Higher rank quantum-classical correspondence

J. Hilgert, T. Weich, L.L. Wolf, ArXiv:2103.05667 (2021).

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For a compact Riemannian locally symmetric space $\Gamma\backslash G/K$ of arbitrary rank we determine the location of certain Ruelle-Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle-Taylor resonances and establish a spectral gap which is uniform in $\Gamma$ if $G/K$ is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e. a 1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on $G/K$.
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Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. arXiv:210305667. Published online 2021.
Hilgert, J., Weich, T., & Wolf, L. L. (2021). Higher rank quantum-classical correspondence. In arXiv:2103.05667.
@article{Hilgert_Weich_Wolf_2021, title={Higher rank quantum-classical correspondence}, journal={arXiv:2103.05667}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2021} }
Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” ArXiv:2103.05667, 2021.
J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” arXiv:2103.05667. 2021.
Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” ArXiv:2103.05667, 2021.


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