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 are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.
|Translated title of the contribution||Periodic-orbit theory of level correlations|
|Article number||Article no. 044103|
|Pages (from-to)||1 - 4|
|Number of pages||4|
|Journal||Physical Review Letters|
|Publication status||Published - Jan 2007|