We consider autocorrelation functions for supersymmetric quantum mechanical systems (consisting of a fermion and a boson) confined in trigonometric Pöschl–Teller partner potentials. We study the limit of rescaled autocorrelation functions (at random time) as the localization of the initial state goes to infinity. The limiting distribution can be described using pairs of Jacobi theta functions on a suitably defined homogeneous space, as a corollary of the work of Cellarosi and Marklof. A construction by Contreras-Astorga and Fernández provides large classes of Pöschl-Teller partner potentials to which our analysis applies.

我们考虑限制在三角波施尔-泰勒伙伴势中的超对称量子力学系统（由费米子和玻色子组成）的自相关函数。随着初始状态的定位趋于无穷大，我们研究了重新缩放的自相关函数（在随机时间）的极限。作为 Cellarosi 和 Marklof 工作的推论，可以在适当定义的齐次空间上使用成对的 Jacobi theta 函数来描述极限分布。Contreras-Astorga 和 Fernández 的构建提供了大量 Pöschl-Teller 合作伙伴潜力，我们的分析适用于这些潜力。