A phenomenological position and energy resolving Lindblad approach to quantum kinetics

A general theoretical approach to study the quantum kinetics in a system coupled to a bath is proposed. Starting with the microscopic interaction, a Lindblad master equation is established, which goes beyond the common secular approximation. This allows for the treatment of systems, where coherences are generated by the bath couplings while avoiding the negative occupations occurring in the Bloch-Wangsness-Redfield kinetic equations. The versatility and accuracy of the approach is verified by its application to three entirely different physical systems: (i) electric transport through a double-dot system coupled to electronic reservoirs, (ii) exciton kinetics in coupled chromophores in the presence of a heat bath, and (iii) the simulation of quantum cascade lasers, where the coherent electron transport is established by scattering with phonons and impurities.