Boundary Chaos: Spectral Form Factor

• URL: http://arxiv.org/abs/2312.12452v2
• Date: Fri, 13 Sep 2024 12:53:59 GMT
• Title: Boundary Chaos: Spectral Form Factor
• Authors: Felix Fritzsch, Tomaž Prosen,
• Abstract summary: Random matrix spectral correlations are a defining feature of quantum chaos. We study such correlations in a minimal model of chaotic many-body quantum dynamics. We find they coincide with random matrix theory, possibly after a non-zero Thouless time.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Random matrix spectral correlations is a defining feature of quantum chaos. Here, we study such correlations in a minimal model of chaotic many-body quantum dynamics where interactions are confined to the system's boundary, dubbed \textit{boundary chaos}, in terms of the spectral form factor and its fluctuations. We exactly calculate the latter in the limit of large local Hilbert space dimension $q$ for different classes of random boundary interactions and find it to coincide with random matrix theory, possibly after a non-zero Thouless time. The latter effect is due to a drastic enhancement of the spectral form factor, when integer time and system size fulfill a resonance condition. We compare our semiclassical (large $q$) results with numerics at small local Hilbert space dimension ($q=2,3$) and observe qualitatively similar features as in the semiclassical regime.

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