes}
\end{figure}

We further analyzed the $\omega$ dependence of the transport coefficients.
Figure \ref{re_q=2} contains the real part of the conductivity
{\it vs} $\omega$ for $q/\sqrt G=2,5$ and various values of the temperature.
The lowest value of the temperature yields rather small values for
this real part, while for larger temperatures the real part tends
to the value 1, which is the outcome for the topological black
hole.
Comparing, one may see that the real part of the conductivity becomes
smaller as we increase the charge $q$.
Unfortunately, numerical instabilities also increase and we have not been able to produce reliable numerical results above $q/\sqrt G =5$.
In the cases we studied, it appears that the superconductor is {\em gapless}.
However, a gap is likely to develop above a certain value of the charge $q$, as
indicated by the trend in the graphs as $q$ increases.

Finally, figure \ref{im_q=2} contains the imaginary part of the
conductivity {\it vs} $\omega$ for $q/\sqrt G =2,5$ and various values of the
temperature.
Some features are more clearly visible in the latter case. The imaginary
part is multiplied by $\omega$ to tame the pole at
$\omega=0.$ The imaginary part seems to vanish at some
frequency, which moves to the left as the temperature increases.

\begin{figure}[!b]
\centering
\includegraphics[scale=0.3,angle=-90]{Re_q=2.ps}
\includegraphics[scale=0.3,angle=-90]{Re_q=5.ps}
\caption{The real part of the conductivity {\em vs} $\omega$
for $q/\sqrt G=2$ (left) and $q/\sqrt G=5$ (right) and $T=0.0032, 0.032, 0.064.$ The lowest curve
corresponds to the lowest temperature.} \label{re_q=2}
\end{figure}

\begin{figure}[!t]
\centering
\includegraphics[scale=0.3,angle=-90]{Im_q=2.ps}
\includegraphics[scale=0.3,angle=-90]{Im_q=5.ps}
\caption{The imaginary part of the conductivity multiplied by
$\omega$ {\em vs} $\omega$ for $q/\sqrt G=2$ (left) and $q/\sqrt G=5$ (right) and $T=0.0032, 0.032,
0.064.$ The uppermost curve corresponds to the lowest
temperature.} \label{im_q=2}
\end{figure}

\section{Conclusions}
\label{sec6}

We  presented a model of an exact gravity dual of a gapless superconductor in
which a condensate forms as a result of the coupling of a
charged scalar field to gravity. The charged scalar field
 responsible for the condensation is a solution of the field
 equations~\cite{Martinez:2004nb,Martinez:2005di} and below a critical temperature dresses up a vacuum
 black hole of a constant negative curvature horizon (TBH) with scalar hair.
 Perturbing the background Maxwell field and using the AdS/CFT correspondence,
we determined the conductivity of the boundary theory and analysed
the behaviour of the normal  and superconducting fluid densities
using both analytical and numerical techniques.

The condensation of the scalar field we considered had a purely
geometrical origin being due entirely to its coupling to gravity.
Hairy charged black hole solutions are also known to exist in the
case of a {\it real} scalar field~\cite{Martinez:2005di}. It would
be interesting to extend these solutions to the case of a {\it
complex} (charged) scalar field $\phi$ and analyse the entire range
of parameters labeling the solutions, including the charges of the
black hole and the scalar field. This should yield an interesting
landscape consisting of chargeless as well as charged
superconductors,  as in the flat
case~\cite{Hartnoll:2008vx,Hartnoll:2008kx}. Work in this direction
is in progress.

\section*{Acknowledgments}

Work
supported by the NTUA research program PEVE07.
G.~S.~was
supported in part by the US Department of Energy under grant
DE-FG05-91ER40627.

redpajama_set_name: RedPajamaArXiv


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STOCKTON – Three of five trends are headed in the right direction on University of the Pacific's second literacy report card for San Joaquin County.
As part of its Beyond Our Gates program, the university is measuring third-grade English-language arts proficiency, preschool enrollment, new mothers without a high school diploma, truancy rates and library books borrowed per capita.
•	Trends are improving on preschool enrollment, new moms without a diploma and truancy.
•	Library usage countywide remained roughly the same from 2012.
•	English-language arts proficiency scores dropped behind last year and further behind state averages.
Read Friday's Record for more on this story by staff writer Kevin Parrish.


