A topological model of the Aharonov-Bohm scattering is presented, where the usual set-up is modelled by a genus-one Riemann surface with two cusps, i.e. leaks infinitely far away. This constant negative-curvature surface is uniformized by the Hecke congruence subgroup FΓ0 (11) of the modular group. The fluxes through the holes are described by the even Dirichlet character for Γ0 (11). The scattering matrix having only off-diagonal elements (no reflection) is calculated. The fluctuating part of the off-diagonal entries shows a non-trivial dependence on the fluxes as well. The scattering resonances are related to the non-trivial zeros of a Dirichlet L-function. The chaotic nature of the scattering is related to the distribution of primes in arithmetical progressions.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)