Influence of the Heisenberg Principle on the Ideal Bose Gas

TL;DR

This paper modifies the ideal Bose gas model to incorporate the Heisenberg principle, resolving unphysical predictions like zero incompressibility and providing a more realistic description of its thermodynamic properties.

Contribution

A novel modification of the ideal Bose gas that enforces the Heisenberg principle, resulting in finite incompressibility and altered specific heat behavior.

Findings

Finite (in)compressibility at all temperatures and densities

Maximum in specific heat at the critical temperature

Preservation of the relation between critical temperature and density

Abstract

The ideal Bose gas has two major shortcomings: at zero temperature, all the particles 'condense' at zero energy or momentum, thus violating the Heisenberg principle; the second is that the pressure below the critical point is independent of density resulting in zero incompressibility (or infinite isothermal compressibility) which is unphysical. We propose a modification of the ideal Bose gas to take into account the Heisenberg principle. This modification results in a finite (in)compressibility at all temperatures and densities. The main properties of the ideal Bose gas are preserved, i.e. the relation between the critical temperature and density, but the specific heat has a maximum at the critical temperature instead of a discontinuity. Of course interactions are crucial for both cases in order to describe actual physical systems.