非束缚量子粒子的吸收和分析--一一
Absorption and analysis of unbound quantum particles -- one by one
摘要：
在量子物理学中，对非束缚多体系统的理论研究通常是相当复杂的--这是由于它们的大空间扩展和所谓的{ \it维数灾难}的结合。通常，这样的系统是在截断的数值域上研究的--以丢失信息为代价。在这里，我们提出的方法来计算未结合的粒子受到一个{ \it复杂的吸收潜力}的微分概率。除了衰减出射波之外，该吸收体还用于通过投影到单粒子散射状态来探测它们，从而使多粒子散射状态的计算变得多余。在基于林德布拉德方程的形式主义内，通过解析第一次吸收后剩余粒子的动力学来获得来自后续吸收的单差光谱。虽然框架自然地推广到任何数量的粒子，明确的，紧凑的和直观的微分概率分布的表达式推导出两个粒子的情况下。该方法的适用性示出了涉及两个粒子模型系统的数值例子。这些例子，解决散射和光电离，演示了如何可以确定未结合粒子的能量分布上的数值域远远小于系统的实际扩展。
英文摘要：
In quantum physics, the theoretical study of unbound many-body systems is typically quite complex -- owing to the combination of their large spatial extension and the so-called {\it curse of dimensionality}. Often, such systems are studied on truncated numerical domains -- at the cost of losing information. Here we present methods for calculating differential probabilities for unbound particles which are subjected to a {\it complex absorbing potential}. In addition to attenuating outgoing waves, this absorber is also used to probe them by projection onto single-particle scattering states, thus rendering the calculation of multi-particle scattering states superfluous. Within formalism based on the Lindblad equation, singly differential spectra from subsequent absorptions are obtained by resolving the dynamics of the remaining particles after the first absorption. While the framework generalizes naturally to any number of particles, explicit, compact and intuitive expressions for the differential probability distributions are derived for the two-particle case. The applicability of the method is illustrated by numerical examples involving two-particle model-systems. These examples, which address scattering and photo ionization, demonstrate how energy distributions of unbound particles may be determined on numerical domains considerably smaller than the actual extension of the system.
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