RT Journal Article
T1 Spectral statistics in noninteracting many-particle systems
A1 Relaño Pérez, Armando
A1 Muñoz Muñoz, Laura
A1 Faleiro, E.
A1 Molina, R. A.
A1 Retamosa Granado, Joaquín
AB 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.
PB American Physical Society
SN 1539-3755
YR 2006
FD 2006-03
LK https://hdl.handle.net/20.500.14352/51278
UL https://hdl.handle.net/20.500.14352/51278
LA eng
NO Muñoz L, Faleiro E, Molina R A, Relaño A and Retamosa J 2006 Spectral statistics in noninteracting many-particle systems Phys. Rev. E 73 036202
NO © 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.
NO Gobierno de España
DS Docta Complutense
RD 6 abr 2025