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Landau Theory for Non-Equilibrium Steady States

by Camille Aron, Claudio Chamon

Submission summary

As Contributors: Camille Aron
Arxiv Link: https://arxiv.org/abs/1910.04777v1
Date submitted: 2019-10-18
Submitted by: Aron, Camille
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Statistical and Soft Matter Physics
Approach: Theoretical

Abstract

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.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

Submission 1910.04777v1 on 18 October 2019

Reports on this Submission

Anonymous Report 1 on 2019-10-29 Invited Report

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,
non-analytical contributions?

3) Would one need additional order parameters in order to describe
time-dependent nonequilibrium?

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
any uncertainty.

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.

  • validity: top
  • significance: top
  • originality: top
  • clarity: top
  • formatting: perfect
  • grammar: perfect

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