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Spectral statistics in noninteracting many-particle systems

AuthorsMuñoz, L.; Faleiro, E.; Molina, Rafael A. CSIC ORCID; Relaño, Armando; Retamosa, Joaquín
Keywords[PACS] Quantum chaos; semiclassical methods
[PACS] Numerical simulations of chaotic systems
[PACS] Statistical theory and fluctuations
Issue Date2-Mar-2006
PublisherAmerican Physical Society
CitationPhysical Review E 73(3): 036202 (2006)
AbstractIt is widely accepted that the statistical properties of energy level spectra provide an essential characterization of quantum chaos. Indeed, the spectral fluctuations of many different systems like quantum billiards, atoms, or atomic nuclei have been studied. However, noninteracting many-body systems have received little attention, since it is assumed that they must exhibit Poisson-like fluctuations. Apart from a heuristic argument of Bloch, there are neither systematic numerical calculations nor a rigorous derivation of this fact. Here we present a rigorous study of the spectral fluctuations of noninteracting identical particles moving freely in a mean field emphasizing the evolution with the number of particles N as well as with the energy. Our results are conclusive. For N2 the spectra of these systems exhibit Poisson fluctuations provided that we consider sufficiently high excitation energies. Nevertheless, when the mean field is chaotic there exists a critical energy scale Lc; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.
Description14 pages, 3 tables, 13 figures.--PACS nrs.:05.45.Mt; 05.45.Pq; 24.60.-k
Publisher version (URL)http://link.aps.org/doi/10.1103/PhysRevE.73.036202
Appears in Collections:(CFMAC-IEM) Artículos
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