Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap
Peter J Forrester
RANDOM MATRICES-THEORY AND APPLICATIONS | WORLD SCIENTIFIC PUBL CO PTE LTD | Published : 2021
We consider properties of the ground state density for the d-dimensional Fermi gas in an harmonic trap. Previous work has shown that the d-dimensional Fourier transform has a very simple functional form. It is shown that this fact can be used to deduce that the density itself satisfies a third-order linear differential equation, previously known in the literature but from other considerations. It is shown too how this implies a closed form expression for the 2kth non-negative integer moments of the density, and a second-order recurrence. Both can be extended to general Rek > -d/2. The moments, and the smoothed density, permit expansions in 1/M2, where M = M + (d + 1)/2, with M denoting the s..View full abstract
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Awarded by Australian Research Council Centre of Excellence ACEMS
yThis research is part of the program of study supported by the Australian Research Council Centre of Excellence ACEMS, and the project DP170102028. The support by D. Wang (NUS), G. Akemann (Bielefeld) and D. Dai (City University) for visits to their home institutions over the time span of the project is much appreciated, as is correspondence from K. Bencheikh, and the careful reading of a referee.