Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature

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.
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Dernière modification le : samedi 15 juillet 2017 - 01:08:10

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David S. Dean, Pierre Le Doussal, Satya. N. Majumdar, Gregory Schehr. Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature. Journal of Statistical Mechanics: Theory and Experiment, IOP Science, 2017, 2017 (6), pp.063301 (1-39). 〈10.1088/1742-5468/aa6dda〉. 〈hal-01558139〉

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