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International Workshop on Computational Electronics

Trajectory-based representations of quantum transport theory and their connection with semi-classical physics

J.R. Barker

Published Nov 27, 2002• 0 citations
Publisher

Abstract

It is argued that rigorous trajectory formulations of quantum transport phenomena are feasible and that trajectory based simulation methods corresponding to ensemble Monte Carlo methods or hydrodynamic modelling are possible provided the unavoidable accompanying pilot fields are included within the formalism.
DOI
10.1109/iwce.1998.742692

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The quantum trajectory method in the hydrodynamical formulation of Madelung-Bohm-Takabayasi quantum mechanics is an example of showing the cognitive importance of scientific illustrations and metaphors in computational quantum chemistry and electrical engineering. The method involves several numerical schemes of solving a set of hydrodynamical equations of motion for probability density fluids, based on the propagation of those probability density trajectories. The quantum trajectory method gives rise to, for example, an authentic quantum electron transport theory of motion to, among others, classically-minded applied scientists who probably have less of a commitment to traditional quantum mechanics. They were not the usual audience of quantum mechanics and simply choose to use a non-Copenhagen type interpretation to their advantage. Thus, the metaphysical issues physicists had a trouble with are not the main concern of the scientists. With the advantages of a visual and illustrative trajectory, the quantum theory of motion by Bohm effectively bridges quantum and classical physics, especially, in the mesoscale domain. Without having an abrupt shift in actions and beliefs from the classical to the quantum world, scientists and engineers are able to enjoy human cognitive capacities extended into the quantum mechanical domain.
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