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Non-equilibrium Optical Conductivity in Materials with Localized Electronic States

A wide range of disordered materials contain electronic states that are spatially well localized. In this work, we investigated the electrical response of such systems in non-equilibrium conditions to external electromagnetic field. We obtained the expression for optical conductivity valid for any non-equilibrium state of electronic subsystem. In the case of incoherent non-equilibrium state, this expression contains only the positions of localized electronic states, Fermi's golden rule transition probabilities between the states and the populations of electronic states. The same form of expression is valid both in the case of weak electron-phonon interaction and weak electron-impurity interaction that act as perturbations of electronic Hamiltonian. The derivation was performed by expanding the general expression for AC conductivity in powers of small electron-phonon interaction or electron-impurity interaction parameter. Applications of the expression to two model systems, a simple one- dimensional Gaussian disorder model and the model of a realistic three-dimensional organic polymer material, were presented, as well.