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This hyperdocument was derived from an article published in Reviews of Modern Physics, Vol. 62, pp. 745-791 [1990].

Boundary Conditions for Open Quantum Systems Driven Far from Equilibrium

William R. Frensley


This is a study of simple kinetic models of open systems, in the sense of systems which can exchange conserved particles with their environment. The system is assumed to be one-dimensional and situated between two particle reservoirs. Such a system is readily driven far from equilibrium if the chemical potentials of the reservoirs differ appreciably. The openness of the system modifies the spatial boundary conditions on the single-particle Liouville-von Neumann equation, leading to a non-Hermitian Liouville operator. If the open-system boundary conditions are time-reversible, exponentially growing (unphysical) solutions are introduced into the time-dependence of the density matrix. This problem is avoided by applying time-irreversible boundary conditions to the Wigner distribution function. These boundary conditions model the external environment as ideal particle reservoirs with properties analogous to those of a blackbody. This time-irreversible model may be numerically evaluated in a discrete approximation, and has been applied to the study of a resonant-tunneling semiconductor diode. The physical and mathematical properties of the irreversible kinetic model, in both its discrete and continuum formulations are examined in detail. The model demonstrates the distinction in kinetic theory between commutator superoperators, which may become non-Hermitian to describe irreversible behavior, and anticommutator superoperators, which remain Hermitian and are used to evaluate physical observables.


William R. Frensley
Thu Jun 8 17:53:37 CDT 1995