Complex non-Hermitian Potentials and Real-Time Time-Dependent Density Functional Theory: A Master Equation Approach

TL;DR

This paper introduces a master equation approach that incorporates complex non-Hermitian potentials into real-time time-dependent density functional theory, enabling more accurate simulation of quantum transport in open, many-particle systems.

Contribution

It develops a novel framework linking non-Hermitian potentials with open quantum system dynamics within TDDFT, improving simulation of nonequilibrium steady states.

Findings

Equivalence between superoperators and non-Hermitian terms established.

Method allows convergence to steady states in quantum transport simulations.

Framework extends TDDFT to open systems with imaginary potentials.

Abstract

The simulation of quantum transport in a realistic, many-particle system is a nontrivial problem with no quantitatively satisfactory solution. While real-time propagation has the potential to overcome the shortcomings of conventional transport methods, this approach is prone to finite size effects that are associated with modeling an open system on a closed spatial domain. Using a master equation framework, we exploit an equivalence between the superoperators coupling an open system to external particle reservoirs and non-Hermitian terms defined at the periphery of a quantum device. By taking the mean-field limit, the equation of motion for the single-particle reduced density matrix becomes equivalent to real-time time-dependent density functional theory in the presence of imaginary source and sink potentials. This method may be used to converge nonequilibrium steady states for a many-body quantum system using a previously reported constraint algorithm.