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Autocorrelation functions for quantum particles in supersymmetric Pöschl-Teller potentials

Part of: Dynamical systems with hyperbolic behavior General mathematical topics and methods in quantum theory Discontinuous groups and automorphic forms Noncompact transformation groups Limit theorems Exponential sums and character sums

Published online by Cambridge University Press:  28 October 2020

Francesco Cellarosi
Francesco Cellarosi*
Affiliation:
Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, 48 University Avenue, Kingston, ON K7K 3N6, Canada
*
e-mail:fc19@queensu.ca
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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.

Keywords

Supersymmetric quantum mechanicsPöschl-Teller potentialsautocorrelation functionsJacobi theta functionshomogenous dynamicsequidistribution of horocycle lifts

MSC classification

Primary: 81Q60: Supersymmetry and quantum mechanics
Secondary: 81P40: Quantum coherence, entanglement, quantum correlations 60F05: Central limit and other weak theorems 11F27: Theta series; Weil representation; theta correspondences 11L15: Weyl sums 22F30: Homogeneous spaces 37D40: Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.)
Type
Article
Information
Canadian Mathematical Bulletin , Volume 64 , Issue 4 , December 2021 , pp. 840 - 852
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Copyright
© Canadian Mathematical Society 2020

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Footnotes

The author acknowledges the support of the NSERC Discovery Grant “Statistical and Number-Theoretical Aspects of Dynamical Systems”.

References

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