Wavefront dislocations in the Aharonov-Bohm effect and its water wave analogue

摘要: The authors study the wavefronts (i.e. surfaces of constant phase) wave discussed by Aharonov and Bohm, representing a beam particles with charge q scattered an impenetrable cylinder radius R containing magnetic flux Phi . Defining quantum parameter alpha =q /h, they show that for case R=0 psi AB possesses wavefront dislocation on line, whose strength number crests ending dislocation) equals nearest integer to When passes through half-integer values, changes, unlinking reconnecting along nodal surface. In mechanics this phase structure is unobservable, but devise analogue where surface waves water encounter irrotational 'bathtub' vortex; in depends frequency circulation vortex. Experiments structures agreeing those predicted. unusual function which incident cannot be clearly separated all asymptotic directions; discuss its properties using new method.