Statistics of the maximal distance and momentum in a trapped Fermi gas at low temperature
Language
en
Article de revue
This item was published in
Journal of Statistical Mechanics: Theory and Experiment. 2017-06-07, vol. 2017, n° 6, p. 063301 (1-39)
IOP Publishing
English 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. ...Read more >
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.Read less <
English Keywords
Extreme value statistics
Quantum gases
Random matrix theory and extensions
Origin
Hal imported