Quantum and thermal Casimir interaction between a sphere and a plate: Comparison of Drude and plasma models

TL;DR

This study compares the Casimir interaction between a sphere and a plate using plasma and Drude models at various temperatures, revealing material-dependent behaviors and non-trivial temperature effects.

Contribution

It provides analytical and numerical comparisons of Casimir forces for different models, highlighting non-universal interactions and corrections beyond the proximity force approximation.

Findings

Material-dependent asymptotic interactions for plasma models.

Non-monotonic temperature dependence of Casimir free energy for Drude metals.

Negative entropy observed over a range of separations.

Abstract

We calculate the Casimir interaction between a sphere and a plate, both described by the plasma model, the Drude model, or generalizations of the two models. We compare the results at both zero and finite temperatures. At asymptotically large separations we obtain analytical results for the interaction that reveal a non-universal, i.e., material dependent interaction for the plasma model. The latter result contains the asymptotic interaction for Drude metals and perfect reflectors as different but universal limiting cases. This observation is related to the screening of a static magnetic field by a London superconductor. For small separations we find corrections to the proximity force approximation (PFA) that support correlations between geometry and material properties that are not captured by the Lifshitz theory. Our results at finite temperatures reveal for Drude metals a non-monotonic temperature dependence of the Casimir free energy and a negative entropy over a sizeable range of separations.