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.
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- 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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