Thermal Casimir effect with soft boundary conditions

TL;DR

This paper investigates the thermal Casimir effect between parallel plates with soft boundary conditions induced by quadratic interactions, revealing complex distance-dependent behaviors and the influence of boundary openness on the force.

Contribution

It introduces a model of soft boundary conditions via quadratic interactions, analyzing their impact on the Casimir effect and boundary behavior in different regimes.

Findings

Dirichlet limit breaks down at short distances for electrolyte-like boundaries.

Dirichlet limit breaks down at large distances for dipole-like boundaries.

The Casimir force on an internal plate depends on the external field presence.

Abstract

We consider the thermal Casimir effect in systems of parallel plates coupled to a mass-less free field theory via quadratic interaction terms which suppress (i) the field on the plates (ii) the gradient of the field in the plane of the plates. These boundary interactions correspond to (i) the presence of an electrolyte in the plates and (ii) a uniform field of dipoles, in the plates, which are polarizable in the plane of the plates. These boundary interactions lead to Robin type boundary conditions in the case where there is no field outside the two plates. In the appropriate limit, in both cases Dirichlet boundary conditions are obtained but we show that in case (i) the Dirichlet limit breaks down at short inter-plate distances and in (ii) it breaks down at large distances. The behavior of the two plate system is also seen to be highly dependent on whether the system is open or closed. In addition we analyze the Casimir force on a third plate placed between two outer plates. The force acting on the central plate is shown to be highly sensitive to whether or not the fluctuating scalar field is present in the region exterior to the two confining plates.