A model for the electron glass

Relaxation dynamics of the three-dimensional Coulomb glass model

In this paper, we analyze the dynamics of the Coulomb glass lattice model in three dimensions near a local equilibrium state by using mean-field approximations. We specifically focus on understanding the role of localization length (ξ) and the temperature (T) in the regime where the system is not far from equilibrium. We use the eigenvalue distribution of the dynamical matrix to characterize relaxation laws as a function of localization length at low temperatures. The variation of the minimum eigenvalue of the dynamical matrix with temperature and localization length is discussed numerically and analytically. Our results demonstrate the dominant role played by the localization length on the relaxation laws. For very small localization lengths, we find a crossover from exponential relaxation at long times to a logarithmic decay at intermediate times. No logarithmic decay at the intermediate times is observed for large localization lengths.

Localization, anomalous diffusion, and slow relaxations: a random distance matrix approach

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum), for low densities, and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results.

Effective temperature in relaxation of Coulomb glasses

We study relaxation in two-dimensional Coulomb glasses up to macroscopic times. We use a kinetic Monte Carlo algorithm especially designed to escape efficiently from deep valleys around metastable states. We find that, during the relaxation process, the site occupancy follows a Fermi-Dirac distribution with an effective temperature much higher than the real temperature T. Long electron-hole excitations are characterized by T(eff), while short ones are thermalized at T. We argue that the density of states at the Fermi level is proportional to T(eff) and is a good thermometer to measure it. T(eff) decreases extremely slowly, roughly as the inverse of the logarithm of time, and it should affect hopping conductance in many experimental circumstances.