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Dipole diffusion in a random electrical potential

We study the Langevin dynamics of a dipole diffusing in a random electrical field E derived from a quenched Gaussian potential. We show that in a suitable adiabatic limit (where the dynamics of the dipole moment is much faster than the dynamics of its position), one can reduce the coupled stochastic equations to an effective Langevin equation for a particle diffusing in an effective potential with a spatially varying and anisotropic local diffusivity $κ_{ij}$. Analytic results, close to the adiabatic limit, for the diffusion constant $κ_e$ are found in one dimension and a finite temperature dynamical transition is found. The system is also studied numerically. In particular, we study the anomalous diffusion exponent in the low temperature regime. Our findings strongly support the conclusion that the location of the dynamical transition and the anomalous diffusion exponents are determined by purely static considerations, i.e. they are independent of the relative values of the diffusion constants of the particle position and its dipole moment.