Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling

Tara Kalsi; Alessandro Romito; Henning Schomerus

doi:10.22331/q-2025-02-26-1651

Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling

Tara Kalsi, Alessandro Romito, and Henning Schomerus

Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom

Published:	2025-02-26, volume 9, page 1651
Editor:	Michele Campisi
Eprint:	arXiv:2310.11355v3
Doi:	https://doi.org/10.22331/q-2025-02-26-1651
Citation:	Quantum 9, 1651 (2025).

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Abstract

A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that the scaling predictions are matched by a privileged stochastic process and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all time scales.

Featured image: Interpretation of the spectral scaling parameter $a$ as the center of mass (red) of the eigenvalue distribution (blue).

Popular summary

Complex quantum systems evolve into states that mimic thermodynamic equilibrium, in which the state of the system is completely random.
This paper studies the approach to these equilibrium conditions. It identifies a variable that systematically changes as the equilibrium is approached, and expresses other system properties in terms of it.
This reveals a rigorous structure behind the flow towards the random state, in which different stages show similar behaviour if studied on an appropriate scale.

► BibTeX data

@article{Kalsi2025spectralchaosbounds,
  doi = {10.22331/q-2025-02-26-1651},
  url = {https://doi.org/10.22331/q-2025-02-26-1651},
  title = {Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling},
  author = {Kalsi, Tara and Romito, Alessandro and Schomerus, Henning},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1651},
  month = feb,
  year = {2025}
}

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[2] Sophia N. Fricke, Haiyan Mao, Manas Sajjan, Jeremy Demarteau, Brett A. Helms, Ashok Ajoy, Velencia Witherspoon, Sabre Kais, and Jeffrey A. Reimer, "Out-of-time-order correlators bridge classical transport and quantum dynamics", The Journal of Chemical Physics 164 13, 134201 (2026).

[3] Tara Kalsi, Alessandro Romito, and Henning Schomerus, "Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos", arXiv:2410.15872, (2024).

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