[{"publication":"Duke Math. Journal ","type":"journal_article","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"}],"status":"public","_id":"51204","external_id":{"arxiv":["2402.02530"]},"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","language":[{"iso":"eng"}],"year":"2026","citation":{"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} }","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.","short":"C. Lutsko, T. Weich, L.L. Wolf, Duke Math. Journal  (to appear) (2026).","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>.","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).","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.","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)."},"date_updated":"2026-02-18T10:37:47Z","volume":"(to appear)","date_created":"2024-02-06T20:35:36Z","author":[{"first_name":"Christopher","last_name":"Lutsko","full_name":"Lutsko, Christopher"},{"orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"orcid":"0000-0001-8893-2045","last_name":"Wolf","id":"45027","full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart"}],"title":"Polyhedral bounds on the joint spectrum and temperedness of locally  symmetric spaces"},{"publication":"arXiv:2603.26949","type":"preprint","status":"public","abstract":[{"text":"In this paper we generalize the geodesic flow on (finite) homogeneous graphs to a multiparameter flow on compact quotients of Euclidean buildings. Then we study the joint spectra of the associated transfer operators acting on suitable Lipschitz spaces. The main result says that outside an arbitrarily small neighborhood of zero in the set of spectral parameters the Taylor spectrum of the commuting family of transfer operators is contained in the joint point spectrum.","lang":"eng"}],"user_id":"220","_id":"65255","external_id":{"arxiv":["2603.26949"]},"language":[{"iso":"eng"}],"citation":{"ieee":"J. Hilgert, D. Kahl, and T. Weich, “Spectral theory for transfer operators on compact quotients of Euclidean buildings,” <i>arXiv:2603.26949</i>. 2026.","chicago":"Hilgert, Joachim, Daniel Kahl, and Tobias Weich. “Spectral Theory for Transfer Operators on Compact Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>, 2026.","ama":"Hilgert J, Kahl D, Weich T. Spectral theory for transfer operators on compact quotients of Euclidean buildings. <i>arXiv:260326949</i>. Published online 2026.","apa":"Hilgert, J., Kahl, D., &#38; Weich, T. (2026). Spectral theory for transfer operators on compact quotients of Euclidean buildings. In <i>arXiv:2603.26949</i>.","short":"J. Hilgert, D. Kahl, T. Weich, ArXiv:2603.26949 (2026).","bibtex":"@article{Hilgert_Kahl_Weich_2026, title={Spectral theory for transfer operators on compact quotients of Euclidean buildings}, journal={arXiv:2603.26949}, author={Hilgert, Joachim and Kahl, Daniel and Weich, Tobias}, year={2026} }","mla":"Hilgert, Joachim, et al. “Spectral Theory for Transfer Operators on Compact Quotients of Euclidean Buildings.” <i>ArXiv:2603.26949</i>, 2026."},"year":"2026","date_created":"2026-03-31T08:30:34Z","author":[{"first_name":"Joachim","full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert"},{"full_name":"Kahl, Daniel","id":"55661","last_name":"Kahl","first_name":"Daniel"},{"full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"}],"date_updated":"2026-03-31T08:31:01Z","title":"Spectral theory for transfer operators on compact quotients of Euclidean buildings"},{"intvolume":"       288","citation":{"ama":"Weich T, Budde J. Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>. 2025;288(1). doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>","chicago":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i> 288, no. 1 (2025). