Adiabatic sound velocity and compressibility of a trapped d-dimensional ideal anyon gas

TL;DR

This paper calculates the adiabatic sound velocity and compressibility of trapped ideal anyon gases in various dimensions using Haldane fractional exclusion statistics, comparing results with experimental data on unitary fermions.

Contribution

It introduces a method to compute sound velocity and compressibility for anyons in arbitrary dimensions, including specific trap geometries, and relates findings to experimental results.

Findings

Sound velocity for anyons in cigar-shaped traps matches experimental data with g=0.287.

Derived sound velocity for disk-shaped traps is approximately 0.406 times the Fermi velocity.

Low-temperature and high-temperature behaviors are analyzed in detail.

Abstract

The adiabatic sound velocity and compressibility for harmonically trapped ideal anyons in arbitrary dimensions are calculated within Haldane fractional exclusion statistics. The corresponding low-temperature and high-temperature behaviors are studied in detail. To compare with the experimental result of unitary fermions, the sound velocity for anyons in the cigar-shaped trap is derived. The sound velocity for anyons in the disk-shaped trap is also calculated. With the parameter g=0.287, the sound velocity of unitary fermions in the cigar-shaped trap modeled by anyons is in good agreement with the experimental result, while that of unitary fermions in the disk-shaped trap is v_{0}/v_{F}=0.406 with Fermi velocity v_{F}.