Temperature Correction to Casimir-Lifshitz Free Energy at Low Temperatures: Semiconductors

摘要

The Casimir force and free energy at low temperatures has been the subject offocus for some time. We calculate the temperature correction to theCasimir-Lifshitz free energy between two parallel plates made of dielectricmaterial possessing a constant conductivity at low temperatures, describedthrough a Drude-type dielectric function. For the transverse magnetic (TM) modesuch a calculation is new. A further calculation for the case of the TE mode isthereafter presented which extends and generalizes previous work for metals. Anumerical study is undertaken to verify the correctness of the analyticresults.