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>.","ieee":"T. Weich and J. Budde, “Wave Front Sets of Nilpotent Lie Group Representations,” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi: <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>.","apa":"Weich, T., &#38; Budde, J. (2025). Wave Front Sets of Nilpotent Lie Group Representations. <i>Journal of Functional Analysis</i>, <i>288</i>(1). <a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\">https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684</a>","bibtex":"@article{Weich_Budde_2025, title={Wave Front Sets of Nilpotent Lie Group Representations}, volume={288}, DOI={<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>}, number={1}, journal={Journal of Functional Analysis}, author={Weich, Tobias and Budde, Julia}, year={2025} }","short":"T. Weich, J. Budde, Journal of Functional Analysis 288 (2025).","mla":"Weich, Tobias, and Julia Budde. “Wave Front Sets of Nilpotent Lie Group Representations.” <i>Journal of Functional Analysis</i>, vol. 288, no. 1, 2025, doi:<a href=\"https://doi.org/ https://doi.org/10.1016/j.jfa.2024.110684\"> https://doi.org/10.1016/j.jfa.2024.110684</a>."},"has_accepted_license":"1","doi":" https://doi.org/10.1016/j.jfa.2024.110684","date_updated":"2024-09-25T08:18:44Z","oa":"1","volume":288,"author":[{"full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"full_name":"Budde, Julia","last_name":"Budde","first_name":"Julia"}],"status":"public","type":"journal_article","file_date_updated":"2022-06-22T09:56:39Z","_id":"32099","project":[{"grant_number":"491392403","_id":"356","name":"TRR 358 - B02: TRR 358 - Spektraltheorie in höherem Rang und unendlichem Volumen (Teilprojekt B02)"},{"_id":"355","name":"Mikrolokale Methoden für hyperbolische Dynamiken","grant_number":"422642921"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","year":"2025","issue":"1","title":"Wave Front Sets of Nilpotent Lie Group Representations","date_created":"2022-06-22T09:56:43Z","file":[{"content_type":"application/pdf","relation":"main_file","date_updated":"2022-06-22T09:56:39Z","date_created":"2022-06-22T09:56:39Z","creator":"weich","file_size":978990,"access_level":"open_access","file_name":"2103.02968.pdf","file_id":"32100"}],"publication":"Journal of Functional Analysis","ddc":["510"],"language":[{"iso":"eng"}]},{"language":[{"iso":"eng"}],"article_number":"76","user_id":"45027","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"external_id":{"arxiv":["2304.09573"]},"_id":"51207","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$\\Gamma$."}],"type":"journal_article","publication":"Geom Dedicata","doi":"https://doi.org/10.1007/s10711-024-00904-4","title":"Temperedness of locally symmetric spaces: The product case","author":[{"id":"49178","full_name":"Weich, Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"first_name":"Lasse Lennart","last_name":"Wolf","orcid":"0000-0001-8893-2045","id":"45027","full_name":"Wolf, Lasse Lennart"}],"date_created":"2024-02-06T21:00:55Z","volume":218,"date_updated":"2024-05-07T11:44:34Z","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>","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>.","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>.","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} }","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>.","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>"},"intvolume":"       218","year":"2024"},{"language":[{"iso":"ger"}],"user_id":"220","department":[{"_id":"97"},{"_id":"643"},{"_id":"548"}],"_id":"55193","status":"public","type":"book","doi":"10.1007/978-3-662-67357-7","title":"Ebene euklidische Geometrie. 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Hilgert, “Ruelle-Taylor resonances of Anosov actions,” <i>J. Europ. Math. Soc.</i>, vol. 27, no. 8, pp. 3085–3147, 2024, doi: <a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>.","ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C, Hilgert J. Ruelle-Taylor resonances of Anosov actions. <i>J Europ Math Soc</i>. 2024;27(8):3085–3147. doi:<a href=\"https://doi.org/10.4171/JEMS/1428\">https://doi.org/10.4171/JEMS/1428</a>"},"date_updated":"2026-02-18T10:33:34Z","oa":"1","volume":27,"author":[{"orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick"},{"first_name":"Colin","last_name":"Guillarmou","full_name":"Guillarmou, Colin"},{"first_name":"Joachim","id":"220","full_name":"Hilgert, Joachim","last_name":"Hilgert"}],"doi":"https://doi.org/10.4171/JEMS/1428","type":"journal_article","status":"public","_id":"32101","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"user_id":"49178","file_date_updated":"2022-06-22T09:56:47Z"},{"title":"SRB Measures of Anosov