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

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Abstract
The authors display complex wavefunctions psi j for the jth eigenstate of a particle moving freely in a domain D (whose reflecting boundary gives classically chaotic motion) threaded by a single line of magnetic flux whose strength (in quantum units) is alpha . The wavefronts (phase contours of psi j) show the expected dislocation singularities both away from the flux line (where their strength is +or-1) and at the flux line (where the strength is the integer closest to alpha ). psi 5 shows two dislocations away from the flux line for all alpha , and the birth of a dislocation at the flux line as alpha passes the value 1/2. psi 50 shows 43 dislocations, in reasonable agreement with a semiclassical theory based on regarding psi N as a complex Gaussian random function, which predicts N dislocations in the asymptotic limit N to infinity .

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