Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors

TL;DR

This paper analyzes the difference in Casimir free energy between grounded and isolated conductors at high temperatures, providing a simple electrostatic capacitance-based expression and approximate formulas for close conductors.

Contribution

It introduces a general, simple expression for the Casimir free energy difference based on capacitance matrices and applies proximity force approximation for close conductors.

Findings

Derived a capacitance matrix-based formula for energy difference.

Provided approximate expressions for close conductors.

Linked high-temperature Casimir behavior to real material corrections.

Abstract

We evaluate the difference between the Casimir free energies corresponding to either grounded or isolated perfect conductors, at high temperatures. We show that a general and simple expression for that difference can be given, in terms of the electrostatic capacitance matrix for the system of conductors. For the case of close conductors, we provide approximate expressions for that difference, by evaluating the capacitance matrix using the proximity force approximation. Since the high-temperature limit for the Casimir free energy for a medium described by a frequency-dependent conductivity diverging at zero frequency coincides with that of an isolated conductor, our results may shed light on the corrections to the Casimir force in the presence of real materials.