Dissipative tunnel transport: state of the problem and prospects

This review is devoted to analysis of the quantum dissipative tunneling theory with application to the problem of electron transport. The authors analyze the features of the quantum particle tunnel dynamics interacting with a heat-bath. The article describes the existing methods for describing this dynamics (such as the instanton - method, VKB - method etc.). The researchers review the perspectives for development of this direction and corresponding unsolved problems. The article also considers physical realizations with preferential method of tunnel decay.