Coherent electron dynamics in a two-dimensional random system with mobility edges

We study numerically the dynamics of a one-electron wavepacket in a two-dimensional random lattice with long-range correlated diagonal disorder in the presence of a uniform electric field. The time-dependent Schrodinger equation is used for this purpose. We find that the wavepacket displays Bloch-like oscillations associated with the appearance of a phase of delocalized states in the strong correlation regime. The amplitude of oscillations directly reflects the bandwidth of the phase and allows us to measure it. The oscillations reveal two main frequencies whose values are determined by the structure of the underlying potential in the vicinity of the wavepacket maximum.

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations.