Casimir entropy for magnetodielectrics

Abstract

Abstract. We find the analytic expressions for the Casimir free energy, entropy and pressure at low temperature in the configuration of two parallel plates made of magnetodielectic material. The cases of constant and frequency-dependent dielectic permittivity and magnetic permeability of the plates are considered. Special attention is paid to the account of dc conductivity. It is shown that in the case of finite static dielectric permittivity and magnetic permeability the Nernst heat theorem for the Casimir entropy is satisfied. If the dc conductivity is taken into account, the Casimir entropy goes to a positive nonzero limit depending on the parameters of a system when the temperature vanishes, i.e., the Nernst theorem is violated. The experimental situation is also discussed.

Analytic results for the Casimir free energy between ferromagnetic metals

“…In the latter case it is known [2,4,47,48] that the Lifshitz theory violates the Nernst heat theorem and the Casimir entropy at T = 0 is positive. For magnetic dielectrics this positive quantity remains independent on the magnetic properties [46]. This makes unique the case of ferromagnetic metals considered here.…”

Nernst heat theorem for the Casimir-Polder interaction between a magnetizable atom and ferromagnetic dielectric plate

“…8 For two dielectric plates described with omitted conductivity at a constant current (dc conductivity), the Casimir entropy satisfies the Nernst theorem and violates it otherwise. [9][10][11] The same holds for two plates made of ferromagnetic dielectric 12 and for the Casimir-Polder entropy of a polarizable atom interacting with nonmagnetic dielectric plate. 13 Thus, for a dielectric plate, thermodynamic properties depend on the used model of dielectric response even if an atom is not magnetizable.…”

Casimir free energy of dielectric films: classical limit, low-temperature behavior and control

“…Computations show that F (l 1) decreases for 1% when the plate thickness d increases from 1 µm to ∞. For Ge the reflection coefficients in (51) are equal to r (f,s) TM (0) ≈ −0.16 and r (p,v) TM (0) ≈ −0.84, i.e., are both negative. This leads to R (f,p) TM (0) < 0.…”

“…For Al 2 O 3 film of a = 1 µm thickness the contribution of F (l 1) to F changes in the limits of 0.3% when d varies from 1 µm to ∞. Then we take into account that the reflection coefficients in (51) r (f,v) TM (0) ≈ −0.82, one obtains from Eq. (11) that the Casimir free energies of sufficiently thick films are negative.…”