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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 159
Classical motion in two-dimensional crystals B. Nobbe
The classical motion of an electron of high enough energy in a two-dimensional crystal is diffusive for many potentials with Coulomb singularities. A simple model of the dynamics is developed, which predicts the dependence of the diffusion constant $D$ on the particle energy $E$ in the high energy limit: $D(E) sim const cdot E^{3/2}$.\ This diffusion law is checked for a concrete crystal, by numerical integrating the Hamilton equations for an ensemble of initial conditions. Finally this method is compared with other models of the classical dynamics in a crystal, especially the Sinai billiard.
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