Power Spectrum of Long Eigenlevel Sequences in Quantum Chaotic Systems

Abstract

We present a nonperturbative analysis of the power spectrum of energy level fluctuations in fully chaotic quantum structures. Focusing on systems with broken time-reversal symmetry, we employ a finite-N random matrix theory to derive an exact multidimensional integral representation of the power spectrum. The N→∞ limit of the exact solution furnishes the main result of this study-a universal, parameter-free prediction for the power spectrum expressed in terms of a fifth Painlevé transcendent. Extensive numerics lends further support to our theory which, as discussed at length, invalidates a traditional assumption that the power spectrum is merely determined by the spectral form factor of a quantum system.