Quantum Transport Equations of Particle Systems

Jens Fricke

V.V. Brkovic

We treat the quantum transport of an interacting system of electrons, impurities and phonons. The dynamic system is in a time-dependent electric field. We analyzed quantum transport process by using the quantum generalized Langevin equation, in which the system is shown to be equivalent to a quantum particle in a heat bath. After eliminating the heat-bath variables, the equation of motion for the quantum particle is written in a form of quantum generalized Langevin equation, with a memory term which reflects the retarded effects of the heat bath on the quantum particle.

A. Ron

Giulio Amato, Heinz‐Peter Breuer, Sandro Wimberger +2 more

We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, nonstationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total particle number, a system of nonlinear quantum-classical master equations describes the concurrent many-particle time evolution on the lattice and in the reservoirs. The finiteness of the reservoirs makes a macroscopic current emerge, which decreases exponentially in time and asymptotically drives the many-particle configuration into an equilibrium state where the particle flow ceases. We analytically derive the timescale of this equilibration process, and, furthermore, investigate the imprint of many-particle interferences on the transport process.

Petr Král

A linear response formalism is developed for evaluation of transport coefficients in quantum many-particle systems. The method is based on a systematic linearization of nonequilibrium Kadanoff-Baym transport equations in an integral form in ac electric fields. Simple and consistent approximations can be performed in the resulting set of transport equations, which replace vertex equations in the Kubo formalism. The method is illustrated by the example of an ac and dc conductivity and conductance for a quasi-one-dimensional electron system with an electron--phonon interaction for three-dimensional acoustical phonons. After approximations standard in metals, the solved transport equations coincide with the Holstein equation. \textcopyright{} 1996 The American Physical Society.