Finite Size Effects in Equations of State under non-trivial Boundary Conditions

TL;DR

This paper investigates how finite size effects and boundary conditions influence the equations of state for quantum particles in a one-dimensional box, revealing deviations from ideal gas behavior due to wall interactions.

Contribution

It introduces a study of finite size effects with mixed boundary conditions and derives equations of state resembling van der Waals equations for quantum gases.

Findings

Finite size effects cause deviations from ideal gas laws.

Boundary conditions significantly influence energy spectra.

Wall interactions can mimic particle interactions in equations of state.

Abstract

We study free particles in a one-dimensional box with combinations of two types of boundary conditions: the Dirichlet condition and a one-parameter family of quasi-Neumann conditions at the two walls. We calculate energy spectra approximately and obtain equations of state having the same (one-dimensional) volume dependence as van der Waals equations of state. The dependence of the equations of state is examined for particles obeying Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac statistics. Our results suggest that the deviation from ideal gas may also be realized as finite size effects due to the interaction between the particles and the walls.