Casimir force, causality, and the Gurzhi model

Abstract

An extended Drude model, termed as the Gurzhi model, which takes into account the electronphonon and electron-electron interactions, is applied to calculate the Casimir force between two metallic plates. It is shown that although the dielectric permittivity of the Gurzhi model has a first order pole in the upper half-plane of complex frequencies and, thus, violates the causality principle, it can be used in a restricted frequency interval in combination with the experimental permittivity determined by the optical data for the complex index of refraction. The imaginary part of the Gurzhi dielectric permittivity of Au at low frequencies demonstrates better agreement with the permittivity given by the optical data than the simple Drude model. The Casimir pressure between two Au plates is computed using the Gurzhi, Drude and plasma model approaches, taking into account the optical data, as well as with the simple Drude and plasma models. The contribution of the electron-electron scattering to the Casimir pressure is estimated. Although a comparison with the measurement data of two precise experiments show that the Gurzhi model does not resolve the Casimir puzzle, the obtained results suggest further clarification of this fundamental problem.

Theory-experiment comparison for the Casimir force between metallic test bodies: A spatially nonlocal dielectric response

“…I, the problem of disagreement between theoretical predictions of the fundamental Lifshitz theory using the well-tested Drude model with the experimental data for metallic test bodies remains unresolved for almost 20 years. Many attempts of its resolution have been undertaken (including a consideration of the frequency-dependent relaxation parameter [108], i.e., the so-called Gurzhi model), but the problem is as yet unresolved. Similar problem arises for dielectric materials [45,109].…”

Experimental and theoretical investigation of the thermal effect in the Casimir interaction from graphene

“…Note that it is even impossible to experimentally test the transverse components of their spatially nonlocal generalizations in the off-mass-shell area [42]. This may be the reason why the Lifshitz theory using the standard Drude model or its generalization for the case of frequency-dependent relaxation parameter (the so-called Gurzhi model) fails to predict the correct values of the Casimir force between metallic test bodies [110].…”