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Defining classical and quantum chaos through adiabatic transformations
by Cedric Lim, Kirill Matirko, Anatoli Polkovnikov, Michael O. Flynn
Submission summary
| Authors (as registered SciPost users): | Michael Flynn |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2401.01927v1 (pdf) |
| Date submitted: | 2024-01-19 21:08 |
| 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 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. Our exposition clearly showcases the common structures underlying quantum and classical chaos and allows us to distinguish integrable, chaotic but non-thermalizing, and ergodic 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.
Current status:
Reports on this Submission
Strengths
1. The manuscript tackles an important and timely topic in theoretical physics, providing a unified approach to understanding chaos in both classical and quantum domains.
2. The use of fidelity susceptibility as a measure of chaos is innovative and offers new insights into distinguishing between integrable, chaotic but non-thermalizing, and ergodic regimes.
3. The paper is well-organized, and the arguments are generally clear and supported by thorough theoretical and numerical analysis.
Weaknesses
1. While the manuscript provides a comprehensive overview of the fidelity susceptibility and its relation to chaos, the connection between this measure and traditional notions of chaos (e.g., Lyapunov exponents) needs further elaboration. A more detailed discussion on how the proposed formalism aligns or diverges from classical chaos indicators would be beneficial.
2. The manuscript mentions the slow convergence of quantum spectral functions to their classical counterparts near integrability. To highlight this convergence behavior explicitly, it would be useful to include more quantitative comparisons between quantum and classical results, possibly through additional figures or detailed discussions. Perhaps more details on the numerical methods should be provided, especially for the exact diagonalization and the treatment of finite-size effects.
3. Identifying and characterizing the intermediate regime between integrable and ergodic behavior is intriguing. Additional examples or case studies illustrating the intermediate regime would enhance the reader's understanding.
Report
The manuscript addresses a significant and complex topic with a novel approach that has the potential to advance our understanding of chaos in classical and quantum systems. Given that the authors address the points raised in this report, I would recommend the manuscript for publication in SciPost Physics.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)