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. Preprints2020, 2020050180
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. Preprints2020, 2020050180
APA Style
Pandey, D., Oriols, X., & Albareda, G. (2020). Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations. Preprints. https://doi.org/
Chicago/Turabian Style
Pandey, D., Xavier Oriols and Guillermo Albareda. 2020 "Including Arbitrary Geometric Correlations into One-Dimensional Time-Dependent Schrödinger Equations" Preprints. https://doi.org/
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.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
