SciPost Submission Page

Bistabilities and domain walls in weakly open quantum systems

by Florian Lange, Achim Rosch

Submission summary

As Contributors: Florian Lange · Achim Rosch
Arxiv Link: (pdf)
Date accepted: 2020-10-06
Date submitted: 2020-09-15 11:43
Submitted by: Rosch, Achim
Submitted to: SciPost Physics
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approaches: Theoretical, Computational, Phenomenological


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.

Published as SciPost Phys. 9, 057 (2020)

Author comments upon resubmission

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.

Reports on this Submission

Anonymous Report 3 on 2020-10-5 Invited Report


I thank the authors to reply to all points and to carefully address them. I recommend publication of the manuscript in the present form.

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

Anonymous Report 2 on 2020-9-18 Invited Report

  • Cite as: Anonymous, Report on arXiv:2007.08182v3, delivered 2020-09-18, doi: 10.21468/SciPost.Report.2008


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

Anonymous Report 1 on 2020-9-18 Invited 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: -

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