SciPost Submission Page
Eigenstate thermalization to non-monotonic distributions in strongly-interacting chaotic lattice gases
by Vladimir A. Yurovsky, Amichay Vardi
Submission summary
| Authors (as registered SciPost users): | Vladimir Yurovsky |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2501.08967v3 (pdf) |
| Date submitted: | Sept. 30, 2025, 12:44 p.m. |
| Submitted by: | Vladimir Yurovsky |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We find non-monotonic equilibrium energy distributions, qualitatively different from the Fermi-Dirac and Bose-Einstein forms, in strongly-interacting many-body chaotic systems. The effect emerges in systems with finite energy spectra, supporting both positive and negative temperatures, in the regime of quantum ergodicity. The results are supported by exact diagonalization calculations for chaotic Fermi-Hubbard and Bose-Hubbard models, when they have Wigner-Dyson statistics of energy spectra and demonstrate eigenstate thermalization. The proposed effects may be observed in experiments with cold atoms in optical lattices.
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
Author comments upon resubmission
We thank the referees for careful reading. The manuscript is modified according to their suggestions and comments.
List of changes
The 2nd paragraph in Sec. 4 (started from “Consider”) is extended and definitions therein are clarified, in response to referee 2.
Further discussion of the difference between the mesoscopic systems Fig. 1 and the macroscopic systems Fig. 2 has been added to Sec. 4 and the beginning of Sec. 5, in response to the question raised by referee 1.
In the end of Sec. 5 we discuss relation to superstatistics and cite the references suggested by referee 1.
In the beginning of App. C, the discussion of the level spacing ratio is extended, in response to referee 2.
Current status:
Reports on this Submission
Report
Let me add some comments to further clarify my opinion.
The authors strongly emphasize the finding of non-monotonic deviations
from the Bose-Einstein and Fermi-Dirac statistics. While they agree with me
that a deviation from the free-particle statistics is not surprising in itself for
a strongly interacting system, they stress the peculariarity of the "non-monotonicity". But what does this "non-monotonicity" means?
Which is the peculiarity of the system revealed by the non-monotonicity? What do we learn/understand from it? Which is the difference between interacting systems with "monotonous" and "non-monotonous" deviations from the free-particle statistics?
Statements such us "Our main point is that the interactions mix different microcanonical shells of the non-interacting system, so that the microcanonical occupation means over the interacting system’s energy shell do not match any of the corresponding microcanonical means over non-interacting shells" seem indeed quite trivial from a general perspective, neither particularly deep or particularly profound.
Also the final sentence
"Unlike previously observed non-monotonic occupa-
tion distributions in weakly-interacting mesoscopic systems [28], this strong-interaction effect appears due to the mixing of microcanonical shells with temperatures of opposite sign and survives in large systems. The distribution deviations may be observed experimentally with cold atoms in optical lattices."
is not very convincing about the general relevance of the results. An explanation
of the relation between the mixing of microcanonical shells with different temperatures and the presence of non-monotonic nature of deviations from free particle statistics should be at least attempted, more convincing and extended arguments presented to convince a general audience to the meaning/relevance of this finding. Last, but not least, the connection drawn in the last sentence with possible experiments is definitely too vague.
Recommendation
Accept in alternative Journal (see Report)
Strengths
The strengths of the work have been listed in my previous report. I am goingo to repeat them here below. 1. The authors present numerical investigations of quantum strongly-interacting many-body systems. By direct numerical diagonalization of the Hamiltonian they are able to show that these systems, for sufficiently strong coupling depart from their reference single-body statistical distribution (i.e., Fermi-Dirac or Bose-Einstein). 2. The authors argue that the reason for this discrepancy is due to an effect of mixing independent microcanonical distribution, in a way affine to the mechanisms theorized for the generation of superstatistical distributions [see, e.g.,, C. Beck and E.G.D. Cohen, "Superstatistics", Phys. A, 322, 267275 (2003)] or [S. Davis, "Fluctuating temperature outside superstatistics: Thermodynamics of small systems", Phys. A, 589, 126665 (2022)]. 3. On the basis of the theory argued in point (2), the authors predict the possibility of non-monotonic distributions as a function of the energy: i.e. a mixture of positive and negative temperature distribution. This prediction is novel, as far as I know.
Weaknesses
I had pointed to two weaknesses in my previous report.
- The explicit reference to the superstatistical literature, which basically predates the theory advanced in this work, is lacking.
- The interpretation of the numerical results advanced by the authors is suggestive and plausible but, at this stage, is just a speculation.
I feel that the authors have satisfactorily replied to these issues in their revised version
Report
Recommendation
Publish (meets expectations and criteria for this Journal)