Optical BCS conductivity at imaginary frequencies and dispersion energies of superconductors

Abstract

We present an efficient expression for the analytic continuation to arbitrary complex frequencies of the complex optical and AC conductivity of a homogeneous superconductor with arbitrary mean free path. Knowledge of this quantity is fundamental in the calculation of thermodynamic potentials and dispersion energies involving type-I superconducting bodies. When considered for imaginary frequencies, our formula evaluates faster than previous schemes involving Kramers--Kronig transforms. A number of applications illustrates its efficiency: a simplified low-frequency expansion of the conductivity, the electromagnetic bulk self-energy due to longitudinal plasma oscillations, and the Casimir free energy of a superconducting cavity.

20 pages, 7 figures, calculation of Casimir energy added

References in corpus (6)

• Experiment and theory in the Casimir effect
• Casimir effect in a superconducting cavity and the thermal controversy
• Casimir energy and entropy between dissipative mirrors
• Recent Developments in the Casimir Effect
• Temperature dependence of the magnetic Casimir-Polder interaction
• Thermal and dissipative effects in Casimir physics

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