Geodesic
Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller potentials
Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 840-852

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DOI

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.
DOI : 10.4153/S0008439520000879
Mots-clés : Supersymmetric quantum mechanics, Pöschl-Teller potentials, autocorrelation functions, Jacobi theta functions, homogenous dynamics, equidistribution of horocycle lifts 
Cellarosi, Francesco. Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller potentials. Canadian mathematical bulletin, Tome 64 (2021) no. 4, pp. 840-852. doi: 10.4153/S0008439520000879
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     author = {Cellarosi, Francesco},
     title = {Autocorrelation functions for quantum particles in supersymmetric {P\"oschl-Teller} potentials},
     journal = {Canadian mathematical bulletin},
     pages = {840--852},
     year = {2021},
     volume = {64},
     number = {4},
     doi = {10.4153/S0008439520000879},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000879/}
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