[{"language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"51204","external_id":{"arxiv":["2402.02530"]},"status":"public","abstract":[{"text":"Given a real semisimple connected Lie group $G$ and a discrete torsion-free\r\nsubgroup $\\Gamma < G$ we prove a precise connection between growth rates of the\r\ngroup $\\Gamma$, polyhedral bounds on the joint spectrum of the ring of\r\ninvariant differential operators, and the decay of matrix coefficients. In\r\nparticular, this allows us to completely characterize temperedness of\r\n$L^2(\\Gamma\\backslash G)$ in this general setting.","lang":"eng"}],"publication":"Duke Math. Journal ","type":"journal_article","title":"Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces","volume":"(to appear)","date_created":"2024-02-06T20:35:36Z","author":[{"last_name":"Lutsko","full_name":"Lutsko, Christopher","first_name":"Christopher"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"orcid":"0000-0001-8893-2045","last_name":"Wolf","id":"45027","full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart"}],"date_updated":"2026-02-18T10:37:47Z","citation":{"apa":"Lutsko, C., Weich, T., &#38; Wolf, L. L. (2026). Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. <i>Duke Math. Journal </i>, <i>(to appear)</i>.","bibtex":"@article{Lutsko_Weich_Wolf_2026, title={Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces}, volume={(to appear)}, journal={Duke Math. Journal }, author={Lutsko, Christopher and Weich, Tobias and Wolf, Lasse Lennart}, year={2026} }","short":"C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal  (to appear) (2026).","mla":"Lutsko, Christopher, et al. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>Duke Math. Journal </i>, vol. (to appear), 2026.","ama":"Lutsko C, Weich T, Wolf LL. Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces. <i>Duke Math Journal </i>. 2026;(to appear).","chicago":"Lutsko, Christopher, Tobias Weich, and Lasse Lennart Wolf. “Polyhedral Bounds on the Joint Spectrum and Temperedness of Locally  Symmetric Spaces.” <i>Duke Math. Journal </i> (to appear) (2026).","ieee":"C. Lutsko, T. Weich, and L. L. Wolf, “Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces,” <i>Duke Math. Journal </i>, vol. (to appear), 2026."},"year":"2026"},{"doi":"https://doi.org/10.1007/s10711-024-00904-4","title":"Temperedness of locally symmetric spaces: The product case","volume":218,"date_created":"2024-02-06T21:00:55Z","author":[{"orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"first_name":"Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","id":"45027","full_name":"Wolf, Lasse Lennart"}],"date_updated":"2024-05-07T11:44:34Z","intvolume":"       218","citation":{"ama":"Weich T, Wolf LL. Temperedness of locally symmetric spaces: The product case. <i>Geom Dedicata</i>. 2024;218. doi:<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>","ieee":"T. Weich and L. L. Wolf, “Temperedness of locally symmetric spaces: The product case,” <i>Geom Dedicata</i>, vol. 218, Art. no. 76, 2024, doi: <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>Geom Dedicata</i> 218 (2024). <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","apa":"Weich, T., &#38; Wolf, L. L. (2024). Temperedness of locally symmetric spaces: The product case. <i>Geom Dedicata</i>, <i>218</i>, Article 76. <a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>","short":"T. Weich, L.L. Wolf, Geom Dedicata 218 (2024).","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Temperedness of Locally Symmetric Spaces: The Product Case.” <i>Geom Dedicata</i>, vol. 218, 76, 2024, doi:<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>.","bibtex":"@article{Weich_Wolf_2024, title={Temperedness of locally symmetric spaces: The product case}, volume={218}, DOI={<a href=\"https://doi.org/10.1007/s10711-024-00904-4\">https://doi.org/10.1007/s10711-024-00904-4</a>}, number={76}, journal={Geom Dedicata}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2024} }"},"year":"2024","language":[{"iso":"eng"}],"article_number":"76","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"45027","_id":"51207","external_id":{"arxiv":["2304.09573"]},"status":"public","abstract":[{"lang":"eng","text":"Let $X=X_1\\times X_2$ be a product of two rank one symmetric spaces of\r\nnon-compact type and $\\Gamma$ a torsion-free discrete subgroup in $G_1\\times\r\nG_2$. We show that the spectrum of $\\Gamma \\backslash X$ is related to the\r\nasymptotic growth of $\\Gamma$ in the two direction defined by the two factors.\r\nWe obtain that $L^2(\\Gamma \\backslash G)$ is tempered for large class of\r\n$\\Gamma$."