Non-universal Casimir forces at Bose-Einstein condensation of an ideal gas: effect of Dirichlet boundary conditions

TL;DR

This paper investigates how Dirichlet boundary conditions affect the decay behavior of thermal Casimir forces in an ideal Bose gas near Bose-Einstein condensation, revealing non-universal decay laws differing from other boundary conditions.

Contribution

It demonstrates that Dirichlet boundary conditions lead to a non-universal 1/D^2 decay of the Casimir force, contrasting with universal decay laws under periodic and Neumann conditions.

Findings

Casimir force decays as 1/D^2 with Dirichlet b.c.

Next order correction is lnD/D^3.

Decay law differs from periodic and Neumann cases.

Abstract

We analyze the Casimir forces for an ideal Bose gas enclosed between two infinite parallel walls separated by the distance D. The walls are characterized by the Dirichlet boundary conditions. We show that if the thermodynamic state with Bose-Einstein condensate present is correctly approached along the path pertinent to the Dirichlet b.c. then the leading term describing the large-distance decay of thermal Casimir force between the walls is 1/D^2 with a non-universal amplitude. The next order correction is lnD/D^3. These observations remain in contrast with the decay law for both the periodic and Neumann boundary conditions for which the leading term is 1/D^3 with a universal amplitude. We associate this discrepancy with the non-zero D-dependent positive value of the one-particle ground state energy in the case of Dirichlet boundary conditions.