量子随机洛伦兹气体中的共振分布
Resonance distribution in the quantum random Lorentz gas
摘要：
考虑任意维量子粒子在由定点散射体组成的随机洛伦兹气体中的多重散射模型。本文提出了一种有效的方法来数值计算波数复平面内散射共振密度的分布图，而不需要逐个求出散射共振密度。该方法适用于两个碰撞模型的个人散射体，即共振模型，和非共振硬球模型。与前者所获得的结果进行了比较，文献。特别地，围绕单散射体共振的螺旋臂被识别为邻近共振。此外，硬球模型被用来揭示以前未知的结构中的共振密度。最后，它显示了如何安德森局域化影响的共振宽度的分布，特别是在一维的情况下。
英文摘要：
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of scattering resonances in the complex plane of the wavenumber without finding them one by one. The method is applied to two collision models for the individual scatterers, namely a resonant model, and a non-resonant hard-sphere model. The results obtained with the former are compared to the literature. In particular, the spiral arms surrounding the single-scatterer resonance are identified as proximity resonances. Moreover, the hard-sphere model is used to reveal previously unknown structures in the resonance density. Finally, it is shown how Anderson localization affects the distribution of resonance widths, especially in the one-dimensional case.
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