Classical generalization of the Drude formula for the optical conductivity

A simple classical generalization of the Drude formula is derived based on the impulse response approach and Poisson statistics. The new feature is a parameter c, which is a measure of persistence of velocity. With negative values of c, it is possible to mimic the infrared properties of poor metals that display a minimum in the optical conductivity at zero frequency. The electron current in these cases reverses direction before decaying to zero. Specific examples considered are Hg and its amalgams, liquid Te, and the quasicrystal ${\mathrm{Al}}_{63.5}{\mathrm{Cu}}_{24.5}{\mathrm{Fe}}_{12}.$ Discussion is offered on the connection with interband transitions, on the distinction between the electron lifetime and the transport relaxation time, and on other generalizations of the Drude formula.