Spectral statistics in noninteracting many-particle systems
| dc.contributor.author | Relaño Pérez, Armando | |
| dc.contributor.author | Muñoz Muñoz, Laura | |
| dc.contributor.author | Faleiro, E. | |
| dc.contributor.author | Molina, R. A. | |
| dc.contributor.author | Retamosa Granado, Joaquín | |
| dc.date.accessioned | 2023-06-20T10:49:05Z | |
| dc.date.available | 2023-06-20T10:49:05Z | |
| dc.date.issued | 2006-03 | |
| dc.description | © 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. | |
| dc.description.abstract | 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. | eng |
| dc.description.department | Depto. de Estructura de la Materia, Física Térmica y Electrónica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Gobierno de España | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/27718 | |
| dc.identifier.citation | 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 | |
| dc.identifier.doi | 10.1103/PhysRevE.73.036202 | |
| dc.identifier.issn | 1539-3755 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevE.73.036202 | |
| dc.identifier.relatedurl | http://journals.aps.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51278 | |
| dc.issue.number | 3 | |
| dc.journal.title | Physical Review E | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 536 | |
| dc.subject.keyword | Quantum Integrability | |
| dc.subject.keyword | Level Spacings | |
| dc.subject.keyword | Fluctuations | |
| dc.subject.keyword | Ensembles | |
| dc.subject.ucm | Termodinámica | |
| dc.subject.unesco | 2213 Termodinámica | |
| dc.title | Spectral statistics in noninteracting many-particle systems | |
| dc.type | journal article | |
| dc.volume.number | 73 | |
| dcterms.references | [1] H.-J. Stöckmann, Quantum Chaos (Cambridge University Press, Cambridge, UK, 1999). [2] M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 (1977). [3] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984). [4] G. Casati, F. Valz-Gris, and I. Guarneri, Lett. Nuovo Cimento Soc. Ital. Fis. 28, 279 (1980). [5] C. Bloch, in Physique Nucléaire, edited by C. DeWitt and V. Gillet (Gordon and Breach, New York, 1969), p. 303. [6] V. K. B. Kota, Phys. Rep. 347, 223 (2001). [7] H. A. Weidenmüller, Phys. Rev. A 48, 1819 (1993). [8] J. Sakhr and N. D. Whelan, Phys. Rev. E 67, 066213 (2003). [9] G. Tanner, K. Richter, and J.-M. Rost, Rev. Mod. Phys. 72, 497 (2000). [10] J. Sakhr and N. D. Whelan, Phys. Rev. A 62, 042109 (2000). [11] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981). [12] M. Srednicki, Phys. Rev. E 66, 046138 (2002). [13] L. Benet, T. Rupp, and H. A. Weidenmüller, Ann. Phys. (N.Y.) 292, 67 (2001). [14] J. B. French and S. S. M. Wong, Phys. Lett. 33B, 449 (1970). [16] St. Weigert, Physica D 56, 107 (1992). [17] S. Weigert and G. Muller, Chaos, Solitons, and Fractals 5, 1419 (1995). [18] W. M. Zhang and D. H. Feng, Phys. Rep. 252, 1 (1995). [19] A. Relaño, J. Dukelsky, J. M. G. Gómez, and J. Retamosa, Phys. Rev. E 70, 026208 (2004). [20] J. R. Huzenga and L. G. Moretto, Annu. Rev. Nucl. Sci. 22, 427 (1972). [21] P. Leboeuf, A. G. Monastra, and A. Relaño, Phys. Rev. Lett. 94, 102502 (2005). [22] H. A. Bethe, Rev. Mod. Phys. 9, 69 (1937); H. A. Bethe, Phys. Rev. 50, 332 (1936). [23] T. Ericson, Nucl. Phys. 11, 481 (1959); A. G. W. Cameron, Can. J. Phys. 36, 1040 (1958). [24] Handbook of Mathematical Formulas, edited by M. Abramowitz and I. A. Stegun (Dover Publications, New York, 1972). [25] R. E. Walpole, R. H. Myers, and S. L. Myers, Probability and Statistics for Engineers and Scientists, 6th ed. (Prentice-Hall, Englewood Cliffs, NJ, 2001). [26] M. L. Mehta, Random Matrices (Academic Press, New York, 1991). [27] A. Relaño, J. M. G. Gómez, R. A. Molina, J. Retamosa, and E. Faleiro, Phys. Rev. Lett. 89, 244102 (2002). [29] J. M. G. Gómez, R. A. Molina, A. Relaño, and J. Retamosa, Phys. Rev. E 66, 036209 (2002). [30] M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984). [31] E. Faleiro, J. M. G. Gómez, R. A. Molina, L. Muñoz, A. Relaño, and J. Retamosa, Phys. Rev. Lett. 93, 244101 (2004). [32] J. M. G. Gómez, A. Relaño, J. Retamosa, E. Faleiro, M. Vranicar, and M. Robnik, Phys. Rev. Lett. 94, 084101 (2005). [33] M. S. Santhanam and J. N. Bandyopadhyay, Phys. Rev. Lett. 95, 114101 (2005). [34] J. B. French, V. K. B. Kota, A. Pandey, and S. Tomsovic, Ann. Phys. (N.Y.) 181, 198 (1988). | |
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