Actions","date_created":"2022-06-22T09:56:23Z","year":"2024","ddc":["510"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["https://arxiv.org/abs/2103.12127"]},"file":[{"date_created":"2022-06-22T09:56:08Z","creator":"weich","date_updated":"2022-06-22T09:56:08Z","access_level":"open_access","file_name":"2103.12127.pdf","file_id":"32098","file_size":745870,"content_type":"application/pdf","relation":"main_file"}],"publication":"Journal of Differential Geometry","doi":" DOI: 10.4310/jdg/1729092452","oa":"1","date_updated":"2025-01-02T15:39:43Z","author":[{"full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"},{"last_name":"Guedes Bonthonneau","full_name":"Guedes Bonthonneau, Yannick","first_name":"Yannick"},{"first_name":"Colin","full_name":"Guillarmou, Colin","last_name":"Guillarmou"}],"volume":128,"citation":{"ama":"Weich T, Guedes Bonthonneau Y, Guillarmou C. SRB Measures of Anosov Actions. <i>Journal of Differential Geometry</i>. 2024;128:959-1026. doi:<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>","chicago":"Weich, Tobias, Yannick Guedes Bonthonneau, and Colin Guillarmou. “SRB Measures of Anosov Actions.” <i>Journal of Differential Geometry</i> 128 (2024): 959–1026. <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>.","ieee":"T. Weich, Y. Guedes Bonthonneau, and C. Guillarmou, “SRB Measures of Anosov Actions,” <i>Journal of Differential Geometry</i>, vol. 128, pp. 959–1026, 2024, doi: <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>.","apa":"Weich, T., Guedes Bonthonneau, Y., &#38; Guillarmou, C. (2024). SRB Measures of Anosov Actions. <i>Journal of Differential Geometry</i>, <i>128</i>, 959–1026. <a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\">https://doi.org/ DOI: 10.4310/jdg/1729092452</a>","bibtex":"@article{Weich_Guedes Bonthonneau_Guillarmou_2024, title={SRB Measures of Anosov Actions}, volume={128}, DOI={<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>}, journal={Journal of Differential Geometry}, author={Weich, Tobias and Guedes Bonthonneau, Yannick and Guillarmou, Colin}, year={2024}, pages={959–1026} }","mla":"Weich, Tobias, et al. “SRB Measures of Anosov Actions.” <i>Journal of Differential Geometry</i>, vol. 128, 2024, pp. 959–1026, doi:<a href=\"https://doi.org/ DOI: 10.4310/jdg/1729092452\"> DOI: 10.4310/jdg/1729092452</a>.","short":"T. Weich, Y. Guedes Bonthonneau, C. Guillarmou, Journal of Differential Geometry 128 (2024) 959–1026."},"intvolume":"       128","page":"959-1026","has_accepted_license":"1","file_date_updated":"2022-06-22T09:56:08Z","project":[{"grant_number":"491392403","name":"TRR 358 - Geodätische Flüsse und Weyl Kammer Flüsse auf affinen Gebäuden (Teilprojekt B04)","_id":"358"},{"_id":"355","name":"Mikrolokale Methoden für hyperbolische Dynamiken","grant_number":"422642921"}],"_id":"32097","user_id":"49178","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"status":"public","type":"journal_article"},{"type":"journal_article","publication":"Indagationes Mathematicae","status":"public","_id":"58103","user_id":"220","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0019-3577"]},"issue":"1","year":"2024","citation":{"apa":"Bux, K.-U., Hilgert, J., &#38; Weich, T. (2024). Spectral correspondences for finite graphs without dead ends. <i>Indagationes Mathematicae</i>, <i>36</i>(1), 188–217. <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">https://doi.org/10.1016/j.indag.2024.05.001</a>","bibtex":"@article{Bux_Hilgert_Weich_2024, title={Spectral correspondences for finite graphs without dead ends}, volume={36}, DOI={<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>}, number={1}, journal={Indagationes Mathematicae}, publisher={Elsevier BV}, author={Bux, K.-U. and Hilgert, Joachim and Weich, Tobias}, year={2024}, pages={188–217} }","short":"K.-U. Bux, J. Hilgert, T. Weich, Indagationes Mathematicae 36 (2024) 188–217.","mla":"Bux, K. U., et al. “Spectral Correspondences for Finite Graphs without Dead Ends.” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, Elsevier BV, 2024, pp. 188–217, doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>.","ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Spectral correspondences for finite graphs without dead ends,” <i>Indagationes Mathematicae</i>, vol. 36, no. 1, pp. 188–217, 2024, doi: <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>.","chicago":"Bux, K.