Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller potentials

Abstract

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 2020 Mathematics Subject Classification: 81Q60,