• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,064 questions , 2,215 unanswered
5,347 answers , 22,731 comments
1,470 users with positive rep
818 active unimported users
More ...

  Renormalization Group for non-equilibrium

+ 20 like - 0 dislike

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such that long-wave/asymptotic behaviour of $H_{\Lambda}$ is the same as of $H_{\Lambda'}$ after rescaling by $\Lambda/\Lambda'$. The idea of this definition implies an exact starting point for RG formalisms, with technical details varying between the fields and approximation methods. (For examples, see arXiv:1012.5604 and Wikipedia article).

Now, for non-equilibrium condensed-matter systems there is research direction aiming at generalization of the RG approach to a steady state, e.g., a voltage-biased strongly interacting quatum dot (or Kondo impuryity). For examples, see arXiv:0902.1446 and related references.

I would like to understand the conceptional foundations for the non-equlibrium RG.

What is the definition of an RG transofrmation in a non-equilibirum, steady state ensemble?

I see a problem in the fact that the non-equilibirum desnity matrix which is used to define the problem is not a function of the Hamiltonian alone, thus it is not clear to me how is the effect of the change in the cut-off is split between the Hamiltonian (running couplings) and the density matrix (renormaltizaton of the boundary/external conditions?)

This post has been migrated from (A51.SE)
asked Sep 17, 2011 in Theoretical Physics by Slaviks (610 points) [ no revision ]
retagged Mar 7, 2014 by dimension10
Something I know about! I'm on a phone right now, but I'll just leave a reference and expand on an answer later: http://m.iopscience.iop.org/1751-8121/40/9/002/

This post has been migrated from (A51.SE)
Looks refreshingly interesting, haven't seen this applied to non-equilibrium quantum transport problems.

This post has been migrated from (A51.SE)
@genneth: Please, answer before the bounty falls away...

This post has been migrated from (A51.SE)

1 Answer

+ 4 like - 0 dislike

This is less ambitious than your question (general non-equilibrium states): Near equilibrium correlation functions are described by hydrodynamic theories with stochastic forces, for example the famous models A-J of Hohenberg and Halperin (Reviews of Modern Physics 49, 435 (1977)). In these models I can use the standard RG technology of integrating out short range modes and get running coupling constants. This is known as the "dynamic RG" or sometimes "mode-coupling" theory. The most important result is the critical scaling of transport coefficients (thermal conductivity, sound attenuation, etc.) near second order phase transitions. There have also been attempts to write down RG equations for the CTP (a.k.a. Schwinger-Keldysh) effective action, see for example Dalvit, Mazzitelli, "Exact CTP renormalization group equation for the coarse grained effective action", Phys. Rev. D54, 6338 (1996), arXiv:hep-th/9605024.

This post has been migrated from (A51.SE)
answered Nov 9, 2011 by tmschaefer (720 points) [ no revision ]

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights