Drude model and Lifshitz formula

Abstract

Since nearly 10 years, it is known that inserting the permittivity of the Drude model into the Lifshitz formula for free energy causes a violation of the third law of thermodynamics. In this paper we show that the standard Matsubara formulation for free energy contains a contribution that is non-perturbative in the relaxation parameter. We argue that the correct formula must have a perturbative expansion and conclude that the standard Matsubara formulation with the permittivity of the Drude model inserted is not correct. We trace the non-perturbative contribution in the complex frequency plane, where it shows up as a self-intersection or a bifurcation of the integration path.

accepted for publication in EPJC

References in corpus (10)

• Observation of the thermal Casimir force
• Novel constraints on light elementary particles and extra-dimensional physics from the Casimir effect
• Control of the Casimir force by the modification of dielectric properties with light
• Demonstration of optically modulated dispersion forces
• Limits on Nonstandard Forces in the Submicrometer Range
• Contribution of drifting carriers to the Casimir-Lifshitz and Casimir-Polder interactions with semiconductor materials
• Casimir energy and entropy between dissipative mirrors
• Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii
• On the Casimir entropy for a ball in front of a plane
• Resource Letter VWCPF-1: Van der Waals and Casimir-Polder forces

Cited by in corpus (11)

• The Casimir effect as a sum-over-modes in dissipative systems
• Comparison between experiment and theory for the thermal Casimir force
• Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors
• How to confirm and exclude different models of material properties in the Casimir effect
• Electromagnetic vacuum energy for two parallel slabs in terms of surface, wave guide and photonic modes
• Casimir and Casimir-Polder forces with dissipation from first principles
• Quantum electrodynamics of a free particle near dispersive dielectric or conducting boundaries
• Plasma model and Drude model permittivities in Lifshitz formula
• Accounting for dissipation in the scattering approach to the Casimir energy
• Thermally Excited Quasiparticles in Metals, Dispersion Forces, and the Thermal Anomaly
• Vacuum and thermal energies for two oscillators interacting through a field