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首页> 外文期刊>Journal of Physics, A. Mathematical and General: A Europhysics Journal >Chaotic Aharonov-Bohm scattering on surfaces of constant negative curvature
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Chaotic Aharonov-Bohm scattering on surfaces of constant negative curvature

机译：恒定负曲率表面上的混沌Aharonov-Bohm散射

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摘要

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 Gamma(0)(11) of the modular group. The fluxes through the holes are described by the even Dirichlet character for Gamma(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. [References: 20]
机译：提出了Aharonov-Bohm散射的拓扑模型，其中通常的设置是通过一个具有两个尖点的1类Riemann曲面来建模的，即无限远的泄漏。该恒定的负曲率表面被模块化组的Hecke同余子组Gamma（0）（11）均匀化。通过孔的通量由Gamma（0）（11）的偶数Dirichlet字符描述。计算仅具有非对角线元素（无反射）的散射矩阵。非对角线入口的波动部分也显示出对通量的非平凡依赖。散射共振与Dirichlet L函数的非平凡零点有关。散射的混沌性质与算术级数中素数的分布有关。 [参考：20]

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