Quantum transport for a many-body system using a quantum Langevin-equation approach
- 15 October 1987
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 36 (11), 5798-5808
- https://doi.org/10.1103/physrevb.36.5798
Abstract
We treat the quantum transport of an interacting system of electrons, impurities, and phonons, in a time-dependent electric field, by using the quantum generalized Langevin equation (GLE), in which the system is shown to be equivalent to a quantum particle in a heat bath. We follow here the philosophy of Ford, Lewis, and O’Connell, who have demonstrated the usefulness of the GLE approach to heat-bath problems. The center of mass of the electrons acts like a quantum particle, while the relative electrons and phonons play the role of heat bath. They are coupled through the electron-impurity and electron-phonon interactions. After eliminating the heat-bath variables, the equation of motion for the quantum particle is written in a form of a quantum generalized Langevin equation, with a memory term which reflects the retarded effects of the heat bath on the quantum particle. The evaluation of the memory term immediately leads to a result for the susceptibility from which we can calculate the conductivity directly, in contrast to Kubo-type calculations which require the evaluation of correlation functions as an intermediate step. As a demonstration of the directness of our approach, we show that the usual random-phase-approximation conductivity results are easily derived. In addition, we derive an expression for the memory function, which incorporates higher-order electron-impurity scattering.Keywords
This publication has 29 references indexed in Scilit:
- Memory effects in transport theory: An exact modelPhysical Review A, 1987
- Brownian Motion and Nonequilibrium Statistical MechanicsScience, 1986
- Quantum field-theoretical methods in transport theory of metalsReviews of Modern Physics, 1986
- On the description of transport phenomenaPhysics Reports, 1978
- Exact formulae for the electrical resistivityAdvances in Physics, 1975
- Discussion of a new theory of electrical resistivityPhysical Review B, 1974
- A Continued-Fraction Representation of the Time-Correlation FunctionsProgress of Theoretical Physics, 1965
- Transport, Collective Motion, and Brownian MotionProgress of Theoretical Physics, 1965
- Quantum Theory of Electrical Transport PhenomenaPhysical Review B, 1957
- Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction ProblemsJournal of the Physics Society Japan, 1957