Casimir force, causality, and the Gurzhi model
An extended Drude model, termed the Gurzhi model, which takes into account the electron-phonon 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. Finally, the contribution of the electron-electron scattering to the Casimir pressure is estimated. Although a comparison with the measurement data of two precise experiments shows that the Gurzhi model does not resolve the Casimir puzzle, the obtained results suggest further clarification of this fundamental problem.