A new approach to modelling quantum distributions and quantum trajectories for density matrix and Green function simulation of nano-devices

Abstract

In this paper we present a new formalism for quantum transport distribution functions based on density matrices and non-equilibrium Green's functions that have practical computational advantages and better interpretive power than Wigner function and other phase-space distributions that rely on the centre-relative construction thus leading to non-compact support on phase-space. The new approach uses a mixed position-momentum basis and has manifest compact support in phase space, proving detailed accounting for nodal regions in both position and momentum. The relevant equations of motion and possible computational schemes are discussed within exactly soluble models that illustrate the formalism and its interpretation. The near-classical limit is easily obtained and lends itself to pathvariable iterative methods including Monte Carlo schemes. The new distribution functions are complex valued and lead to coupled drift-diffusion style equations of motion. The methodology is compared with Wigner functions, density gradient and Bohm trajectory methods.

A review of quantum transport in field-effect transistors

“…But a path integral equation can be constructed from the equation of motion for the density matrix, and this serves as the basis for developing a Monte Carlo procedure. More importantly, this procedure is not limited to just the lowest-order scattering processes [235]. General Monte Carlo techniques coupled with the density matrix have been discussed by Jacoboni [236].…”