SciPost Submission Page
Landau Theory for Non-Equilibrium Steady States
by Camille Aron, Claudio Chamon
|As Contributors:||Camille Aron|
|Submitted by:||Aron, Camille|
|Submitted to:||SciPost Physics|
|Subject area:||Statistical and Soft Matter Physics|
We examine how systems in non-equilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the non-analytic potential arises from the different density of states of the baths. In periodically driven-dissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The mean-field critical exponents become dependent on the low-energy features of the two most singular baths. We propose an extension beyond mean field.
Submission & Refereeing History
Reports on this Submission
Anonymous Report 1 on 2019-10-29 Invited Report
Report on: Landau Theory for Non-Equilibrium Steady States
by C. Aron and C. Chamon
This paper by Aron and Chamon addresses the field theoretical
description of several cases of driven-dissipative (spin)
systems. Different types of non-equilibrium are considered, such as
coupling to multiple heat baths which have different temperatures and
also driving via a time-periodic external magnetic field. Both cases
are generic and there is much interest in studying the ensuing
non-equilibrium properties of systems with large numbers of coupled
degrees of freedom.
In the paper the authors show how one can derive a corresponding free
energy functional from the (standard) self-consistency condition of
the behaviour of a single spin in an external field and the mean
magnetization of the system. Their treatment applies close to a
continuous phase transition and the procedure is clearly explained in
equilibrium and then generalized and used in nonequilibrium. Both
"bottom-up" and "top-down" approaches are used in order to obtain the
functional form the resulting Landau potential.
The authors argue and then for specific cases explicitly derive the
corrections to the standard phi^4 free energy and show that these
additional terms feature non-analytical power-law dependence on the
order parameter. A concluding section contains an enlightening
discussion of various substantial points.
The paper contains high quality theoretical work and I recommend
publication in SciPost Physics. I summarize three main points and
several minor points below and leave it to the authors to address
these in order to potentially improve their paper further.
1) A bit more detail around the Lindblad equation (26) and solution
(27) would help readability. I guess many readers who have been
familiar with the material presented so far will struggle at this
point. I would hope that giving a little more background and
explanations could help (without having to turn this section into a
full-blown tutorial of dissipative quantum dynamics).
2) Could the gradient terms (Sec.5) not also feature new,
3) Would one need additional order parameters in order to describe
Minor points are the following.
p.7 "The equations (4) and (5) still apply to a non-equilibrium
scenario." Concerning (5), I guess this applies only to the first
equality. Maybe specify.
p.7 I guess "fully-connected" refers to the sums in (14) running over
all pairs, not just next neighbours. Maybe spell this out to avoid
Beginning of Sec.4.1. Define variable omega. A bit of description of
the concept of the hybridization functions would help
Typos: class of of, an homogeneous, can indeed defined.