}],"publication":"Geom Dedicata","type":"journal_article"},{"date_created":"2024-03-26T08:52:05Z","author":[{"last_name":"Arends","id":"43994","full_name":"Arends, Christian","first_name":"Christian"},{"first_name":"Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","id":"45027","full_name":"Wolf, Lasse Lennart"},{"first_name":"Jasmin","last_name":"Meinecke","full_name":"Meinecke, Jasmin"},{"last_name":"Barkhofen","full_name":"Barkhofen, Sonja","id":"48188","first_name":"Sonja"},{"full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"last_name":"Bartley","full_name":"Bartley, Tim","id":"49683","first_name":"Tim"}],"volume":6,"date_updated":"2025-12-04T13:38:49Z","publisher":"American Physical Society (APS)","doi":"10.1103/physrevresearch.6.l012043","title":"Decomposing large unitaries into multimode devices of arbitrary size","issue":"1","publication_status":"published","publication_identifier":{"issn":["2643-1564"]},"citation":{"chicago":"Arends, Christian, Lasse Lennart Wolf, Jasmin Meinecke, Sonja Barkhofen, Tobias Weich, and Tim Bartley. “Decomposing Large Unitaries into Multimode Devices of Arbitrary Size.” <i>Physical Review Research</i> 6, no. 1 (2024). <a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">https://doi.org/10.1103/physrevresearch.6.l012043</a>.","ieee":"C. Arends, L. L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, and T. Bartley, “Decomposing large unitaries into multimode devices of arbitrary size,” <i>Physical Review Research</i>, vol. 6, no. 1, Art. no. L012043, 2024, doi: <a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">10.1103/physrevresearch.6.l012043</a>.","ama":"Arends C, Wolf LL, Meinecke J, Barkhofen S, Weich T, Bartley T. Decomposing large unitaries into multimode devices of arbitrary size. <i>Physical Review Research</i>. 2024;6(1). doi:<a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">10.1103/physrevresearch.6.l012043</a>","mla":"Arends, Christian, et al. “Decomposing Large Unitaries into Multimode Devices of Arbitrary Size.” <i>Physical Review Research</i>, vol. 6, no. 1, L012043, American Physical Society (APS), 2024, doi:<a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">10.1103/physrevresearch.6.l012043</a>.","bibtex":"@article{Arends_Wolf_Meinecke_Barkhofen_Weich_Bartley_2024, title={Decomposing large unitaries into multimode devices of arbitrary size}, volume={6}, DOI={<a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">10.1103/physrevresearch.6.l012043</a>}, number={1L012043}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Arends, Christian and Wolf, Lasse Lennart and Meinecke, Jasmin and Barkhofen, Sonja and Weich, Tobias and Bartley, Tim}, year={2024} }","short":"C. Arends, L.L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, T. Bartley, Physical Review Research 6 (2024).","apa":"Arends, C., Wolf, L. L., Meinecke, J., Barkhofen, S., Weich, T., &#38; Bartley, T. (2024). Decomposing large unitaries into multimode devices of arbitrary size. <i>Physical Review Research</i>, <i>6</i>(1), Article L012043. <a href=\"https://doi.org/10.1103/physrevresearch.6.l012043\">https://doi.org/10.1103/physrevresearch.6.l012043</a>"},"intvolume":"         6","year":"2024","user_id":"48188","department":[{"_id":"623"},{"_id":"15"}],"_id":"52876","language":[{"iso":"eng"}],"article_number":"L012043","keyword":["General Physics and Astronomy"],"type":"journal_article","publication":"Physical Review Research","status":"public"},{"publication":"Communications in Mathematical Physics","type":"journal_article","abstract":[{"text":"Given a geometrically finite hyperbolic surface of infinite volume it is a\r\nclassical result of Patterson that the positive Laplace-Beltrami operator has\r\nno $L^2$-eigenvalues $\\geq 1/4$. In this article we prove a generalization of\r\nthis result for the joint $L^2$-eigenvalues of the algebra of commuting\r\ndifferential operators on Riemannian locally symmetric spaces $\\Gamma\\backslash\r\nG/K$ of higher rank. We derive dynamical assumptions on the $\\Gamma$-action on\r\nthe geodesic and the Satake compactifications which imply the absence of the\r\ncorresponding principal eigenvalues. A large class of examples fulfilling these\r\nassumptions are the non-compact quotients by Anosov subgroups.","lang":"eng"}],"status":"public","external_id":{"arxiv":["2205.03167"]},"_id":"31189","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"user_id":"49178","language":[{"iso":"eng"}],"publication_identifier":{"unknown":["1275-1295"]},"year":"2023","intvolume":"       403","citation":{"ama":"Weich T, Wolf LL. Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>. 2023;403. doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","ieee":"T. Weich and L. L. Wolf, “Absence of principal eigenvalues for higher rank locally symmetric  spaces,” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","chicago":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i> 403 (2023). <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>.","apa":"Weich, T., &#38; Wolf, L. L. (2023). Absence of principal eigenvalues for higher rank locally symmetric  spaces. <i>Communications in Mathematical Physics</i>, <i>403</i>. <a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>","bibtex":"@article{Weich_Wolf_2023, title={Absence of principal eigenvalues for higher rank locally symmetric  spaces}, volume={403}, DOI={<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>}, journal={Communications in Mathematical Physics}, author={Weich, Tobias and Wolf, Lasse Lennart}, year={2023} }","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","mla":"Weich, Tobias, and Lasse Lennart Wolf. “Absence of Principal Eigenvalues for Higher Rank Locally Symmetric  Spaces.” <i>Communications in Mathematical Physics</i>, vol. 403, 2023, doi:<a href=\"https://doi.org/10.1007/s00220-023-04819-1\">https://doi.org/10.1007/s00220-023-04819-1</a>."