Moments of the ground state density for the d-dimensional Fermi gas in an harmonic trap

DOI10.1142/S2010326321500180zbMath1483.81172arXiv1909.09918OpenAlexW3005861758MaRDI QIDQ3385476

Peter J. Forrester

Publication date: 18 December 2021

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.09918

zbMATH Keywords

momentsHarer-Zagier recursion\(d\)-dimensional Fermi gas

Mathematics Subject Classification ID

Random matrices (algebraic aspects) (15B52) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Statistical mechanics of gases (82D05) Applications of computability and recursion theory (03D80) Statistical thermodynamics (82B30) Fermionic systems in quantum theory (81V74)

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Cites Work

• Unnamed Item
• A recursion formula for the moments of the Gaussian orthogonal ensemble
• Random matrices with complex Gaussian entries
• Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. {T}he continuous case
• The Euler characteristic of the moduli space of curves
• Planar diagrams
• Moments of random matrices and hypergeometric orthogonal polynomials
• Raney distributions and random matrix theory
• The rate of convergence for spectra of GUE and LUE matrix ensembles
• Moments of the transmission eigenvalues, proper delay times, and random matrix theory. I
• ASYMPTOTIC EXPANSIONS FOR THE GAUSSIAN UNITARY ENSEMBLE
• Wigner distribution function for a harmonically trapped gas of ideal fermions and bosons at arbitrary temperature and dimensionality
• Moments of the Gaussian β ensembles and the large-N expansion of the densities
• Simple analytical results for harmonically trapped quantum gases
• Harmonically trapped fermion gases: exact and asymptotic results in arbitrary dimensions
• Linear differential equations for the resolvents of the classical matrix ensembles
• On the density profile in Fourier space of harmonically confined ideal quantum gases inddimensions