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The so-called Born-Huang ansatz is a fundamental tool in the context ofab-initio molecular dynamics, viz., it allows to effectively separate fast andslow degrees of freedom and thus treating electrons and nuclei at differentmathematical footings. Here we consider the use of a Born-Huang-like expansionof the three-dimensional time-dependent Schr\"odinger equation to separatetransport and confinement degrees of freedom in electron transport problemsthat involve geometrical constrictions. The resulting scheme consists of aneigenstate problem for the confinement degrees of freedom (in the transversedirection) whose solution constitutes the input for the propagation of a set ofcoupled one-dimensional equations of motion for the transport degree of freedom(in the longitudinal direction). This technique achieves quantitative accuracyusing an order less computational resources than the full dimensionalsimulation for a prototypical two-dimensional constriction.

Including arbitrary geometric correlations into one-dimensional time-dependent Schr\"{o}dinger equations