Spectral statistics in noninteracting many-particle systems



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Relaño Pérez, Armando and Muñoz, L. and Faleiro, E. and Molina, R. A. and Retamosa Granado, Joaquín (2006) Spectral statistics in noninteracting many-particle systems. Physical Review E, 73 (3). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.73.036202


It 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 N >= 2 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 L-c; beyond this scale, the fluctuations deviate from the Poisson statistics as a reminiscence of the statistical properties of the mean field.

Item Type:Article
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© 2006 The American Physical Society. We are particularly indebted to P. A. Mello for enlightening discussions. We also thank K. Wood for his help with this manuscript. This work is supported in part by Spanish Government Grants No. BFM2003-04147 and No. FTN2003-08337-C04-04.

Uncontrolled Keywords:Quantum Integrability, Level Spacings, Fluctuations, Ensembles
Subjects:Sciences > Physics > Thermodynamics
ID Code:27718
Deposited On:17 Dec 2014 13:13
Last Modified:17 Dec 2014 13:13

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