-U., Joachim Hilgert, and Tobias Weich. “Spectral Correspondences for Finite Graphs without Dead Ends.” <i>Indagationes Mathematicae</i> 36, no. 1 (2024): 188–217. <a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">https://doi.org/10.1016/j.indag.2024.05.001</a>.","ama":"Bux K-U, Hilgert J, Weich T. Spectral correspondences for finite graphs without dead ends. <i>Indagationes Mathematicae</i>. 2024;36(1):188-217. doi:<a href=\"https://doi.org/10.1016/j.indag.2024.05.001\">10.1016/j.indag.2024.05.001</a>"},"page":"188-217","intvolume":"        36","publisher":"Elsevier BV","date_updated":"2025-01-13T16:00:06Z","date_created":"2025-01-08T09:39:58Z","author":[{"first_name":"K.-U.","full_name":"Bux, K.-U.","last_name":"Bux"},{"first_name":"Joachim","full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","id":"49178","full_name":"Weich, Tobias"}],"volume":36,"title":"Spectral correspondences for finite graphs without dead ends","doi":"10.1016/j.indag.2024.05.001"},{"citation":{"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>","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>.","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>.","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>","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} }","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>.","short":"C. Arends, L.L. Wolf, J. Meinecke, S. Barkhofen, T. Weich, T. Bartley, Physical Review Research 6 (2024)."},"intvolume":"         6","year":"2024","issue":"1","publication_status":"published","publication_identifier":{"issn":["2643-1564"]},"doi":"10.1103/physrevresearch.6.l012043","title":"Decomposing large unitaries into multimode devices of arbitrary size","date_created":"2024-03-26T08:52:05Z","author":[{"id":"43994","full_name":"Arends, Christian","last_name":"Arends","first_name":"Christian"},{"id":"45027","full_name":"Wolf, Lasse Lennart","orcid":"0000-0001-8893-2045","last_name":"Wolf","first_name":"Lasse Lennart"},{"first_name":"Jasmin","full_name":"Meinecke, Jasmin","last_name":"Meinecke"},{"id":"48188","full_name":"Barkhofen, Sonja","last_name":"Barkhofen","first_name":"Sonja"},{"id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","first_name":"Tobias"},{"first_name":"Tim","full_name":"Bartley, Tim","id":"49683","last_name":"Bartley"}],"volume":6,"publisher":"American Physical Society (APS)","date_updated":"2025-12-04T13:38:49Z","status":"public","type":"journal_article","publication":"Physical Review Research","language":[{"iso":"eng"}],"article_number":"L012043","keyword":["General Physics and Astronomy"],"user_id":"48188","department":[{"_id":"623"},{"_id":"15"}],"_id":"52876"},{"external_id":{"arxiv":["2205.03167"]},"_id":"31189","user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"}],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Communications in Mathematical Physics","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","date_updated":"2024-02-06T20:52:40Z","date_created":"2022-05-11T10:38:11Z","author":[{"orcid":"0000-0002-9648-6919","last_name":"Weich","full_name":"Weich, Tobias","id":"49178","first_name":"Tobias"},{"first_name":"Lasse Lennart","full_name":"Wolf, Lasse Lennart","id":"45027","last_name":"Wolf"}],"volume":403,"title":"Absence of principal eigenvalues for higher rank locally symmetric  spaces","doi":"https://doi.org/10.1007/s00220-023-04819-1","publication_identifier":{"unknown":["1275-1295"]},"year":"2023","citation":{"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>.","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>.","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>","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>","short":"T. Weich, L.L. Wolf, Communications in Mathematical Physics 403 (2023).","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} }","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>."},"intvolume":"       403"},{"title":"Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions","author":[{"full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte","first_name":"Philipp"},{"first_name":"Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich","id":"49178","full_name":"Weich, Tobias"}],"date_created":"2024-02-06T20:58:35Z","date_updated":"2024-02-11T19:56:01Z","citation":{"ieee":"P. Schütte and T. Weich, “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions,” <i>arXiv:2308.13463</i>. 