Power spectrum and form factor in random diagonal matrices and integrable billiards
arXiv:2011.02210 · doi:10.1016/j.aop.2020.168393
Abstract
Triggered by a controversy surrounding a universal behaviour of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) -- that the power spectrum is merely determined by the spectral form factor -- breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.
40 pages, 8 figures
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- Approaching Thouless Energy and Griffiths Regime in Random Spin Systems By Singular Value Decomposition
- Power spectrum of the circular unitary ensemble
- Power spectra and autocovariances of level spacings beyond the Dyson conjecture
- Long-ranged spectral correlations in eigenstate phases
- Statistics of local level spacings in single- and many-body quantum chaos