量子随机Lorentz气体的多重散射模型
Multiple scattering model of the quantum random Lorentz gas
摘要：
在任意维的欧氏空间中，建立了量子粒子与随机洛伦兹气体相互作用的多重散射模型。在模型的核心部分，详细推导了点散射体的散射振幅，并用散射长度表示。计算了该模型的截面和散射矩阵等基本性质。此外，该模型是为了验证光学定理，从而概率守恒。最后，数值计算了Lorentz气体小于和大于平均自由程两种情况下的微分截面和总截面，得到了散射体数目足够多时的Airy衍射峰。这一发现与灭绝悖论有关。
英文摘要：
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point scatterers is derived in detail, and expressed in terms of the scattering length. The fundamental properties of the model, such as the cross section and the scattering matrix, are calculated. In addition, the model is shown to verify the optical theorem and thus probability conservation. Finally, the differential and total cross sections are numerically computed in two situations whether the Lorentz gas is smaller or larger than the mean free path. A distinct Airy diffraction peak is obtained for a large enough number of scatterers. This observation is related to the extinction paradox.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
