# Renormalization Group for non-equilibrium

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?)

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Something I know about! I'm on a phone right now, but I'll just leave a reference and expand on an answer later: m.iopscience.iop.org/1751-8121/40/9/002 –  genneth Nov 4 '11 at 0:42
Looks refreshingly interesting, haven't seen this applied to non-equilibrium quantum transport problems. –  Slaviks Nov 4 '11 at 11:10
@genneth: Please, answer before the bounty falls away... –  András Bátkai Nov 5 '11 at 8:32