1997/02/05 by Jens Bolte, Bolte, Jens
Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum chaos and dynamical systems #Quantum optics and atomic interactions #chao-dyn #nlin.CD
paper · pdf · doi:10.48550/arxiv.chao-dyn/9702003
48 pages, LaTeX, uses amssymb
arxiv created 1997/02/05 · openalex publication_date 1997/02/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.