Aharonov-Bohm and other Cyclic Phenomena

Yakir Aharonov

Barry R. Holstein

The subject of anholonomy in physics has recently been emphasized via discussions of the Berry phase. A particular example of this phenomenon, which does not require the adiabatic condition is the familiar Aharonov-Bohm (AB) effect. We herein review the AB effect and show that two additional phenomena, namely the Aharonov-Casher effect and rotating superconducting quantum interference device systems, can be analysed using identical mathematical frameworks.

Myron Evans, Jean Pierre Vigier

David K. Ferry

Apostol Vourdas

A unified approach to Aharonov-Bohm, Aharonov-Casher and which-path experiments is presented, using an enlarged Hilbert space. This Hilbert space contains quasi-periodic Aharonov-Bohm wavefunctions R ( x +2 ) = R ( x )exp(i ) with various values of . Thus it can describe which-path Aharonov-Bohm experiments where the phase is uncertain due to decoherence that occurs as a result of the observation of the paths of the electric charges. The same Hilbert space contains quasi-periodic Aharonov-Casher wavefunctions which describe magnetic flux tubes winding around an electric charge and which are related through a Fourier transform to the Aharonov-Bohm wavefunctions. The duality between these two phenomena is discussed. The decoherence occuring in which-path experiments is studied quantitatively. Magnetic and electric superselection rules, appropriate for the Aharonov-Bohm and Aharonov-Casher experiments correspondingly, are also discussed.