The simulation of electron diffusion in solids at finite temperature

We show how the transport of properties of electrons in disordered solids c an be simulated taking into account atomic motion. The time-dependent Schro dinger equation and the molecular dynamics equation are solved in tandem fo r electronic diffusion and as a test of the methods we obtain metallic beha viour and variable range hopping in appropriate circumstances. We also desc ribe a stable algorithm which introduces dissipation into the Schrodinger e quation via imaginary components for the energy levels enabling electrons t o be removed from a system as is necessary in device simulation. This is im portant because the often used leap frog method becomes unstable in this si tuation.