Power spectrum and form factor in random diagonal matrices and integrable billiards

Triggered by a controversy surrounding universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on model random diagonal matrices (RDM), often associated with Poisson spectral universality class, and examine how form factor get affected two-sided truncations RDM spectra. Having developed nonperturbative description both statistics, perform their detailed asymptotic analysis to demonstrate explicitly traditional assumption (lying at heart controversy) – that is merely determined breaks down for truncated This observation has important consequences as further argue bounded integrable dynamics are described heavily rather than complete High-precision numerical simulations semicircular irrational rectangular billiards lend independent support these conclusions.