Interplay of Aharonov-Bohm and Berry phases

Topological phases can arise as a system undergoes a cyclic motion. The phase accumulated by a charge encircling a magnet ic fluxon is the A h a r o n o v B o h m (AB) effect [ 1 ] (AB) , or, for a magnetic moment encircling a line of charge, the A h a r o n o v C a s h e r (AC) effect [2] . Cyclic mot ion of a state in Hi lber t space can also give rise to the Berry phase [3] . The lat ter phase may be dis t inguished from the AB and the AC phases. While the AB (or AC) phase appears in the Hami l ton ian of any physical system containing a fluxon and a poin t charge (or a magnet ic moment and a line of charge), the Berry phase applies only in the adiabat ic l imit , i.e. if the system includes "heavy" degrees of f reedom whose mot ion can be regarded as adiabat ic . Our purpose is to draw at tent ion to an interplay o f the AB (or AC) phase and the Berry phase. It occurs in a charge-f luxon system when the charge (or f luxon) is in the ground state o f some potent ia l and its locat ion is therefore smeared. The interplay of the phases is manifested as the heavy fluxon goes through the "c loud" of charge. As will be shown below, in this case, the mot ion of the fluxon induces adiabat ic modif ica t ions in the ground state which leads to a Berry phase complement ing the AC phase collected