Thermal and transport properties of a non-relativistic quantum gas interacting through a delta-shell potential

TL;DR

This paper investigates the thermodynamic and transport properties of a non-relativistic quantum gas interacting via a delta-shell potential, extending two-body physics to many-body systems and analyzing effects near the unitary limit.

Contribution

It extends Gottfried's two-body delta-shell potential work to many-body physics, deriving thermodynamic functions and transport coefficients including quantum corrections.

Findings

Calculated the second virial coefficient for the gas.

Derived thermodynamic functions with quantum corrections.

Analyzed transport coefficients like diffusion and viscosity.

Abstract

This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of non-relativistic particles when the thermal De-Broglie wavelength of a particle is smaller than the range of the potential and the density is such that average distance between particles is smaller than the range. The ability of the delta-shell potential to reproduce some basic properties of the deuteron are examined. Relations for moments of bound states are derived. The virial expansion is used to calculate the first quantum correction to the ideal gas pressure in the form of the second virial coefficient. Additionally, all thermodynamic functions are calculated up to the first order quantum corrections. For small departures from equilibrium, the net flows of mass, energy and momentum, characterized by the coefficients of diffusion, thermal conductivity and shear viscosity, respectively, are calculated. Properties of the gas are examined for various values of physical parameters including the case of infinite scattering length when the unitary limit is achieved.