Semiclassical formulae For Wigner distributions

P. Schütte, S. Barkhofen, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).

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Journal Article | English
Abstract
In this paper we give an overview over some aspects of the modern mathematical theory of Ruelle resonances for chaotic, i.e. uniformly hyperbolic, dynamical systems and their implications in physics. First we recall recent developments in the mathematical theory of resonances, in particular how invariant Ruelle distributions arise as residues of weighted zeta functions. Then we derive a correspondence between weighted and semiclassical zeta functions in the setting of negatively curved surfaces. Combining this with results of Hilgert, Guillarmou and Weich yields a high frequency interpretation of invariant Ruelle distributions as quantum mechanical matrix coefficients in constant negative curvature. We finish by presenting numerical calculations of phase space distributions in the more physical setting of 3-disk scattering systems.
Publishing Year
Journal Title
Journal of Physics A: Mathematical and Theoretical
Volume
55
Issue
24
Article Number
244007
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Schütte P, Barkhofen S, Weich T. Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b
Schütte, P., Barkhofen, S., & Weich, T. (2022). Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical, 55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b
@article{Schütte_Barkhofen_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b}, number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd}, author={Schütte, Philipp and Barkhofen, Sonja and Weich, Tobias}, year={2022} }
Schütte, Philipp, Sonja Barkhofen, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical 55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.
P. Schütte, S. Barkhofen, and T. Weich, “Semiclassical formulae For Wigner distributions,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.
Schütte, Philipp, et al. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.

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