## SciPost Submission Page

# 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:

### Submission & Refereeing History

## 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.