SciPost Submission Page
Defining classical and quantum chaos through adiabatic transformations
by Cedric Lim, Kirill Matirko, Hyeongjin Kim, Anatoli Polkovnikov, Michael O. Flynn
Submission summary
| Authors (as registered SciPost users): | Michael Flynn |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202412_00029v1 (pdf) |
| Date submitted: | 2024-12-17 09:45 |
| Submitted by: | Flynn, Michael |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textit{adiabatic transformations}. The complexity of adiabatic transformations which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations serves as a measure of chaos. This complexity is quantified by the (properly regularized) fidelity susceptibility. Physically this measure quantifies long time instabilities of physical observables due to small changes in the Hamiltonian of the system. Our exposition clearly showcases the common structures underlying quantum and classical chaos and allows us to distinguish integrable, chaotic but non-thermalizing, and ergodic/mixing regimes. We apply the fidelity susceptibility to a model of two coupled spins and demonstrate that it successfully predicts the universal onset of chaos, both for finite spin $S$ and in the classical limit $S\to\infty$. Interestingly, we find that finite $S$ effects are anomalously large close to integrability.
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Author comments upon resubmission
List of changes
First, we note that changes to the manuscript in this version are written in blue text for the referee's convenience.
-Significantly expanded conceptual/pedagogical discussions of the introduction, see in particular Fig. 2 and surrounding discussion.
-Expanded the content and discussion of physics near integrability, see Fig. 12.
-Added a new section (6.3) which explains how phase space averages can be broken down into trajectories over regular or chaotic regions.