Very slow relaxation in systems lacking translational symmetry, with emphasis on disordered insulators

Abstract

Abstract The paper addresses the problem of very slow relaxations of electrons observed in a large variety of materials. Three aspects of the slow relaxations are explicitly considered: a.c. conductivity, dispersive transport, and the electron glass. Interactions have previously been proposed as the primary cause for the very slow relaxation process. It is argued here that while interactions are important in making slow rates even slower, the primary cause for the very slow relaxations is localization, and thus lack of translational symmetry. Specifically, it is shown that the appropriate a.c. conductivity, dispersive transport, as well as the electron glass can exist without interactions. The time evolution of the entropy and of the polarizability are calculated for non-interacting electrons in a disordered insulator. It is found that a temperature exists where the polarizability changes dramatically, but the entropy varies smoothly. The effects of interactions are discussed on a qualitative level.