Working Paper Article Version 1 This version is not peer-reviewed

Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations

Version 1 : Received: 9 May 2020 / Approved: 10 May 2020 / Online: 10 May 2020 (17:59:42 CEST)

How to cite: Pandey, D.; Oriols, X.; Albareda, G. Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations. Preprints 2020, 2020050180 Pandey, D.; Oriols, X.; Albareda, G. Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations. Preprints 2020, 2020050180

Abstract

The so-called Born-Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows to effectively separate fast and slow degrees of freedom and thus treating electrons and nuclei at different mathematical footings. Here we consider the use of a Born-Huang-like expansion of the three-dimensional time-dependent Schr\"odinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a prototypical two-dimensional constriction.

Subject Areas

nanojunction; constriction; quantum electron transport; quantum confinement; dimensionality reduction, stochastic Schrödinger equations; geometric correlations

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