  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.
