New approach to periodic orbit theory of spectral correlations

Periodic-orbit theory of level correlations.

We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmit conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the nonoscillatory and the oscillatory part of the universal spectral correlator ...

Periodic Orbit Theory and Spectral Statistics for Quantum Graphs

Periodic orbit theory and spectral statistics for scaling quantum graphs

The explicit solution to the spectral problem of quantum graphs found recently in [20], is used to produce the exact periodic orbit theory description for the probability distributions of spectral statistics, including the distribution for the nearest neighbor separations, s n = k n − k n−1 , and the distribution of the spectral oscillations around the average, δk n = k n − ¯ k n .

Periodic Orbit Theory

New Approach to Inverse Spectral Theory