2023.","chicago":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","ama":"Schütte P, Weich T. Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. <i>arXiv:230813463</i>. Published online 2023.","apa":"Schütte, P., &#38; Weich, T. (2023). Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions. In <i>arXiv:2308.13463</i>.","mla":"Schütte, Philipp, and Tobias Weich. “Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions.” <i>ArXiv:2308.13463</i>, 2023.","bibtex":"@article{Schütte_Weich_2023, title={Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces  -- A Numerical Algorithm via Weighted Zeta Functions}, journal={arXiv:2308.13463}, author={Schütte, Philipp and Weich, Tobias}, year={2023} }","short":"P. Schütte, T. Weich, ArXiv:2308.13463 (2023)."},"year":"2023","language":[{"iso":"eng"}],"department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","external_id":{"arxiv":["2308.13463"]},"_id":"51206","status":"public","abstract":[{"lang":"eng","text":"We present a numerical algorithm for the computation of invariant Ruelle\r\ndistributions on convex co-compact hyperbolic surfaces. This is achieved by\r\nexploiting the connection between invariant Ruelle distributions and residues\r\nof meromorphically continued weighted zeta functions established by the authors\r\ntogether with Barkhofen (2021). To make this applicable for numerics we express\r\nthe weighted zeta as the logarithmic derivative of a suitable parameter\r\ndependent Fredholm determinant similar to Borthwick (2014). As an additional\r\ndifficulty our transfer operator has to include a contracting direction which\r\nwe account for with techniques developed by Rugh (1992). We achieve a further\r\nimprovement in convergence speed for our algorithm in the case of surfaces with\r\nadditional symmetries by proving and applying a symmetry reduction of weighted\r\nzeta functions."}],"publication":"arXiv:2308.13463","type":"preprint"},{"_id":"53410","user_id":"70575","department":[{"_id":"548"}],"keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}],"type":"journal_article","publication":"Annales Henri Poincaré","abstract":[{"text":"<jats:title>Abstract</jats:title><jats:p>We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing, the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou (Ann Henri Poincaré 17(11):3089–3146, 2016) can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.</jats:p>","lang":"eng"}],"status":"public","date_updated":"2024-04-11T12:37:34Z","publisher":"Springer Science and Business Media LLC","author":[{"full_name":"Delarue, Benjamin","id":"70575","last_name":"Delarue","first_name":"Benjamin"},{"full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte","first_name":"Philipp"},{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"date_created":"2024-04-11T12:30:14Z","volume":25,"title":"Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models","doi":"10.1007/s00023-023-01379-x","publication_status":"published","publication_identifier":{"issn":["1424-0637","1424-0661"]},"issue":"2","year":"2023","citation":{"ieee":"B. Delarue, P. Schütte, and T. Weich, “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, pp. 1607–1656, 2023, doi: <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","chicago":"Delarue, Benjamin, Philipp Schütte, and Tobias Weich. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i> 25, no. 2 (2023): 1607–56. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>.","ama":"Delarue B, Schütte P, Weich T. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>. 2023;25(2):1607-1656. doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>","mla":"Delarue, Benjamin, et al. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models.” <i>Annales Henri Poincaré</i>, vol. 25, no. 2, Springer Science and Business Media LLC, 2023, pp. 1607–56, doi:<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>.","bibtex":"@article{Delarue_Schütte_Weich_2023, title={Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models}, volume={25}, DOI={<a href=\"https://doi.org/10.1007/s00023-023-01379-x\">10.1007/s00023-023-01379-x</a>}, number={2}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Delarue, Benjamin and Schütte, Philipp and Weich, Tobias}, year={2023}, pages={1607–1656} }","short":"B. Delarue, P. Schütte, T. Weich, Annales Henri Poincaré 25 (2023) 1607–1656.","apa":"Delarue, B., Schütte, P., &#38; Weich, T. (2023). Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. <i>Annales Henri Poincaré</i>, <i>25</i>(2), 1607–1656. <a href=\"https://doi.org/10.1007/s00023-023-01379-x\">https://doi.org/10.1007/s00023-023-01379-x</a>"},"intvolume":"        25","page":"1607-1656"},{"abstract":[{"lang":"eng","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 $G/K$."}],"publication":"Analysis & PDE","language":[{"iso":"eng"}],"external_id":{"arxiv":["2103.05667"]},"year":"2023","issue":"10","title":"Higher rank quantum-classical correspondence","publisher":"MSP","date_created":"2022-05-11T10:41:35Z","status":"public","type":"journal_article","_id":"31190","user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"91"}],"citation":{"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>","short":"J. Hilgert, T. Weich, L.L. Wolf, Analysis &#38; PDE 16 (2023) 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>.","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} }","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>","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>."},"page":"2241–2265","intvolume":"        16","doi":"https://doi.org/10.2140/apde.2023.16.2241","date_updated":"2026-02-18T10:39:36Z","author":[{"first_name":"Joachim","last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"},{"last_name":"Wolf","orcid":"0000-0001-8893-2045","id":"45027","full_name":"Wolf, Lasse Lennart","first_name":"Lasse Lennart"}],"volume":16},{"citation":{"bibtex":"@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>}, journal={Communications in Mathematical Physics}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }","short":"P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678.","mla":"Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i>, vol. 398, 2023, pp. 655–78, doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","apa":"Schütte, P., Weich, T., &#38; Barkhofen, S. (2023). Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>, <i>398</i>, 655–678. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>","ama":"Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>. 2023;398:655-678. doi:<a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>","chicago":"Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i> 398 (2023): 655–78. <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>.","ieee":"P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” <i>Communications in Mathematical Physics</i>, vol. 398, pp. 655–678, 2023, doi: <a href=\"https://doi.org/10.1007/s00220-022-04538-z\">https://doi.org/10.1007/s00220-022-04538-z</a>."},"intvolume":"       398","page":"655-678","year":"2023","doi":"https://doi.org/10.1007/s00220-022-04538-z","title":"Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems","author":[{"first_name":"Philipp","id":"50168","full_name":"Schütte, Philipp","last_name":"Schütte"},{"first_name":"Tobias","last_name":"Weich","orcid":"0000-0002-9648-6919","full_name":"Weich, Tobias","id":"49178"},{"full_name":"Barkhofen, Sonja","id":"48188","last_name":"Barkhofen","first_name":"Sonja"}],"date_created":"2022-05-04T12:27:46Z","volume":398,"date_updated":"2026-02-18T10:41:07Z","status":"public","abstract":[{"text":"In this article we prove meromorphic continuation of weighted zeta functions in the framework of open hyperbolic systems by using the meromorphically continued restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula proving equality between residues of weighted zetas and invariant Ruelle distributions. We combine this equality with results of Guillarmou, Hilgert and Weich (2021) in order to relate the residues to Patterson-Sullivan distributions. Finally we provide proof-of-principle results concerning the numerical calculation of invariant Ruelle distributions for 3-disc scattering systems.","lang":"eng"}],"type":"journal_article","publication":"Communications in Mathematical