E(k,L) level statistics of classically integrable quantum systems based on the Berry-Robnik approach

Abstract

Theory of the quantal level statistics of classically integrable system, developed by Makino et al. in order to investigate the non-Poissonian behaviors of level-spacing distribution (LSD) and level-number variance (LNV)\cite{MT03,MMT09}, is successfully extended to the study of $E(K,L)$ function which constitutes a fundamental measure to determine most statistical observables of quantal levels in addition to LSD and LNV. In the theory of Makino et al., the eigenenergy level is regarded as a superposition of infinitely many components whose formation is supported by the Berry-Robnik approach in the far semiclassical limit\cite{Robn1998}. We derive the limiting $E(K,L)$ function in the limit of infinitely many components and elucidates its properties when energy levels show deviations from the Poisson statistics.

Published July 2014 in PTEP: https://academic.oup.com/ptep/article/2014/7/073A01/1562895. arXiv admin note: text overlap with arXiv:0902.1282

References in corpus (1)

• Statistical properties of spectral fluctuations for a quantum system with infinitely many components

Cited by in corpus (1)

• Quantum Mechanical Approach to Bifurcation Point Detection in Hamiltonian Dynamical Systems