Higher rank quantum-classical correspondence

J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265.

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Journal Article | English
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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Analysis & PDE

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Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. Analysis & PDE. 2023;16(10):2241–2265.
Hilgert, J., Weich, T., & Wolf, L. L. (2023). Higher rank quantum-classical correspondence. Analysis & PDE, 16(10), 2241–2265.
@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, number={10}, journal={Analysis & PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }
Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE 16, no. 10 (2023): 2241–2265.
J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” Analysis & PDE, vol. 16, no. 10, pp. 2241–2265, 2023.
Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE, vol. 16, no. 10, MSP, 2023, pp. 2241–2265.


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arXiv 2103.05667

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