Schroedinger equation for current carrying states
Abstract
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization of the total energy on the manifold of an arbitrary current density topology results into a non-linear self-consistent Schr\"odinger equation. The applications to electronic transport in two-terminal molecular devices are developed and new macroscopic definition of a molecular current-voltage characteristic is proposed. The Landauer formula for the conductance of an ideal one-dimensional lead is obtained within the approach. The method is examined by modeling of current carrying states of one-dimensional harmonic oscillator.
Cite
@article{arxiv.cond-mat/0209347,
title = {Schroedinger equation for current carrying states},
author = {D. S. Kosov},
journal= {arXiv preprint arXiv:cond-mat/0209347},
year = {2009}
}