Analytical and numerical demonstration of how the Drude dispersive model satisfies Nernst's theorem for the Casimir entropy

Abstract

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model, assuming the relaxation is nonzero at zero temperature (which is the case when impurities are present), gives consistent results for the Casimir free energy at low temperatures. Specifically, we find that the free energy consists essentially of two terms, one leading term proportional to T 2 , and a next term proportional to T 5/2 . Both these terms give rise to zero Casimir entropy as T → 0, thus in accordance with Nernst's theorem.

The Casimir force between real materials: Experiment and theory

“…The respective analytic expression for the lowtemperature behavior of the entropy has been obtained (Høye at al., 2007;Brevik et al, 2008) under the condition ζ l ≪ γ res which is opposite to the inequality (37). The application region and the coefficients of this analytic expression were determined incorrectly because an overestimated value of γ res = γ(T = 300K) was used.…”

“…According to Høye et al (2007) and Brevik et al (2008), the formal satisfaction of the Nernst theorem for the Drude model, as applied to metals with impurities, resolves the problem of thermodynamic consistency of that model combined with the Lifshitz theory. , however, have remarked that a perfect crystal lattice is a truly equilibrium system with a nondegenerate dynamical state of the lowest energy.…”

Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator

“…According to the Drude model approach [6,11,[18][19][20][21], the extrapolation of Im ε(ω) to lower frequencies is performed using the imaginary part of the dielectric permittivity,…”

“…The parameter range, where a violation occurs, was recently rederived and extended also to the geometry of a sphere above a plate [17]. It was demonstrated that for metals with impurities the Nernst heat theorem in the Lifshitz theory is preserved [18][19][20][21]. However, in the case of metals with perfect crystal structure (which is the basic model used in condensed-matter physics) and for dielectrics, a satisfactory solution was not found.…”

Casimir energies: Temperature dependence, dispersion, and anomalies

“…The situation is summarized in recent reviews [31,32]. In particular, the lack of a thermodynamic inconsistency has been conclusively demonstrated [33,34], by showing that the free energy for a Casimir system made from real metal plates with impurities has a quadratic temperature dependence at low temperature. Further evidence for the validity of the notion of excluding the TE zero mode for metals comes from the recent work of Buenzli and Martin [35], corroborating earlier work by these authors and others [36,37], who show from a microscopic viewpoint that the high-temperature behavior of the Casimir force is half that of an ideal metal, a rather conclusive demonstration that the TE zero mode is not present.…”