Although the charity gratefully acknowledges the support from the council through an Our Manchester VCS grant , this does mean that we have to continue fundraising throughout the year to make up any shortfall so that all our services and activities can continue.
CGN runs regular raffles at Sunday teas and some Thursday coffee mornings, and occasional small sales of fancy goods.
Last Thursday, 25th October Arthur held a big raffle with about 30 prizes, which raised £135.
Joan always helps sell raffle tickets and Susan made sure everyone had a chocolate.
We continue to be very grateful for all kinds of donated gifts which can be dropped off at the office, as well as donations and legacies.


She works part-time at our clinic.
Abby is a very thoughtful young lady, who works hard.
She is an integral part of our team. She works part-time at the clinic and is currently doing a Science degree.
Abby is a musician in her spare time and also a talented face painter!


text:
Judgment Search Results Home > Cases Phrase: patents Court: andhra pradesh Year: 1994 Page 1 of about 32 results (0.042 seconds)
A. Hemamalini Vs. A. Pankajanabham and anr.
Court : Andhra Pradesh
Reported in : 1994(3)ALT30; I(1995)DMC258
..... company of the appellant. the parents of the appellant took one or the other pretext and did not send the appellant to the first respondent. on 22.4.1985 the patents of the appellant met the first respondent and informed the latter that the appellant was missing from the house from the previous night and they also disclosed to the first .....
S. Smmaiah and ors. Vs. Andhra Pradesh State Electricity Board and ors ...
Reported in : 1994CriLJ3830
..... the order dismissing an application filed for punishing the contemnor for contempt of court is a 'judgment' within the meaning of clause 15 of the letters patent (madras). 16. in this connection, we may refer to the judgment of the supreme court reported in union of india v. mohindra supply co., ..... act' to the contemnor. when once the competent legislature restricted the right of appeal, that restriction applies or prevails over clause 15 of the letters patent (madras), as the said clause is subject to the provisions prescribing right of appeal provided under the act. restrictions and limitations with regard to ..... for punishing the contemnor under the contempt of courts act, is dismissed, can have recourse for filing an appeal under clause 15 of the letters patent (madras), even though no appeal lies under s. 19(1) of 'the act'. 13. a similar contention fell for consideration in the said ..... bench against the order of a learned single judge dismissing the application filed for punishing the respondents, an appeal lies under clause 15 of letters patent as the judgment affected the rights of the appellants and, therefore, it is a 'judgment' within the meaning of the said clause. in support ..... of the petitioners as helpers is based on principles of recruitment ........' 4. this appeal is sought to be filed under clause 15 of the letters patent act by the appellants questioning the dismissal of contempt petition. office raised an objection that no appeal lies under s. 19(1) of the contempt .....
Nov 11 1994 (HC)
P. Raj Kumar Vs. N. Krishna
Reported in : 1994(3)ALT597
..... appellate judge not examining these questions, inasmuch as from the materials the order of eviction, should be totally set aside. this court is not persuaded by either of the pleas. patently, the learned appellate judge has totally failed in dealing with the matters in accordance with law much less satisfactorily. there is also the evidence on record to come to a .....
G. Padma Vs. Dr. Bavineni Vijaya Lakshmi and Others
Reported in : AIR1995AP63; 1994(3)ALT318
..... .7. we must record that there was a strain on the part of the learned counsel for the appellant to show that clause 15 of the letters. patent overrides the code. this submission is of no avail at all for deciding the question of maintainability of a writ appeal as against the decision in a petition ..... court. however, the review petition was heard by one of the two learned judges. 'when an appeal was sought to be preferred under clause 15 of the letters patent, it was held by the bench of the high court of calcutta that no such appeal would lie. the learned judges of the bench in achyutham v. annapur ..... bench is dealt with by one of the two judges on the ground that the other judge was not available, an appeal under clause 15 of the letters patent is not maintainable. while doing so, the learned judges of the bench of this court referred to and relied on the pronouncement of a bench of the ..... is being done by one of the two judges available. we do not think we could be more expatiate than what we have expressed as above. this implication is patent to our mind.5. however, the endeavour of mr. t. lakshminarayana, learned counsel for the appellant, is to mainatin that as per the terms of clause 15 ..... or any of them shall hear the application, and no other judge or judges of the court shall hear the same.'3. the implications of the rule are patent and unambiguous. if the judge or judges or any one of the judges, who made the original verdict, a review of which is sought for, continues or .....
