Periodic-orbit theory of universal level correlations in quantum chaos

Abstract

Using Gutzwiller's semiclassical periodic-orbit theory we demonstrate universal behaviour of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random-matrix theory.

44 pages, 11 figures, changed title; final version published in New J. Phys. + additional appendices B-F not included in the journal version

References in corpus (10)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• Semiclassical Theory of Chaotic Conductors
• Semiclassical Approach to Chaotic Quantum Transport
• Resummation and the semiclassical theory of spectral statistics
• Full counting statistics of chaotic cavities from classical action correlations
• Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems
• Classical basis for quantum spectral fluctuations in hyperbolic systems
• Field Theory Approach to Quantum Interference in Chaotic Systems