Absorption and Injection Models for Open Time-Dependent Quantum Systems

TL;DR

This paper introduces a model that significantly reduces computational costs in simulating open time-dependent quantum systems by leveraging superposition, analytical free evolution, and absorbing layers, applicable to various quantum transport scenarios.

Contribution

The paper presents a novel modeling approach that decreases computational burden by two orders of magnitude for simulating open quantum systems, applicable to multiple equations and research fields.

Findings

Reduction of computational burden by about two orders of magnitude per spatial dimension.

Negligible error introduced by the model.

Applicable to Schrödinger and tight-binding equations.

Abstract

In the time-dependent simulation of pure states dealing with transport in open quantum systems, the initial state is located outside of the active region of interest. Using the superposition principle and the analytical knowledge of the free time-evolution of such state outside the active region, together with absorbing layers and remapping, a model for a very significant reduction of the computational burden associated to the numerical simulation of open time-dependent quantum systems is presented. The model is specially suited to study (many-particle and high-frequency effects) quantum transport, but it can also be applied to any other research field where the initial time-dependent pure state is located outside of the active region. From numerical simulations of open quantum systems described by the (effective mass) Schr\"{o}dinger and (atomistic) tight-binding equations, a reduction of the computational burden of about two orders of magnitude for each spatial dimension of the domain with a negligible error is presented.