4.4 Article

Hole probability for noninteracting fermions in a d-dimensional trap

期刊

EPL
卷 137, 期 5, 页码 -

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IOP Publishing Ltd
DOI: 10.1209/0295-5075/ac4aca

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  1. ANR [ANR-17-CE30-0027-01 RaMaTraF]

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The study focuses on the hole probability of N noninteracting fermions, obtaining a universal scaling function and a super-exponential tail for the probability P(R) of a sphere region. The results are in good agreement with existing numerical simulations. At the order of the radius of the Fermi gas, the hole probability is described by a large deviation form.
The hole probability, i.e., the probability that a region is void of particles, is a benchmark of correlations in many body systems. We compute analytically this probability P(R) for a sphere of radius R in the case of N noninteracting fermions in their ground state in a d-dimensional trapping potential. Using a connection to the Laguerre-Wishart ensembles of random matrices, we show that, for large N and in the bulk of the Fermi gas, P(R) is described by a universal scaling function of k(F)R, for which we obtain an exact formula (k(F) being the local Fermi wave vector). It exhibits a super-exponential tail P(R) proportional to e(-kappa d(kFR)d+1) where kappa(d) is a universal amplitude, in good agreement with existing numerical simulations. When R is of the order of the radius of the Fermi gas, the hole probability is described by a large deviation form which is not universal and which we compute exactly for the harmonic potential. Similar results also hold in momentum space. Copyright (C) 2022 EPLA

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