SciPost Submission Page
Dynamics of a non-Hermitian Floquet Wannier-Stark system
by Hong Peng Zhang, Kun Liang Zhang and Zhi Song
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Hong Peng Zhang |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202404_00005v1 (pdf) |
| Date submitted: | 2024-04-05 09:35 |
| Submitted by: | Zhang, Hong Peng |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
We study the dynamics of the non-Hermitian Floquet Wannier-Stark system in the framework of the tight-binding approximation, where the hopping strength is a periodic function of time with Floquet frequency $\mathcal{\omega }$. It is shown that the energy level of the instantaneous Hamiltonian is still equally spaced and\ independent of time $% t $ and the Hermiticity of the hopping term. In the case of off resonance, the dynamics are still periodic, while the occupied energy levels spread out\ at the resonance, exhibiting $t^{z}$ behavior. Analytical analysis and numerical simulation show that the level-spreading dynamics for real and complex hopping strengths\ exhibit distinct behaviors and are well described by the dynamical exponents $z=1$ and $z=1/2$, respectively.
Current status:
Reports on this Submission
Strengths
Well readable manuscript.
Weaknesses
Most ideas of this work are well known already in the community. In particular, works by Andrey Kolovsky based on his review from from 2002 and later papers, are the basic reference for Wannier-Stark problems without interaction. No interactions are treated here, then the problem is (basically) analytically accessible and less interesting, in particular for separable potentials that reduce always to one dimension only. Some issues must be fixed, see my report.
Report
While the general setting is okay and the manuscript is well written, its contents lacks novelty. It is also no review-style paper since many relevant citations are missing. Most ideas of this work are well known already in the community. In particular, works by Andrey Kolovsky based on his review from from 2002 and later papers, are the basic reference for Wannier-Stark problems without interaction in one and more dimensions (being in separable or non separable Stark ladders). No interactions are treated here, then the problem is (basically) analytically accessible and less interesting, in particular for the separable potentials here studied that effectively reduce always to one dimension only. Some issues must be fixed:
1) what is a Dirac probability distribution? Mathematically speaking this is well defined and not related to its use here, see around eq. (14-15).
2) For a non hermitian Hamiltonian, the left and right eigenstates are not necessarily orthonormal. This property is used throughout here, e.g. around eq. (15). The distinction between left and right eigenvectors should be made and proper motivations and definitions be given. What are the conditions for orthonormality?
3) P(t) is not at all necessarily period for real kappa, as stated in p. 5 in comparison to the figures! Please correct such statements.
4) ref. 13 lacks two more authors, some ref.s are not complete with missing publishing company and place.
5) a discussion is missing on how complex hopping can be realised in an experimental platform. Usually, some approximations are involved which should also be discussed. What does complex hopping do in the time evolution (conservation of probability, expected differences from real hopping case, ...), all this should be anticipated to prepare the reader for the results found here. I guess most of this has been studied before and a context setting should be given with appropriate references.
Without a proper resetting of the citations and reference to the most important literature this manuscript should not be published.
Requested changes
Update of reference list, in particular add the many papers on the very topic of this submission, by Andrey Kolovsky and co-workers. Experimentally relevant papers by the Bloch and Goldman groups. See also the list 1)-5) of things to fix in the report.
Recommendation
Reject
Author: Hong Peng Zhang on 2024-05-27 [id 4514]
(in reply to Report 1 on 2024-05-16)Taking into account some formulas and for the convenience of writing, we have submitted a PDF file in the attachment to respond to the reviewer's comments and criticisms, with specific responses highlighted in blue.
Attachment:
reply1.pdf