Recent Results on Thermal Casimir Force Between Dielectrics and Related Problems

Abstract

We review recent results obtained in the physics of the thermal Casimir force acting between two dielectrics, dielectric and metal, and between metal and semiconductor. The detailed derivation for the low-temperature behavior of the Casimir free energy, pressure and entropy in the configuration of two real dielectric plates is presented. For dielectrics with finite static dielectric permittivity it is shown that the Nernst heat theorem is satisfied. Hence, the Lifshitz theory of the van der Waals and Casimir forces is demonstrated to be consistent with thermodynamics. The nonzero dc conductivity of dielectric plates is proved to lead to a violation of the Nernst heat theorem and, thus, is not related to the phenomenon of dispersion forces. The low-temperature asymptotics of the Casimir free energy, pressure and entropy are derived also in the configuration of one metal and one dielectric plate. The results are shown to be consistent with thermodynamics if the dielectric plate possesses a finite static dielectric permittivity. If the dc conductivity of a dielectric plate is taken into account this results in the violation of the Nernst heat theorem. We discuss both the experimental and theoretical results related to the Casimir interaction between metal and semiconductor with different charge carrier density. Discussions in the literature on the possible influence of spatial dispersion on the thermal Casimir force are analyzed. In conclusion, the conventional Lifshitz theory taking into account only the frequency dispersion remains the reliable foundation for the interpretation of all present experiments.

Thermal Casimir–Polder force between an atom and a dielectric plate: thermodynamics and experiment

“…These additions exponentially decay to zero with vanishing temperature [21,22,23]. However, the term with l = 0 is modified because according to (3) r TM (0, y) = r 0 is replaced withr TM (0, y) = 1.…”

Temperature correction to Casimir-Lifshitz free energy at low temperatures: Semiconductors

“…Rather, the purpose * Electronic address: simen.a.ellingsen@ntnu.no † Electronic address: iver.h.brevik@ntnu.no ‡ Electronic address: johan.hoye@phys.ntnu.no § Electronic address: milton@nhn.ou.edu of this paper is to examine another purported temperature anomaly. In several recent papers [19,20,21,22] Geyer, Klimchitskaya, and Mostepanenko have claimed that in real dielectrics, which possess a very small, but nonzero conductivity which vanishes at T = 0, a similar discontinuity in the transverse magnetic reflection coefficient occurs, which would lead to a similar violation of the Nernst theorem. The same applies to semiconductors whose conductivity vanishes as temperature drops to zero.…”

“…While this calculation does not solve the thermal anomaly brought forth in Refs. [19,20,21] and reviewed in section I, it serves to further illuminate the mathematical behaviour of the free energy of poor conductors at very low temperatures when different models for the dielectric response of the materials are employed. A similar calculation is subsequently performed for the TE mode, which extends that of Ref.…”

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

“…5, coinciding with the impedances of the normal skin effect and infrared optics in the appropriate frequency regions, violates thermodynamics. This should be compared with the results of [44,45,46,47,48] devoted to the Casimir interaction between two dielectrics and between metal and dielectric. In both cases the account of an actual dielectric response at quasistatic frequencies (i.e., the account of nonzero dc conductivity) results in contradiction with thermodynamics, whereas the extrapolation of the dielectric behavior at high frequencies to zero frequency satisfies the thermodynamic test.…”

“…If, however, the dc conductivity of dielectric materials is taken into account, the Nernst heat theorem for the entropy of a fluctuating field is violated [44,45]. The same is true in the metal-dielectric configuration [46] depending on the finiteness of the static permittivity of a dielectric plate [47,48]. Thus, thermodynamics provides a test for the validity of various models of material properties: only the thermodynamicallyconsistent models should be used.…”