Wigner Paths Method in Quantum Transportwith Dissipation

Abstract

The concept of Wigner paths in phase space both provides a pictorial representation of the quantum evolution of the system of interest and constitutes a useful tool for numerical solutions of the quantum equation describing the time evolution of the system. A Wigner path is defined as the path followed by a “simulative particle” carrying a σ-contribution of the Wigner function through the Wigner phase-space, and is formed by ballistic free flights separated by scattering processes (both scattering with phonons and with an arbitrary potential profile can be included), as for the case of semiclassical particles. Thus, the integral transport equation can be solved by a Monte Carlo technique by means of simulative particles following classical trajectories, in complete analogy to the “Weighted Monte Carlo” solution of the Boltzmann equation in the integral form.

The Wigner-function approach to non-equilibrium electron transport

“…Such an approach provides a very simple physical interpretation of the broadening of free wave-packets: contributions of higher momenta move faster than contributions with lower momenta. It has been shown numerically, and analytically for a Gaussian wave-packet, that also in the case of a particle hitting an infinite potential barrier, for times long enough after the scattering process, the evolution of the WF coincides with that of a classical distribution function [13] (see figure 2).…”

Wigner Function Simulations of Quantum Device-Circuit Interactions

“…In the one space-dimension case, the interaction is expressed through boundary condi-tions at the end of the device, not at ± °°. Indeed, as we will see some of the most important issues in examining barrier device transport involve dissipation 7 , the finite size of the domain and open boundaries 8 .…”