论文标题
二维波散射中对称性的非本地无分流电流
Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering
论文作者
论文摘要
假设相应的电势在线性对称性变换（例如旋转，反射和坐标交换）下是不变的，那么我们探索了两个空间维度的波动机械散射。通常，渐近散射条件不尊重电势的对称性，并且没有系统的方法可以预先确定它们在散射波场上的印记。在这里，我们表明对称性诱导的非本地，无差异电流可能是描述对称性对较高维波散射的后果的有用工具，重点是二维情况。这些非局部电流消失的差异的条件与散射势中对称性的存在一对一，如果散射溶液中的对称性，则为对称性提供了一个系统的途径。它导致对散射过程的描述，该过程在整个空间（包括近场制度）中有效。此外，我们认为散射波函数的通常渐近表示不能说明对潜在对称性的正确描述。在我们的方法中，我们在波场在二维中相对于角动量基础的系数膨胀的对称条件，这确定了不同角动量状态之间的过渡概率。
We explore wave-mechanical scattering in two spatial dimensions assuming that the corresponding potential is invariant under linear symmetry transforms such as rotations, reflections and coordinate exchange. Usually the asymptotic scattering conditions do not respect the symmetries of the potential and there is no systematic way to predetermine their imprint on the scattered wave field. Here we show that symmetry induced, non-local, divergence-free currents can be a useful tool for the description of the consequences of symmetries on higher dimensional wave scattering, focusing on the two-dimensional case. The condition of a vanishing divergence of these non-local currents, being in one-to-one correspondence with the presence of a symmetry in the scattering potential, provides a systematic pathway to to take account if the symmetries in the scattering solution. It leads to a description of the scattering process which is valid in the entire space including the near field regime. Furthermore, we argue that the usual asymptotic representation of the scattering wave function does not account for insufficient account for a proper description of the underlying potential symmetries. Within our approach we derive symmetry induced conditions for the coefficients in the wave field expansion with respect to the angular momentum basis in two dimensions, which determine the transition probabilities between different angular momentum states.
