# Bistabilities and domain walls in weakly open quantum systems

### Submission summary

 As Contributors: Florian Lange · Achim Rosch Arxiv Link: https://arxiv.org/abs/2007.08182v3 (pdf) Date submitted: 2020-09-15 11:43 Submitted by: Rosch, Achim Submitted to: SciPost Physics Discipline: Physics Subject area: Quantum Physics Approaches: Theoretical, Computational, Phenomenological

### Abstract

Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.

###### Current status:
Editor-in-charge assigned

Please find attached our resubmission to SciPost Physics.

### List of changes

In reply to the referees, we made a number of changes. The most important ones are the following:

1) p.8, a new paragraph "Formally, ...." has been added providing a formal justification why the simplified hydrodynamic equations
will reproduced the qualitative features of the full hydrodynamic approach
2) p.11, a new paragraph "While we..." in the conclusion also emphasized that the results apply to a large class of problems
3) p. 10, below Eq. (18), we improved the fitting procedure and added error bars to the results. The new appendix A.3 and Fig. 6 shows a similar analysis of the data obtained by omitting non-thermal noise.
4) Introductory sentence on p. 1 has been reformulated. Similarly, statements on dark states and on the 2nd law of thermodynamics on p . 2 and 8 have been reformulated.
5) Ref. [26] and [27] have been added
6) minor changes to Fig. 2 and Fig. 3 (data is not modified)
7) p. 7, a new header "Simplified hydrodynamic model: order parameter theory" has been used to structure the paper in a better way.

### Submission & Refereeing History

Resubmission 2007.08182v3 on 15 September 2020
Submission 2007.08182v1 on 17 July 2020

## Reports on this Submission

### Report

The revised version of the manuscript has improved significantly. In particular, all concrete issues from my first report have been addressed.

I would furthermore like to thank the authors for the clarifications not only via their revisions, but also their replies. Thanks to them, I recommend publication of the manuscript in its present form.

### Requested changes

Pay attention to placement of figures (in particular Figs. 1 and 3) during production.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Report

The authors addressed all comments and concerns in a reasonable manner. Thus I recommend publication of the paper as it is.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -