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Krylov complexity and chaos in quantum mechanics
- Source :
- JHEP 11 (2023) 040
- Publication Year :
- 2023
-
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.<br />Comment: 41 pages, 35 figures, 8 tables; v2: journal version, appendices added
- Subjects :
- High Energy Physics - Theory
Nonlinear Sciences - Chaotic Dynamics
Quantum Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- JHEP 11 (2023) 040
- Publication Type :
- Report
- Accession number :
- edsarx.2305.16669
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/JHEP11(2023)040