# Self-consistent Treatment of Quantum Gases of D-dimensional Hard Spheres Beyond the Van der Waals Approximation

## TL;DR

This paper develops a self-consistent quantum van der Waals equation of state for D-dimensional hard sphere gases, addressing limitations of traditional approaches and extending applicability to higher densities and convex bodies.

## Contribution

It introduces a novel self-consistent formulation of the quantum VdW EoS for hard spheres in arbitrary dimensions, improving accuracy over classical methods.

## Key findings

- Derived a multicomponent quantum VdW EoS with hard-core repulsion.
- Extended the model to higher densities and convex bodies of any dimension D≥2.
- Identified limitations of alternative virial coefficient treatments.

## Abstract

The necessary conditions to derive the quantum VdW EoS with hard-core repulsion from the quantum partition are discussed. On a plausible example it is shown that an alternative way to account correctly for the 3-rd virial coefficient of classical hard spheres leads to inconsistencies. The multicomponent formulation of the quantum VdW EoS with hard-core repulsion is derived within a self-consisting approximation. For practical applications it is simplified, extended to higher densities and generalized to the case of hard convex bodies of any dimension $D\ge 2$.