A Deterministic Solution of the Wigner Transport Equation with Infinite Correlation Length

TL;DR

This paper introduces a deterministic approach to solving the Wigner transport equation with infinite correlation length, enabling precise quantum transport simulations without uncertainty from finite integral ranges.

Contribution

It presents a novel formulation and numerical solution method for the Wigner transport equation with infinite correlation length, improving simulation accuracy and convergence.

Findings

Achieved stable and accurate quantum transport simulations.

Demonstrated excellent convergence with the coupled Newton-Raphson scheme.

Enabled steady state and transient analysis without integral range limitations.

Abstract

We propose a new formulation of the Wigner transport equation with infinite correlation length. Since the maximum correlation length is not limited to a finite value, there is no uncertainty in the simulation results owing to the finite integral range of the nonlocal potential term. For general and efficient simulation, the WTE is solved self-consistently with the Poisson equation through the finite volume method and the fully coupled Newton-Raphson scheme. Through this, we implemented a quantum transport steady state and transient simulator with excellent convergence.