A model of an open quantum system is presented in which irreversibility is introduced via boundary conditions on the single-particle Wigner distribution function. The Wigner function is calculated in a discrete approximation by solution of the Liouville equation in steady state, and the transient response is obtained by numerical integration of the Liouville equation. This model is applied to the quantum-well resonant-tunneling diode. The calculations reproduce the negative-resistance characteristic of the device, and indicate that the tunneling current approaches steady state within a few hundred femtoseconds of a sudden change in applied voltage.

• Received 16 March 1987

DOI:https://doi.org/10.1103/PhysRevB.36.1570