Semiclassical Trace Formulae and Eigenvalue Statistics in Quantum Chaos
Abstract
A detailed discussion of semiclassical trace formulae is presented and it is demonstrated how a regularized trace formula can be derived while dealing only with finite and convergent expressions. Furthermore, several applications of trace formula techniques to quantum chaos are reviewed. Then local spectral statistics, measuring correlations among finitely many eigenvalues, are reviewed and a detailed semiclassical analysis of the number variance is given. Thereafter the transition to global spectral statistics, taking correlations among infinitely many quantum energies into account, is discussed. It is emphasized that the resulting limit distributions depend on the way one passes to the global scale. A conjecture on the distribution of the fluctuations of the spectral staircase is explained in this general context and evidence supporting the conjecture is discussed.
 Publication:

arXiv eprints
 Pub Date:
 February 1997
 DOI:
 10.48550/arXiv.chaodyn/9702003
 arXiv:
 arXiv:chaodyn/9702003
 Bibcode:
 1997chao.dyn..2003B
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics
 EPrint:
 48 pages, LaTeX, uses amssymb