SciPost Submission Page
Bypassing eigenstate thermalization with experimentally accessible quantum dynamics
by Amit Vikram
Submission summary
| Authors (as registered SciPost users): | Amit Vikram |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202509_00047v1 (pdf) |
| Date submitted: | Sept. 26, 2025, 4:37 a.m. |
| Submitted by: | Amit Vikram |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Eigenstate thermalization has played a prominent role as a determiner of the validity of quantum statistical mechanics since von Neumann's early works on quantum ergodicity. However, its connection to the dynamical process of quantum thermalization relies sensitively on nondegeneracy properties of the energy spectrum, as well as detailed features of individual eigenstates that are effective only over correspondingly large timescales, rendering it generically inaccessible given practical timescales and finite experimental resources. Here, we introduce the notion of energy-band thermalization to address these limitations, by coarse-graining over energy level spacings with a finite energy resolution. We show that energy-band thermalization implies the thermalization of an observable in almost all states (in any orthonormal basis) over accessible timescales without relying on microscopic properties of the energy eigenvalues or eigenstates, and conversely, can be efficiently accessed in experiments via the dynamics of a single mixed state (for a given observable) with only polynomially many resources in the system size. This allows us to directly determine thermalization, including in the presence of conserved charges, from this state: Most strikingly, if an observable thermalizes in this initial state over a finite range of times, then it must thermalize in almost all physical initial states over all longer timescales. As applications, we derive a finite-time Mazur-Suzuki inequality for quantum transport with approximately conserved charges, and establish the thermalization of local observables over finite timescales in almost all accessible states in (generally inhomogeneous) dual-unitary quantum circuits. We also propose measurement protocols for general many-qubit systems. This work initiates a rigorous treatment of quantum thermalization in terms of experimentally accessible quantities.
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Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2025-12-25 (Invited Report)
The referee discloses that the following generative AI tools have been used in the preparation of this report:
I use chat GPT for correcting typo for the reports. I stress that I do not use AI for giving technical contents.
Strengths
1)
In particular, the notion of energy-band thermalization discussed in Section~5 provides a nice resolution to subtleties that many papers typically dismiss by assumption for simplicity.
2)
The discussion in Section~6 offers a robust clarification of finite-time thermalization. To my knowledge, this point has not been discussed clearly in the existing literature.
3)
I have checked the derivations of the inequalities, and they appear to be mathematically correct.
Weaknesses
1)
Although the authors aim to address realistic situations, they do not discuss cases involving multiple observables that may not commute with each other.
2)
In several places, the authors refer to a ``physical basis.'' However, the meaning of this term is unclear to me. In realistic situations, and even from a theoretical perspective, one generally considers superpositions of such bases.
Report
Requested changes
I add the pdf file which including comments and request for revision.
Recommendation
Publish (meets expectations and criteria for this Journal)