{ "id": "1612.03954", "version": "v1", "published": "2016-12-12T22:28:56.000Z", "updated": "2016-12-12T22:28:56.000Z", "title": "Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature", "authors": [ "David S. Dean", "Pierre Le Doussal", "Satya N. Majumdar", "Gregory Schehr" ], "comment": "28 pages, 4 figures", "categories": [ "cond-mat.stat-mech", "cond-mat.quant-gas", "math-ph", "math.MP", "math.PR" ], "abstract": "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.", "revisions": [ { "version": "v1", "updated": "2016-12-12T22:28:56.000Z" } ], "analyses": { "keywords": [ "trapped fermi gas", "low temperature", "maximal distance", "harmonic trap", "obey similar gumbel statistics" ], "note": { "typesetting": "TeX", "pages": 28, "language": "en", "license": "arXiv", "status": "editable" } } }