The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities - Nail Khusnutdinov; Natalia Emelianova (Physics, 2024)
We consider the two planes at zero temperature with isotropic conductivity that are in relative lateral motion with velocity v and interplane distance a. Two models of conductivity are taken into account—the constant and frequency-dependent Drude models. The normal (perpendicular to planes) Casimir force is analyzed in detail for two systems—(i) two planes with identical conductivity and (ii) one plane that is a perfect metal. The velocity correction to the Casimir energy, <semantics>ΔvE</semantics><semantics>∝<mspace width="0.166667em"></mspace></semantics><semantics>v2</semantics>, for small enough velocities is used for all considered cases. In the case of constant conductivity, <semantics>η</semantics>, the energy correction is <semantics>ΔvE<mspace width="0.166667em"></mspace></semantics><semantics>∝<mspace width="0.166667em"></mspace></semantics><semantics>η/a3<mfenced separators="" open="(" close=")">v/η</mfenced>2</semantics> for <semantics>v≪η≪1</semantics>.