The n-level spectral correlations for chaotic systems

Abstract

We study the $n$-level spectral correlation functions of classically chaotic quantum systems without time-reversal symmetry. According to Bohigas, Giannoni and Schmit's universality conjecture, it is expected that the correlation functions are in agreement with the prediction of the Circular Unitary Ensemble (CUE) of random matrices. A semiclassical resummation formalism allows us to express the correlation functions as sums over pseudo-orbits. Using an extended version of the diagonal approximation on the pseudo-orbit sums, we derive the $n$-level correlation functions identical to the $n\times n$ determinantal correlation functions of the CUE.

20 pages, no figure, minor corrections made

References in corpus (6)

• Semiclassical Foundation of Universality in Quantum Chaos
• Periodic-Orbit Theory of Universality in Quantum Chaos
• Periodic-Orbit Theory of Level Correlations
• An exact formula for general spectral correlation function of random Hermitian matrices
• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
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Cited by in corpus (5)

• Periodic-orbit theory of universal level correlations in quantum chaos
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• Semiclassical calculation of spectral correlation functions of chaotic systems
• New approach to periodic orbit theory of spectral correlations
• Full perturbative calculation of spectral correlation functions for chaotic systems in the unitary symmetry class