Dissipative Dynamics of Non-Interacting Fermion Systems and Conductivity

Abstract

In this paper, Non-Equilibrium Steady State that is induced by electric field and the conductivity of non-interacting fermion systems under the dissipative dynamics is discussed. The dissipation is taken into account within a framework of the quantum dynamical semigroup introduced by Davies (1977). We obtain a formula of the conductivity for the stationary state, which is applicable to arbitrary potentials. Our formula gives a justification of an adiabatic factor that is often introduced in practical calculation while using the Kubo formula. In addition, the conductivity of crystals (i.e., periodic potentials) is also discussed.

Entanglement Dynamics Governed by Time-Dependent Quantum Generators

“…The dynamics of open quantum systems remains a topic of intensive research [1][2][3][4]. Quantum evolution can be described by differential equations (master equations) that convey information about the interactions between the system and its environment.…”