Krylov complexity and chaos in quantum mechanics

• URL: http://arxiv.org/abs/2305.16669v2
• Date: Fri, 19 Jan 2024 06:38:53 GMT
• Title: Krylov complexity and chaos in quantum mechanics
• Authors: Koji Hashimoto, Keiju Murata, Norihiro Tanahashi, Ryota Watanabe
• Abstract summary: We numerically evaluate Krylov complexity for operators and states. We find a clear correlation between variances of Lanczos coefficients and classical Lyapunov exponents. Our work provides a firm bridge between Krylov complexity and classical/quantum chaos.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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