SciPost Submission Page
Superdiffusive transport in quasi-particle dephasing models
by Yu-Peng Wang, Chen Fang, Jie Ren
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Jie Ren |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202406_00037v1 (pdf) |
| Date submitted: | 2024-06-17 17:08 |
| Submitted by: | Ren, Jie |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Investigating the behavior of noninteracting fermions subjected to local dephasing, we reveal that quasi-particle dephasing can induce superdiffusive transport. This superdiffusion arises from nodal points within the momentum distribution of local dephasing quasi-particles, leading to asymptotic long-lived modes. By studying the dynamics of the Wigner function, we rigorously elucidate how the dynamics of these enduring modes give rise to Levy walk processes, a renowned mechanism underlying superdiffusion phenomena. Our research demonstrates the controllability of dynamical scaling exponents by selecting quasi-particles and extends its applicability to higher dimensions, underlining the pervasive nature of superdiffusion in dephasing models.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Report
Dear Editor,
The paper by Yu-Peng Wang and collaborators discusses the transport properties of a dissipative chain of fermions in one and higher dimensions.
The paper is original, and while the techniques used are not innovative, the results are robust and quite surprising.
The explanation seems to be the choice of the Lindblad operators, with their modulated structure. Somehow, this seems similar to the study [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.102.100301], which could be useful to cite.
Regarding anomalous transport with disorder, some results were presented in [https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.184202,https://scipost.org/SciPostPhys.12.6.189] which could be included among the outlook works [60,61].
Apart from these minor comments, I suggest the paper for publication in Scipost Physics.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report
The paper discusses superdiffusive spreading of the wavefront of fermions in a non-interacting model with "dispersive" jump operators in the Lindbladian. It is a cute and interesting idea and could be published in SciPost Physics. Our comments and suggestions are below:
1) On page 5, the authors seemed to imply that a difference with KPZ universality is the presence of a propagating wavefront? That claim would be false. The KPZ class arises as the endpoint of the instability of the 1+1d Navier-Stokes equations, for example -- the hydrodynamic modes here are propagating sound waves but with superdiffusive spreading. It's likely that this system does not have KPZ universality even if z=3/2, but the presence of the wavefront is not the reason for the difference. We suggest editing the wording here and throughout the paper to ensure that the reader is not misled about this point.
2) On the use of the term "hydrodynamics" -- hydrodynamics is an emergent description of chaotic many-particle systems, and would not apply to a free fermion model. The paper seems to the phrase "hydrodynamics" in awkward ways and we suggest avoiding this terminology. The paper has an interesting model but it may not be related at all to hydrodynamic phenomena more generally, and the robustness of the phenomena described here to interactions is far from clear, and we would be surprised if the scaling exponents were robust.
3) In Eq.(13) and Appendix B, the authors write down a kind of "master equation" for d_t n(x,k). This equation seems to admit the homogeneous solution n(x,k) = constant, which we found very surprising at first. If this is actually to be expected because the Lindblad jump operators are dephasing and don't correspond to single particle loss, some clarity would be appreciated; some comments in the main text would be helpful.
4) It would be ideal if Eq. (13) could be used to derive the dynamical critical exponent, rather than relying on a heuristic probabilistic argument. This seems doable to us, especially given the previous point: the modes which do not relax to some featureless local equilibrium are probably the ones near the point k_o, so modes in n(x,k) near k_o should be largely responsible for the effect.
5) Further comments on how local the dephasing jump operators need to be would be helpful, given that there is structure in Fourier space.
Recommendation
Ask for minor revision
We thank the reviewer for their careful reading and generally positive evaluation of our manuscript. Below are our responses to the comments and suggestions:
1) We appreciate the reviewer’s insight regarding the propagation of wavefronts in KPZ universality. We recognize that the presence of a propagating wavefront is not inherently a distinction from KPZ universality. In the revised manuscript, we will clarify that the scaling function in our system differs from KPZ, and we attribute this to differing physical origins without making unsupported claims. We will ensure that the text does not mislead readers about this point. 2) We adopted the term "hydrodynamics" from literature that discusses the dynamics of the Wigner function under the framework of "generalized hydrodynamics." We agree with the reviewer that using "hydrodynamics" in our context might be inappropriate for a free fermion model. We will replace "hydrodynamics" with "Wigner function dynamics" throughout the revised manuscript to avoid any confusion. 3) We agree with the reviewer’s observation regarding the homogeneous solution. This can indeed be attributed to the fact that the original Lindbladian is unital, implying that the nonequilibrium steady state is the maximally mixed state (subject to a fixed particle number). The local particle density in this maximally mixed state should be homogeneous, and the correct coarse-grained dynamics should reflect this feature. We have added comments in the main text to clarify this point as suggested. 4) We acknowledge the reviewer’s suggestion to derive the dynamical critical exponent directly from Eq. (13). While we agree that this is a minimalistic approach, our current method using a heuristic probabilistic argument follows directly from existing literature and provides an exact simulation framework for the Wigner dynamics, which is valuable for numerical simulations. Furthermore, the random walk model, including Lévy walks, underpins the superdiffusive behavior observed. Although we currently do not have a straightforward derivation from Eq. (13), we believe the random walk picture is essential for its physical meaning and numerical utility. We will clarify this rationale in the revised manuscript. 5) The reviewer is correct that there is no apparent restriction on the locality of the quasi-particles; they can be as far apart as necessary, provided they are not global operators, which would complicate coarse-graining. We will add further comments to discuss the implications of the structure in Fourier space and the locality of the dephasing jump operators.
Author: Jie Ren on 2024-10-07 [id 4844]
(in reply to Report 4 on 2024-09-14)We thank the reviewer for careful reading and for the recomendation.
We appreciate the reviewer for bringing up the relevant references. We have now included these citations in the revised version of the paper.