Thermodynamics of statistically interacting quantum gas in D dimensions

TL;DR

This paper provides an exact analysis of the thermodynamics of a quantum gas with statistical interactions across multiple dimensions, revealing how behavior transitions between ideal bosons and fermions and identifying phase transitions at high dimensions.

Contribution

It offers the first exact thermodynamic solutions for a statistically interacting quantum gas in arbitrary dimensions, connecting known models and exploring high-dimensional phase transitions.

Findings

Exact thermodynamics derived for all dimensions D

Ideal boson and fermion limits recovered in weak and strong coupling

Phase transition identified at infinite dimensions for T>0

Abstract

We present the exact thermodynamics (isochores, isotherms, isobars, response functions) of a statistically interacting quantum gas in D dimensions. The results in D=1 are those of the thermodynamic Bethe ansatz for the nonlinear Schroedinger model, a gas with repulsive two-body contact potential. In all dimensions the ideal boson and fermion gases are recovered in the weak-coupling and strong-coupling limits, respectively. For all nonzero couplings ideal fermion gas behavior emerges for D>>1 and, in the limit D->infinity, a phase transition occurs at T>0. Significant deviations from ideal quantum gas behavior are found for intermediate coupling and finite D.