Krylov complexity and chaos in quantum mechanics
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Publication:6142610
DOI10.1007/JHEP11(2023)040arXiv2305.16669OpenAlexW4388509892MaRDI QIDQ6142610
Author name not available (Why is that?)
Publication date: 26 January 2024
Published in: (Search for Journal in Brave)
Abstract: Recently, Krylov complexity was proposed as a measure of complexity and chaoticity of quantum systems. We consider the stadium billiard as a typical example of the quantum mechanical system obtained by quantizing a classically chaotic system, and numerically evaluate Krylov complexity for operators and states. Despite no exponential growth of the Krylov complexity, we find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents, and also a correlation with the statistical distribution of adjacent spacings of the quantum energy levels. This shows that the variances of Lanczos coefficients can be a measure of quantum chaos. The universality of the result is supported by our similar analysis of Sinai billiards. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.
Full work available at URL: https://arxiv.org/abs/2305.16669
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