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Interplay of Aharonov‐Bohm and Berry Phases for a Quantum Cloud of Charge a
Author(s) -
POPESCU SANDU,
AHARONOV YAKIR,
COLEMAN SIDNEY,
GOLDHABER ALFRED S.,
NUSSINOV SHMUEL,
REZNIK BENNI,
ROHRLICH DANIEL,
VAIDMAN LEV
Publication year - 1995
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1995.tb39039.x
Subject(s) - tel aviv , physics , library science , computer science
The Aharonov-Bohm (AB) effect’ is simple and topological: an electron encircling a solenoid containing a magnetic flux @ acquires a geometrical phase equal to n e @ / k , where n is equal to the winding number of the electron around the solenoid. However, when a solenoid enters a quantum cloud of charge and there is no way to associate a well-defined path to the electron, the consequences of the AB effect might be complicated. For example, consider an electron bound in a potential well V, in an energy eigenstate. A solenoid crosses the well. How many times did the electron encircle the solenoid? There is no definite answer to this question. Of course, we can decompose the movement of the electron into a superposition of different Feynman paths, compute the phase acquired in each path, and resum, but no simple result will emerge. In general, the final state of the electron (once the solenoid has left the well) is different from the initial one (before the solenoid entered) and it depends on all the different parameters of the problem: the initial state, the potential V, the precise path of the solenoid and its velocity, and the value of the enclosed magnetic flux @. However, we have found a surprising topological effect for a solenoid containing exactly half a flux quantum [a = (%)ao = ( 1 / ) 2 ~ h c / e ] when it adiabatically crosses the quantum “cloud” of an electron in a nondegenerate energy eigenstatef (see