Temperature Correction to Casimir-Lifshitz Free Energy at Low Temperatures: Semiconductors
Simen A. Ellingsen, Iver Brevik, Johan S. H{\o}ye, and Kimball A., Milton
TL;DR
This paper calculates the low-temperature correction to the Casimir-Lifshitz free energy for dielectric plates with constant conductivity, extending previous work to include TM modes and generalizing TE mode results for metals.
Contribution
It provides new calculations for TM mode corrections and extends TE mode analysis to dielectric materials, supported by numerical verification.
Findings
Analytic expressions for TM mode corrections at low temperatures.
Extended TE mode results applicable to dielectric materials.
Numerical validation of the theoretical calculations.
Abstract
The Casimir force and free energy at low temperatures has been the subject of focus for some time. We calculate the temperature correction to the Casimir-Lifshitz free energy between two parallel plates made of dielectric material possessing a constant conductivity at low temperatures, described through a Drude-type dielectric function. For the transverse magnetic (TM) mode such a calculation is new. A further calculation for the case of the TE mode is thereafter presented which extends and generalizes previous work for metals. A numerical study is undertaken to verify the correctness of the analytic results.
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