Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
| hal.structure.identifier | Laboratoire Ondes et Matière d'Aquitaine [LOMA] | |
| dc.contributor.author | DEAN, David S. | |
| hal.structure.identifier | Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] [LPTENS] | |
| dc.contributor.author | LE DOUSSAL, Pierre | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | MAJUMDAR, Satya. N. | |
| hal.structure.identifier | Laboratoire de Physique Théorique et Modèles Statistiques [LPTMS] | |
| dc.contributor.author | SCHEHR, Gregory | |
| dc.date.created | 2016-12-12 | |
| dc.date.issued | 2017-06-07 | |
| dc.identifier.issn | 1742-5468 | |
| dc.description.abstractEn | We consider N non-interacting fermions in an isotropic d-dimensional harmonic trap. We compute analytically the cumulative distribution of the maximal radial distance of the fermions from the trap center at zero temperature. While in d = 1 the limiting distribution (in the large N limit), properly centered and scaled, converges to the squared Tracy–Widom distribution of the Gaussian unitary ensemble in random matrix theory, we show that for all d > 1, the limiting distribution converges to the Gumbel law.These limiting forms turn out to be universal, i.e. independent of the details of the trapping potential for a large class of isotropic trapping potentials. We also study the position of the right-most fermion in a given direction in d dimensions and, in the case of a harmonic trap, the maximum momentum, and show that they obey similar Gumbel statistics. Finally, we generalize these results to low but finite temperature. | |
| dc.language.iso | en | |
| dc.publisher | IOP Publishing | |
| dc.rights.uri | http://creativecommons.org/licenses/by-sa/ | |
| dc.subject.en | Extreme value statistics | |
| dc.subject.en | Quantum gases | |
| dc.subject.en | Random matrix theory and extensions | |
| dc.title.en | Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1088/1742-5468/aa6dda | |
| dc.subject.hal | Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech] | |
| dc.subject.hal | Physique [physics]/Matière Condensée [cond-mat]/Gaz Quantiques [cond-mat.quant-gas] | |
| dc.subject.hal | Physique [physics]/Physique mathématique [math-ph] | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1612.03954 | |
| bordeaux.journal | Journal of Statistical Mechanics: Theory and Experiment | |
| bordeaux.page | 063301 (1-39) | |
| bordeaux.volume | 2017 | |
| bordeaux.issue | 6 | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01558139 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01558139v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Statistical%20Mechanics:%20Theory%20and%20Experiment&rft.date=2017-06-07&rft.volume=2017&rft.issue=6&rft.spage=063301%20(1-39)&rft.epage=063301%20(1-39)&rft.eissn=1742-5468&rft.issn=1742-5468&rft.au=DEAN,%20David%20S.&LE%20DOUSSAL,%20Pierre&MAJUMDAR,%20Satya.%20N.&SCHEHR,%20Gregory&rft.genre=article |
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