},"date_updated":"2024-02-06T20:52:40Z","volume":403,"date_created":"2022-05-11T10:38:11Z","author":[{"full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"last_name":"Wolf","full_name":"Wolf, Lasse Lennart","id":"45027","first_name":"Lasse Lennart"}],"title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","doi":"https://doi.org/10.1007/s00220-023-04819-1"},{"department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"user_id":"49178","_id":"31190","status":"public","type":"journal_article","doi":"https://doi.org/10.2140/apde.2023.16.2241","volume":16,"author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias","first_name":"Tobias"},{"id":"45027","full_name":"Wolf, Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","first_name":"Lasse Lennart"}],"date_updated":"2026-02-18T10:39:36Z","page":"2241–2265","intvolume":"        16","citation":{"ieee":"J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, pp. 2241–2265, 2023, doi: <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","chicago":"Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i> 16, no. 10 (2023): 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","ama":"Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>. 2023;16(10):2241–2265. doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>","short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 2241–2265.","bibtex":"@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, DOI={<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>}, number={10}, journal={Analysis &#38; PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }","mla":"Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” <i>Analysis &#38; PDE</i>, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:<a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>.","apa":"Hilgert, J., Weich, T., &#38; Wolf, L. L. (2023). Higher rank quantum-classical correspondence. <i>Analysis &#38; PDE</i>, <i>16</i>(10), 2241–2265. <a href=\"https://doi.org/10.2140/apde.2023.16.2241\">https://doi.org/10.2140/apde.2023.16.2241</a>"},"language":[{"iso":"eng"}],"external_id":{"arxiv":["2103.05667"]},"abstract":[{"text":"For a compact Riemannian locally symmetric space $\\Gamma\\backslash G/K$ of\r\narbitrary rank we determine the location of certain Ruelle-Taylor resonances\r\nfor the Weyl chamber action. We provide a Weyl-lower bound on an appropriate\r\ncounting function for the Ruelle-Taylor resonances and establish a spectral gap\r\nwhich is uniform in $\\Gamma$ if $G/K$ is irreducible of higher rank. This is\r\nachieved by proving a quantum-classical correspondence, i.e. a\r\n1:1-correspondence between horocyclically invariant Ruelle-Taylor resonant\r\nstates and joint eigenfunctions of the algebra of invariant differential\r\noperators on $G/K$.","lang":"eng"}],"publication":"Analysis & PDE","title":"Higher rank quantum-classical correspondence","date_created":"2022-05-11T10:41:35Z","publisher":"MSP","year":"2023","issue":"10"},{"abstract":[{"text":"The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $M$\r\nis a stochastic process that models a random perturbation of the geodesic flow.\r\nIf $M$ is a orientable compact constant negatively curved surface, we show that\r\nin the limit of infinitely large perturbation the $L^2$-spectrum of the\r\ninfinitesimal generator of a time rescaled version of the process converges to\r\nthe Laplace spectrum of the base manifold. In addition, we give explicit error\r\nestimates for the convergence to equilibrium. The proofs are based on\r\nnoncommutative harmonic analysis of $SL_2(\\mathbb{R})$.","lang":"eng"}],"status":"public","type":"preprint","publication":"arXiv:1909.06183","language":[{"iso":"eng"}],"_id":"31191","external_id":{"arxiv":["1909.06183"]},"user_id":"45027","department":[{"_id":"548"}],"year":"2019","citation":{"mla":"Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>, 2019.","short":"M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019).","bibtex":"@article{Kolb_Weich_Wolf_2019, title={Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces}, journal={arXiv:1909.06183}, author={Kolb, Martin and Weich, Tobias and Wolf, Lasse Lennart}, year={2019} }","apa":"Kolb, M., Weich, T., &#38; Wolf, L. L. (2019). Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. In <i>arXiv:1909.06183</i>.","ama":"Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. <i>arXiv:190906183</i>. Published online 2019.","ieee":"M. Kolb, T. Weich, and L. L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces,” <i>arXiv:1909.06183</i>. 2019.","chicago":"Kolb, Martin, Tobias Weich, and Lasse Lennart Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” <i>ArXiv:1909.06183</i>, 2019."},"title":"Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces","date_updated":"2022-05-24T13:06:58Z","author":[{"first_name":"Martin","full_name":"Kolb, Martin","last_name":"Kolb"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"},{"first_name":"Lasse Lennart","last_name":"Wolf","full_name":"Wolf, Lasse Lennart","id":"45027"}],"date_created":"2022-05-11T10:42:11Z"}]