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Phase transitions of wave packet dynamics in disordered non-Hermitian systems

by Helene Spring, Viktor Könye, Fabian A. Gerritsma, Ion Cosma Fulga, Anton R. Akhmerov

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Submission summary

Authors (as registered SciPost users): Anton Akhmerov · Ion Cosma Fulga · Viktor Könye · Helene Spring
Submission information
Preprint Link:  (pdf)
Code repository:
Data repository:
Date accepted: 2024-04-08
Date submitted: 2024-02-26 13:17
Submitted by: Spring, Helene
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition is close to $1/2$ in propagating-propagating transitions.

List of changes

Listed in full in the replies to referees of the first submission.

Published as SciPost Phys. 16, 120 (2024)

Reports on this Submission

Anonymous Report 3 on 2024-3-23 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2301.07370v2, delivered 2024-03-22, doi: 10.21468/SciPost.Report.8751


The topics in this paper are interesting both from non-Hermitian physics and localization physics points of view.


The authors answered most of the questions/comments in my previous report, and the paper has improved with revisions. I have one additional comment. Recently, the mapping of non-hermitian localization transition to Hermitian one is shown [Luo et al., Physical Review Research 4, L022035 (2022)], where nu in non-hermitian localization-delocalization transition is explained by one of the 10 Hermitian symmetry classes. I would like to know which of the Hermitian symmetry classes the result nu=1/2 in this paper corresponds to. But this is an optional comment, and I don't block publication even if the authors do not answer this question.

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

Anonymous Report 2 on 2024-3-21 (Invited Report)


1. Details an interesting type of localization transition enabled by non-Hermitian systems with point gap winding.


Given that the authors have narrowed their claims to non-Hermitian systems with point-gap winding, I have no more quibbles worth noting. This is an interesting result that ties localization physics to point-gap winding (a topic of recent interest), so it is certainly worth publishing.

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

Anonymous Report 1 on 2024-2-27 (Invited Report)


I have read through the authors’ reply and revised manuscript. Unfortunately, I find the authors’ rebuttal handwaving and unsatisfactory. Thus, I do not recommend publication of this manuscript in SciPost Physics.

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

Author:  Anton Akhmerov  on 2024-02-28  [id 4331]

(in reply to Report 1 on 2024-02-27)

Dear referee,

Can you please be more specific regarding which of our findings or claims you find insufficiently supported or explained in the resubmitted version?

Thank you in advance.

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