We consider diffusion of vibrations in 3d harmonic lattices with strong force-constant disorder. Above some frequency w_IR, corresponding to the Ioffe-Regel crossover, notion of phonons becomes ill defined. They cannot propagate through the system an
d transfer energy. Nevertheless most of the vibrations in this range are not localized. We show that they are similar to diffusons introduced by Allen, Feldman et al., Phil. Mag. B 79, 1715 (1999) to describe heat transport in glasses. The crossover frequency w_IR is close to the position of the boson peak. Changing strength of disorder we can vary w_IR from zero value (when rigidity is zero and there are no phonons in the lattice) up to a typical frequency in the system. Above w_IR the energy in the lattice is transferred by means of diffusion of vibrational excitations. We calculated the diffusivity of the modes D(w) using both the direct numerical solution of Newton equations and the formula of Edwards and Thouless. It is nearly a constant above w_IR and goes to zero at the localization threshold. We show that apart from the diffusion of energy, the diffusion of particle displacements in the lattice takes place as well. Above w_IR a displacement structure factor S(q,w) coincides well with a structure factor of random walk on the lattice. As a result the vibrational line width Gamma(q)=D_u q^2 where D_u is a diffusion coefficient of particle displacements. Our findings may have important consequence for the interpretation of experimental data on inelastic x-ray scattering and mechanisms of heat transfer in glasses.
Despite the fact that the problem of interference mechanism of magnetoresistance in semiconductors with hopping conductivity was widely discussed, most of existing studies were focused on the model of spinless electrons. This model can be justified o
nly when all electron spins are frozen. However there is always an admixture of free spins in the semiconductor. This study presents the theory of interference contribution to magnetoresistance that explicitly includes effects of both frozen and free electron spins. We consider the cases of small and large number of scatterers in the hopping event. For the case of large number of scatterers the approach is used that takes into account the dispersion of the scatterer energies. We compare our results with existing experimental data.
We observed a slow relaxation of magnetoresistance in response to applied magnetic field in selectively doped p-GaAs-AlGaAs structures with partially filled upper Hubbard band. We have paid a special attention to exclude the effects related to temper
ature fluctuations. Though this effect is important, we have found that the general features of slow relaxation still persist. This behavior is interpreted as related to the properties of the Coulomb glass formed by charged centers with account of spin correlations, which are sensitive to an external magnetic field. Variation of the magnetic field changes numbers of impurity complexes of different types. As a result, it effects the shape and depth of the polaron gap formed at the states belonging to the percolation cluster responsible for the conductance. The suggested model explains both the qualitative behavior and the order of magnitude of the slowly relaxing magnetoresistance.
We discuss memory effects in the conductance of hopping insulators due to slow rearrangements of many-electron clusters leading to formation of polarons close to the electron hopping sites. An abrupt change in the gate voltage and corresponding shift
of the chemical potential change populations of the hopping sites, which then slowly relax due to rearrangements of the clusters. As a result, the density of hopping states becomes time dependent on a scale relevant to rearrangement of the structural defects leading to the excess time dependent conductivity.
We discuss memory effects in the conductance of hopping insulators due to slow rearrangements of structural defects leading to formation of polarons close to the electron hopping states. An abrupt change in the gate voltage and corresponding shift of
the chemical potential change populations of the hopping sites, which then slowly relax due to rearrangements of structural defects. As a result, the density of hopping states becomes time dependent on a scale relevant to rearrangement of the structural defects leading to the excess time dependent conductivity.
