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Archive for the ‘quantum fields’ Category

Right now I’m in the midst of a program I helped to organize (and I’m still organizing) at the KITP. The program deals with the question of how to use numerical methods from lattice and gravity to make inroads into interesting (usually very hard) questions about quantum field theory (and quantum gravity) and the dynamics of the strong interactions at finite temperature (like in the heavy ion collisions).

 

We’ve had a lot of great talks about a wide variety of topics. Personally, I really liked the talk by Phillipe DeForcrand on the sign problem. The main reason I like it is because he had really simple examples that illustrate what the sign problem is all about. You can find it here.

And if you want to see what we’ve been hearing about, you can go here and see the full list of talks so far.

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Here is an announcement of a program I will be organizing at the KITP from Jan 17 thru March 9 2012. It is a program on numerical methods for gravity and QFT. The web page of the program is located here.

Here is the image I made to illustrate the program: it is generated by taking a set of modes in a box with a UV cutoff. Then amplitudes are seeded for these modes with random numbers and phases multiplied by the typical quantum uncertainty on each mode. The result is a picture like the one below.

It is also fun to animate it.

Right now I have to start chasing people and reminding them that the (first) deadline for applications is coming soon (April 30th).

In the meantime stay tuned.

Image of Fluctuations of quantum fields

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Quantum tunneling

This week I have been explaining quantum tunneling in quantum mechanics and quantum field theory for my class. It is a fun subject and when I was educated in it a few details were left out. Happily nowadays its easier to find that information. I’m particularly happy with the description of this set of phenomena in the book by Tom Banks: “Modern Quantum Field Theory” , where he actually goes very carefully about how instantons and such are related to the WKB approximation in quantum mechanics, so that one has a rather strong intuitive sense of how these ideas interpolate between the abstract Euclidean formulation of the path integral and a phenomenon that we can understand in other ways.

 

The rest of this article is a rant on technical details without equations. Now that I have advertised where I’m getting my information from, I could stop here. However…

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Last time I pointed to the paper by Green, Komargodski, Seiberg, Tachikawa and Wecht (GKSTW) I was asked to show what I would have done differently. Here is a sketch of some things that I would have put as a part of the main paper (this is not to be assumed to be comprehensive, or careful, nor will I add many references).

Part of the reason to do this is that I think some people out there might benefit from some aspects of this information. What follows is rather technical, so if you’re not well versed in basic SUSY, and on CFT’s,  I apologize in advance: you should not read this then. What I describe bellow is an extended version of the appendix to GKSTW paper. In a good tradition of computer games, this is a third-party add-on. Or you can think of it as a cheap mash-up. Up to you.

Notice: I’ve had some problems with formatting and colors. Temporary fixes have been put in place. Expect updates to text as I find mistakes.

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The Gravity Research Foundation announced the results of the 2010 competition. Here are the results. At UCSB we discussed the prize-winning paper by Mark van Raamsdonk today. It was a very lively discussion and we thought it was a great paper to read. Mark’s paper provided some very tantalyzing evidence that entanglement seems to play a very important role in building up geometry.

On another note, a paper by Daniel Green, Zohar Komargodski, Nathan Seiberg,
Yuji Tachikawa, and Brian Wecht
appeared today. They solve a problem in four dimensional supersymmetric conformal field theories on counting how many marginal deformations there are. As a byproduct, they also solve the problem in 3-d field theories with N=2 Supersymmetry. The paper is beautiful and it is a huge improvement on the work by Leigh and Strassler on the subject many years ago. After reading it I was kicking myself because ‘I could have done it’ (I was interested in the problem and I knew many of the facts. I just didn’t put them together. But if I had thought hard about it I probably could have, although the paper would read rather differently). It’s not surprising that these authors at the Institute for Advanced Study found the solution and that it is written in the particular way that it is written since they have been studying very carefully the superfield formulation of supersymmetric theories in four dimensions. Lubos also commented on the paper.

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Clifford Johnson pointed to me his post on the quest for perfect quantum fluids. In a certain sense, we are used to thinking about fluids as low energy phenomena (relatively low temperature physics). Famous fluids are characterized by fun properties like superfluidity, or ferrofluids that can be a lot fund to play with in an exhibition. The most perfect fluids will be those with little to no viscosity \eta (viscosity is sometimes related to friction, but this can be misleading).

The recent experiment of RHIC that has claimed detection of the quark-gluon plasma also produces some type of liquid with very low viscosity. To compare how this hot liquid compares with a cool liquid one also needs to measure the entropy density s. The quest of who is more perfect than whom depends on the ratio

\frac \eta s

Whoever gets the smallest value wins. These are difficult quantities to measure, but they can sometimes be estimated from other known data. From the point of view of theory, this figure of merit is the one that allows comparison of various theories with different numbers of microscopic degrees of freedom, and it is suggested by various gravity dualities (this way of  comparing fluids came from the work of Kovtun, Policastro, Son, Starinets around 2001-2003, in various papers that have made a big splash in physics).

There is an issue of Physics Today that is dedicated to the topic of perfect fluids from various points of view. The readers of this blog might want to wander there and look at the expository articles on the subject. Room will be left open for discussion and questions, although I don’t promise that I will be able to answer them.

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At some point I promised that I was going to write about my  most recent paper. So here is my promotion. In a sense, that paper is an exercise to understand what does it mean to have quantum gravity in a setup of emergent geometry: this is a situation where geometry is not there a priori, but it is extracted from some collective behavior of a system. I don’t want to go into semantics of what emergence means. For our purposes it is something that is extracted from a non-trivial procedure in systems with a lot of degrees of freedom, where we extract stuff that involves all degrees of freedom simultaneously in a non-trivial  way. The system is quantum mechanical, and therefore there are quantum fluctuations and whatnot, and the whole purpose of our study is to measure some property that can be associated with a distance, but taking into account that the measurement will give you some type of probability distribution on some variable that is supposed to be geometric. Instead of getting something where this is all done analytically, we did it by computer simulations and ran it like an experiment. To top it off, the research was done with an undergraduate student, who ran the simulations and did some of the basic data analysis of the numbers we got.

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