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The London Edinburgh and Dublin Philosophical Magazine and Journal of Science

XLII.Wave functions and permeabilities for a new type of potential barrier

Ronald Percy Bell

Published Mar 1, 1938• 1 citation
Publisher
DOI
10.1080/14786443808562033

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Motions of particles through a permeable barrier are studied from the standpoint of Schrodinger wave dynamics. We consider time evolution of a substance concentration spot in the vicinity of one or two potential barriers. To solve the problem we developed a computer technology for integration of the non-stationary Schrödinger equation. The technology is based on symbol mapping and the matrix exponential method which was applied earlier to solve the classical heat equation. The developed theory is relevant to development of nanotechnology, in particular, to studies on permeability of nanoporous membranes.
A new mechanism for realizing negative permeability with a three-level ladder-type atomic (or molecular) system at microwave frequency is suggested. The explicit expressions for the magnetic permeability of both steady and transient cases are presented. Compared with the previous schemes to realize negative permeability within the framework of classical electromagnetic theory, the most remarkable feature in the present mechanism is that it can realize the isotropic material with negative permeability. Such a permeability can be controllably manipulated by external coupling fields and could lead to potential applications in quantum optical devices.
An approach for two-dimensional (2D) negative permeability in a Λ-type three-level atomic system interacting with a magnetic probe and the superposition of two orthogonal standing-wave fields is proposed. Through theoretical analysis and numerical simulation, two equally and tunable peak maxima of negative magnetic responses are observed in the x-y plane, and around the peak maxima region the negative permeability is isotropic. A new avenue to 2D isotropic negative permeability in isotropic applications, via the quantum optics method, is achieved in our scheme.