Samineni Venkateswarlu and Another Vs. Nagubandi Venkata Narasiah (Die ...
Reported in : AIR1994AP220; 1994(1)ALT626
..... in the letters patent appeal, we see no merits in the contentions raised by the learned counsel for the cross-objectors. hence, the cross-objections are also dismissed. no costs.24. the learned counsel ..... are findings based on facts andalso on consideration of the entire evidence on record. we see no reason to differ with the said findings of the fact in this letters patent appeal.22. in the result, the appeal fails and is accordingly dismissed. no costs.23. we have heard the counsel for the cross-objectors. in view of the reasoning given .....
Valluri Jaganmohini Seetharama Lakshmi and Another Vs. Kopparthi Ramac ...
..... are set aside in so far as items 1 and 2 of suit schedule properties are concerned and are affirmed in so far as item no. 3 thereof. the letters patent appeal is allowed in part. each party shall bear their own costs.15. appeal allowed. ..... b. subhashan reddy, j.1. this letters patent appeal raises two important questions of law as to(1) whether making a provision for pocket expenses amounts to maintenance capable of enlarging into a fulfledged right under section 14( .....
Sheriff Iqbal HussaIn Ahmad Vs. Kota Venkata Subbamma and Others
..... of any compensation or damages to their respective defendants; and (c) the plaintiffs shall be entitled for costs throughout viz. in the suits, first appeals, cross-objections and these letters patent appeals. 11. l.p. as, are allowed as indicated above with costs.12. appeals allowed. ..... 1. at issue in these two letters patent appeals is:'when a specific relief for possession is sought for by a civil action in common law remedy, can a discretion be exercised by the court to grant a .....
Uddagiri Chalama Raju and anr. Vs. Uddagiri Subba Rao (Died) and ors.
..... plaintiffs filed an appeal. a learned single judge of this court after considering the material on record confirmed the judgment of the lower court. against that judgment, this present letters patent appeal is filed.5. sri c. poornaiah, the learned counsel for the appellants contended that there is no custom of jesta bhaga and allotment of any share towards jesta bhaga ..... the account was settled between the parties. thus, we see no force in this contention of the learned counsel for *the appellants.24. we see no ground in the letters patent appeal and the same is dismissed accordingly. no costs.
E. Durvasulu Naidu Vs. E. Rangaiah Naidu and ors.
syed shah mohammed quadri, j.1. this letters patent appeal arises out of the final decree proceedings taken in a partition suit. the plaintiff in o.s.no. 2 of 1975 is the appellant in this l.p.a. .....
The Chief Election Commissioner, Election Commission of India Vs. Dr. ...
..... therefore, of the view that the order passed by the learned single judge is a 'judgment' within the meaning of clause 15 of the letters patent.21. the next aspect which is of foremost importance is whether the view expressed by the learned single judge regarding the powers of high court under ..... especially at paragraph (9) of the judgment.19. the scope and ambit of the expression 'judgment' for the purpose of clause 15 of the letters patent has been succinctly laid down by the supreme court in the leading case of sham babulal khimji v. jayaben, air 1981 sc 1786. the following observations ..... article 226 of the constitution of india are such that could be regarded as a 'judgment' within the meaning of clause 15 of the letters patent. the various observations extracted above would make it fairly clear that the learned judge was of the definite view that a constitutional court exercising jurisdiction under ..... not been disposed of finally. it is also true that it is only against a 'judgment' that an appeal under clause 15 of the letters patent can be filed. but, we are of the view that the views expressed by the learned single judge regarding the maintainability of the writ petition ..... to these arguments the learned counsel for the first respondent- writ petitioner contended that the appeal itself is not maintainable under clause 15 of the letters patent, that article 329(b) does not come in the way of the writ petitioner inasmuch as he is seeking to enforce the fundamental right guaranteed .....


Some companions have uncanny speed, providing their masters with swift transport.
Racer Feats: In addition to the standard feats available to animal companions, a racer can select Acrobatic Steps, Charge Through, Improved Lightning Reflexes, Lightning Stance, Nimble Moves, and Wind Stance.
Fast Movement (Ex): A racer's speed is 10 feet greater than that of typical animals of its kind when it is wearing no armor and carrying a light load.
Sprint (Ex): At 6th level, once per hour a racer can move at 10 times its normal speed when it makes a charge or uses the run action.