The Normal Casimir Force for Lateral Moving Planes with Isotropic Conductivities

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, Delta vE proportional to v2, for small enough velocities is used for all considered cases. In the case of constant conductivity, eta, the energy correction is Delta vE proportional to eta/a3v/eta 2 for vMUCH LESS-THAN eta MUCH LESS-THAN1.