Autocorrelation functions for quantum particles in supersymmetric P\"oschl-Teller Potentials

We consider autocorrelation functions for supersymmetric quantum mechanical systems (consisting of a fermion and a boson) confined in trigonometric P\"oschl-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 Fern\'andez provides large classes of P\"oschl-Teller partner potentials to which our analysis applies.