Casimir Free Energy at High Temperatures: Grounded vs Isolated Conductors

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.

7 pages

References in corpus (4)

• Classical Casimir interaction in the plane-sphere geometry
• The derivative expansion approach to the interaction between close surfaces
• On the Derivative Expansion for the Electromagnetic Casimir Free Energy at High Temperatures
• Derivative expansion for the electromagnetic and Neumann Casimir effects in $2+1$ dimensions with imperfect mirrors

Cited by in corpus (6)

• Classical Casimir free energy for two Drude spheres of arbitrary radii: A plane-wave approach
• Classical Casimir interaction of perfectly conducting sphere and plate
• Universal Casimir interactions in the sphere-sphere geometry
• On the Difference Between the Vacuum Casimir Energies for Grounded and Isolated Conductors
• Exact Casimir interaction of perfectly conducting three-spheres in four euclidean dimensions
• Casimir effect between spherical objects: proximity-force approximation and beyond using plane waves