Aharonov-Bohm Effect for Electron Phase Representing a Quantum Mechanical Average Value

Details Aharonov-Bohm Effect for Electron Phase Representing a Quantum Mechanical Average Value Aharonov-Bohm Effect for Electron Phase Representing a Quantum Mechanical Average Value

2010-07-15

arxiv.org/abs/1007.2538v1

Physics

Quantum Physics

5 pages, no figures

Scientific paper

In the usual Aharonov-Bohm effect, representing an especial case of the Berry phase phenomenon, classical magnetic field within long and thin solenoid (or classical vector potential of the electromagnetic field without this solenoid) causes phase difference and interference shape translation of the quantum propagating (external) electron. In this work we consider a variation of the usual Aharonov-Bohm effect with two solenoids sufficiently close one to the other so that (external) electron cannot propagate between two solenoids but only around both solenoids. Here magnetic field (or classical vector potential of the electromagnetic field) acting at quantum propagating (external) electron represents the quantum mechanical average value or statistical mixture. It is obtained by wave function of single (internal, quantum propagating within some solenoid wire) electron (or homogeneous ensemble of such (internal) electrons) representing a quantum superposition with two practically non-interfering terms. All this implies that phase difference and interference shape translation of the quantum propagating (external) electron represent the quantum mechanical average value or statistical mixture. In this way we obtain a very interesting generalization of the usual Aharonov-Bohm effect and Berry phase concept.

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