### Abstract

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 FΓ_{0} (11) of the modular group. The fluxes through the holes are described by the even Dirichlet character for Γ_{0} (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.

Original language | English |
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Pages (from-to) | 4129-4141 |

Number of pages | 13 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 33 |

Issue number | 22 |

DOIs | |

Publication status | Published - Jun 9 2000 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)