[{"status":"public","publisher":"Oxford University Press (OUP)","_id":"53416","page":"8225-8296","volume":2021,"user_id":"70575","citation":{"mla":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, Oxford University Press (OUP), 2019, pp. 8225–96, doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","bibtex":"@article{Küster_Weich_2019, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2019}, pages={8225–8296} }","ama":"Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>. 2019;2021(11):8225-8296. doi:<a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>","ieee":"B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” <i>International Mathematics Research Notices</i>, vol. 2021, no. 11, pp. 8225–8296, 2019, doi: <a href=\"https://doi.org/10.1093/imrn/rnz068\">10.1093/imrn/rnz068</a>.","apa":"Küster, B., &#38; Weich, T. (2019). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. <i>International Mathematics Research Notices</i>, <i>2021</i>(11), 8225–8296. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>","short":"B. Küster, T. Weich, International Mathematics Research Notices 2021 (2019) 8225–8296.","chicago":"Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” <i>International Mathematics Research Notices</i> 2021, no. 11 (2019): 8225–96. <a href=\"https://doi.org/10.1093/imrn/rnz068\">https://doi.org/10.1093/imrn/rnz068</a>."},"author":[{"last_name":"Küster","first_name":"Benjamin","full_name":"Küster, Benjamin"},{"orcid":"0000-0002-9648-6919","first_name":"Tobias","last_name":"Weich","full_name":"Weich, Tobias","id":"49178"}],"publication_identifier":{"issn":["1073-7928","1687-0247"]},"title":"Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces","year":"2019","intvolume":"      2021","publication_status":"published","date_updated":"2024-04-11T12:36:33Z","language":[{"iso":"eng"}],"doi":"10.1093/imrn/rnz068","issue":"11","publication":"International Mathematics Research Notices","abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n               <jats:p>For a compact Riemannian locally symmetric space $\\mathcal M$ of rank 1 and an associated vector bundle $\\mathbf V_{\\tau }$ over the unit cosphere bundle $S^{\\ast }\\mathcal M$, we give a precise description of those classical (Pollicott–Ruelle) resonant states on $\\mathbf V_{\\tau }$ that vanish under covariant derivatives in the Anosov-unstable directions of the chaotic geodesic flow on $S^{\\ast }\\mathcal M$. In particular, we show that they are isomorphically mapped by natural pushforwards into generalized common eigenspaces of the algebra of invariant differential operators $D(G,\\sigma )$ on compatible associated vector bundles $\\mathbf W_{\\sigma }$ over $\\mathcal M$. As a consequence of this description, we obtain an exact band structure of the Pollicott–Ruelle spectrum. Further, under some mild assumptions on the representations $\\tau$ and $\\sigma$ defining the bundles $\\mathbf V_{\\tau }$ and $\\mathbf W_{\\sigma }$, we obtain a very explicit description of the generalized common eigenspaces. This allows us to relate classical Pollicott–Ruelle resonances to quantum eigenvalues of a Laplacian in a suitable Hilbert space of sections of $\\mathbf W_{\\sigma }$. Our methods of proof are based on representation theory and Lie theory.</jats:p>"}],"date_created":"2024-04-11T12:33:46Z","department":[{"_id":"548"}],"keyword":["General Mathematics"],"type":"journal_article"}]