Quantum states without time-reversal symmetry: wavefront dislocations in a non-integrable Aharonov-Bohm billiard

M V Berry, M Robnik
1986 Journal of Physics A: Mathematical and General  
We display complex wavefunctions (G; for the jth eigenstate of a particle moving freely in a domain Ec (whose reflecting boundary gives classically chaotic motion) threaded by a single line of magnetic flux whose strength (in quantum units) is a. The wavefronts (phase contours of ICJ) show the expected dislocation singularities both away from the flux line (where their strength is *l) and at the flux line (where the strength is the integer closest to a). $s shows two dislocations away from the
more » ... lux line for all a, and the birth of a dislocation at the flux line as a passes the value 4. &, shows 43 dislocations, in reasonable agreement with a semiclassical theory based on regarding IL, as a complex Gaussian random function, which predicts X dislocations in the asymptotic limit N + Co.
doi:10.1088/0305-4470/19/8/018 fatcat:ivoagso2b5dz7eg2fkfsk6bmn4