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Quantum chaos and the arrow of time
by Nilakash Sorokhaibam
Submission summary
| Authors (as registered SciPost users): | Nilakash Sorokhaibam |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2212.03914v9 (pdf) |
| Date submitted: | 2024-04-16 05:53 |
| Submitted by: | Sorokhaibam, Nilakash |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Classical physics possesses an arrow of time in the form of the second law of thermodynamics. But a clear picture of the quantum origin of the arrow of time has been lacking so far. In this letter, we show that an arrow of time arises naturally in quantum chaotic systems. We show that, for an isolated quantum system which is also chaotic, the change in entropy is non-negative when the system is perturbed. At leading order in perturbation theory, this result follows from Berry's conjecture and eigenstate thermalization hypothesis (ETH). We show that this gives rise to a new profound constraint on the off-diagonal terms in the ETH statement. In case of an integrable system, the second law does not hold true because the system does not thermalize to a generalized Gibbs ensemble after a finite perturbation.
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This manuscript presents a fresh idea, as original as it is nontrivial. In short, it suggests that ETH constrains the matrix elements of relevant observables more than it was originally conjectured, if one requires that these matrix elements support the second law of thermodynamics.
More precisely, the manuscript suggests adding a requirement that off-diagonal large energy difference matrix elements of an observable compliant with the second law increase monotonically with entropy.
Numerical tests summoned to support of the above assertion produce convincing results.
Several suggestion for improvement.
1. I would refrain from publishing an assertion that "The main idea of ETH comes from Berry’s conjecture." At the time, there were several interrelated currents of thought, with no obvious causal relationship between them. When lecturing on the subject, I, usually, use Feingold-Perez paper as a logical precursor of the ETH, but I never mean that Mark Srednicki should have cited them or, even, that he knew about the existence of this paper.
2. It would make sense if the authors cite Feingold-Perez paper [M. Feingold and A. Peres, Distribution of matrix elements of chaotic systems, Phys. Rev. A 34 (1986), 591] .
3. Authors assert several times that for ETH to be valid, the observables must be "non-fermionic." I don't think this is correct. True, the classical limit is difficult in the fermionic case, but ETH doesn't require an existence of a classical limit . The formula (1) does, but ETH is bigger than that. It can be reformulated in terms of a loss of memory of the initial conditions = "eigenstates of the same energy all look the same".
4. Authors should say more about the width $W$. Indeed, it is observable-dependent and hence hard to define. But it will suffice to say that $W$ is comparable with the HWHM of f(\omega).
5. I don't think that the function $f$ is "of the order of one, " if anything, that would be impossible on dimensional grounds (all the terms in (1) should be measured in the same units as $O$; but both the "density of states" exponent and the random variable $R$ are dimensionless.) For the observables I am familiar with, $f$ is of the order of $O$.
6. Conclusion section would benefit from repeating the main assertion of the manuscript explicitly.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)