Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
arXiv (Cornell University)(2023)
摘要
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 timescales.
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关键词
scaling,quantum-dynamical
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