  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.
