Real-Time Transport in Open Quantum Systems From $\mathcal{PT}$-Symmetric Quantum Mechanics

TL;DR

This paper introduces a novel approach to real-time quantum transport using $ ext{PT}$-symmetric potentials within RT-TDDFT, enabling dynamic simulation of open quantum systems with continuous particle flux.

Contribution

It proposes $ ext{PT}$-symmetric generating potentials to model open quantum transport, advancing RT-TDDFT methods for dynamic, real-time analysis.

Findings

$ ext{PT}$-symmetric potentials produce positive particle flux.

These potentials can generate continuous incident pulse trains.

The approach advances real-time quantum transport modeling.

Abstract

Nanoscale electronic transport is of intense technological interest, with applications ranging from semiconducting devices and molecular junctions to charge migration in biological systems. Most explicit theoretical approaches treat transport using a combination of density functional theory (DFT) and non-equilibrium Green's functions. This is a static formalism, with dynamic response properties accommodated only through complicated extensions. To circumvent this limitation, the carrier density may be propagated using real-time time-dependent DFT (RT-TDDFT), with boundary conditions corresponding to an open quantum system. Complex absorbing potentials can emulate outgoing particles at the simulation boundary, although these do not account for introduction of charge density. It is demonstrated that the desired positive particle flux is afforded by a class of $\mathcal{PT}$-symmetric generating potentials that are characterized by anisotropic transmission resonances. These potentials add density every time a particle traverses the cell boundary, and may be used to engineer a continuous pulse train for incident packets. This is a first step toward developing a complete transport formalism unique to RT-TDDFT.