Research topics in Statistical Physics

[leo.]

Currently I'm in the last year of the Physics course and I've been thinking about working in a project of undergraduate research, specifically in Statistical Physics. Two years ago I've already done a project like that in Fluid Mechanics combined with Gauge Theories and in that project I've studied the geometry of locomotion of deformable bodies at low Reynolds number. It was more of a mathematical physics project.

Now since I'm almost finishing the undergraduate program I've already taken courses on electrodynamics, quantum mechanics, thermodynamics, mathematical physics and statistical physics.

I've thought on doing this new undergraduate research on Statistical Physics because I like the idea of deriving results about macroscopic systems by looking at the microscopic scale. Since I've taken most of the important courses I want to leverage that now.

My only problem is that I've no idea about what are possible research topics in Statistical Physics. I've searched a little on the internet and the major topics I've found are related to magnetism, like the Ising model. I'm sure, however, that there are many other possible research topics. I really want to find one such research topic where it is possible to leverage things like quantum mechanics and electrodynamics.

So, what are possible research topics in Statistical Physics, other than those related to magnetism like the Ising model? What topics bridge with quantum mechanics and with electrodynamics? I have a good mathematical background also anyway.

Two possibilities which I thought about were:

1. Something related to cosmology. I don't really know if there's anything that can be done with Statistical Physics and cosmology together, but it seems to be nice if there was something in this category.
2. Something related to the study of molecules which applying statistical physics to analyze how things work microscopically we can end up with results of interest for chemistry and biology. I also have just this rough idea, so I don't know a precise research topic that could use this.

Are there any nice research possibilities in any of these two categories? And what about something else?

Thanks very much in advance!

 

[radium]

I would look into quantum phase transitions possibly (although of course you should eventually choose a specific system to focus on).

 

[ZapperZ]

Currently I'm in the last year of the Physics course and I've been thinking about working in a project of undergraduate research, specifically in Statistical Physics. Two years ago I've already done a project like that in Fluid Mechanics combined with Gauge Theories and in that project I've studied the geometry of locomotion of deformable bodies at low Reynolds number. It was more of a mathematical physics project.

Now since I'm almost finishing the undergraduate program I've already taken courses on electrodynamics, quantum mechanics, thermodynamics, mathematical physics and statistical physics.

I've thought on doing this new undergraduate research on Statistical Physics because I like the idea of deriving results about macroscopic systems by looking at the microscopic scale. Since I've taken most of the important courses I want to leverage that now.

My only problem is that I've no idea about what are possible research topics in Statistical Physics. I've searched a little on the internet and the major topics I've found are related to magnetism, like the Ising model. I'm sure, however, that there are many other possible research topics. I really want to find one such research topic where it is possible to leverage things like quantum mechanics and electrodynamics.

So, what are possible research topics in Statistical Physics, other than those related to magnetism like the Ising model? What topics bridge with quantum mechanics and with electrodynamics? I have a good mathematical background also anyway.

Two possibilities which I thought about were:

1. Something related to cosmology. I don't really know if there's anything that can be done with Statistical Physics and cosmology together, but it seems to be nice if there was something in this category.
2. Something related to the study of molecules which applying statistical physics to analyze how things work microscopically we can end up with results of interest for chemistry and biology. I also have just this rough idea, so I don't know a precise research topic that could use this.

Are there any nice research possibilities in any of these two categories? And what about something else?

Thanks very much in advance!

Back up a bit.

If you intend to do this as a formal undergraduate research project, shouldn't you be discussing this first with the faculty member that you wish to work with and who will be supervising your work? There is no point in any of us coming up with topics and suggestions, and then that faculty member does not want you to work on that area.

Zz.

 

[radium]

So is this an actual research project with a faculty member? In that case you should be trying to determine their interests to find someone who can advise you.

 

[leo.]

Indeed it is an actual research project with a faculty member. In truth I've considered working with a physicist and I did talk to him. He just said that being a topic in statistical physics it is fine, so he just suggested me to take a look on what I want to work with within statistical physics without a more specific suggestion of a topic. He just told me to pick something in equilibrium statistical physics.

Because of that I've started searching for what can be done in that area. The most common topics are related to the Ising model. I wanted to do something different though. I thought on something involving cosmology and/or quantum mechanics but I'm still unsure. I've been looking for quantum phase transitions as suggested and found some interesting articles like "Black Holes as Critical Point of Quantum Phase Transition" and "Cosmological Phase Transitions". I've been thinking on something along that lines.

More than that I've found out recently that systems like stars and galaxies can be described within the framework of statistical mechanics. I just don't know of any specific reference on that.

Are there topics which I could look at on those lines?

 

[radium]

So is this faculty member asking for you to come up with your own original research project or just to find a more specific topic?

Based on the first paper you posted, I assume you have heard of AdS/CFT in condensed matter (people also just refer to it as holography). If not then I can explain a bit about it. However, I really think it would be necessary to have taken classes in GR, QFT and advanced quantum matter. It definitely takes a very unconventional approach to condensed matter problems, but what is very profound is thermodynamics and also hydro (on long length and time scales) falls very naturally out of the theory.

Some of the interesting topics people are looking at nowadays which you might like are the application to quantum chaos and entanglement.

 

[leo.]

The faculty member has told me to pick a more specific topic, with the only constraint that it were in equilibrium statistical physics. I believe the details of the research project itself will be discussed after that. So for now I'm looking for the topic.

Now, although I haven't taken classes on GR I have a good background on differential geometry on manifolds which I believe could make one preliminary study of GR to be feasible since in the past I've had (although informally) studied a little about GR. Now QFT I've really never studied. In that point I ask: considering each paper I've linked (regarding black holes and cosmological phase transitions), what each of them requires? Both requires GR and QFT or some of them requires just one of those theories? Because it is quite common here to have undergraduate research projects where some of the time is dedicated to the study of a required theory which the student hadn't learned before, so I think at first perhaps those topics could still be considered.

On the other hand, what about the description of stars and galaxies? Sorry if I'm saying this in a quite "loose" manner, it's just that some years ago I've read a little about it and I don't really remember what could be studied regarding systems like that, but I believe that statistical physics could play a role here.

Now, quantum chaos is something I really wouldn't get into. In the mechanics course I've taken chaotic classical dynamical systems weren't considered, so I've never ever studied them. I believe getting into the quantum version without any notion whatsoever about the classical one wouldn't be a good idea.

I've searched about quantum phase transitions and found that interesting papers about the "cosmological phase transitions". I'm just unsure if I could tackle it, since I would need to first study QFT right? Anyway, thanks very much for the suggestions up to know!

 

[radium]

The first paper I think is explicitly referring to AdS and also is making a lot of reference to the strong coupling large N limit (this is the regime where the gravity side become classical). The large N limit is something you use for an expansion in field theory. You say you have N flavors of fields (N would refer to colors in QCD) and then you calculate the path integral rescaling the fields and doing a saddle point approximation. This would be a sort of semiclassical limit where quantum corrections are 1/N etc. However, it makes a significant difference whether you have vectors or matrices. For the vector large N limit everything decouples via the central limit theorem, but for matrices you still have a strongly coupled theory after you do this. The original paper is by t'Hooft I think and the matrix large N limit is behind Maldacena's conjecture.

I am not very familiar with cosmology by any means but what I can tell from skimming the second paper is that based on what I know about the techniques used (Euclidean field theory, the effective action, Langrangian formalism in general relativity), this would require a pretty extensive knowledge of field theory.