Physics","language":[{"iso":"eng"}],"user_id":"49178","department":[{"_id":"10"},{"_id":"548"},{"_id":"623"},{"_id":"15"}],"_id":"31059","external_id":{"arxiv":["2112.05791"]}},{"status":"public","type":"journal_article","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"}],"user_id":"49178","_id":"35306","page":"851-923","intvolume":"        24","citation":{"mla":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","bibtex":"@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>}, number={3}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Guedes Bonthonneau, Yannick and Weich, Tobias}, year={2022}, pages={851–923} }","short":"Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923.","apa":"Guedes Bonthonneau, Y., &#38; Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>, <i>24</i>(3), 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>","chicago":"Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” <i>Journal of the European Mathematical Society</i> 24, no. 3 (2022): 851–923. <a href=\"https://doi.org/10.4171/jems/1103\">https://doi.org/10.4171/jems/1103</a>.","ieee":"Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” <i>Journal of the European Mathematical Society</i>, vol. 24, no. 3, pp. 851–923, 2022, doi: <a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>.","ama":"Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. <i>Journal of the European Mathematical Society</i>. 2022;24(3):851-923. doi:<a href=\"https://doi.org/10.4171/jems/1103\">10.4171/jems/1103</a>"},"publication_identifier":{"issn":["1435-9855"]},"publication_status":"published","doi":"10.4171/jems/1103","volume":24,"author":[{"full_name":"Guedes Bonthonneau, Yannick","last_name":"Guedes Bonthonneau","first_name":"Yannick"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"date_updated":"2023-01-06T08:47:35Z","publication":"Journal of the European Mathematical Society","language":[{"iso":"eng"}],"keyword":["Applied Mathematics","General Mathematics"],"year":"2022","issue":"3","title":"Ruelle–Pollicott resonances for manifolds with hyperbolic cusps","date_created":"2023-01-05T16:23:34Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH"},{"issue":"24","year":"2022","publisher":"IOP Publishing Ltd","date_created":"2022-05-04T12:23:11Z","title":"Semiclassical formulae For Wigner distributions","publication":"Journal of Physics A: Mathematical and Theoretical","abstract":[{"text":"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.","lang":"eng"}],"external_id":{"arxiv":["2201.04892"]},"language":[{"iso":"eng"}],"intvolume":"        55","citation":{"mla":"Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","bibtex":"@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>}, number={24244007}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd}, author={Barkhofen, Sonja and Schütte, Philipp and Weich, Tobias}, year={2022} }","short":"S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).","apa":"Barkhofen, S., Schütte, P., &#38; Weich, T. (2022). Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(24), Article 244007. <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>","chicago":"Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 24 (2022). <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">https://doi.org/10.1088/1751-8121/ac6d2b</a>.","ieee":"S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 24, Art. no. 244007, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>.","ama":"Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(24). doi:<a href=\"https://doi.org/10.1088/1751-8121/ac6d2b\">10.1088/1751-8121/ac6d2b</a>"},"date_updated":"2024-02-06T20:40:45Z","volume":55,"author":[{"first_name":"Sonja","id":"48188","full_name":"Barkhofen, Sonja","last_name":"Barkhofen"},{"last_name":"Schütte","full_name":"Schütte, Philipp","id":"50168","first_name":"Philipp"},{"first_name":"Tobias","full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919"}],"doi":"10.1088/1751-8121/ac6d2b","type":"journal_article","status":"public","_id":"31057","department":[{"_id":"623"},{"_id":"548"},{"_id":"10"}],"user_id":"49178","article_number":"244007","article_type":"review"},{"publication_identifier":{"issn":["1664-039X"]},"publication_status":"published","issue":"2","year":"2022","intvolume":"        12","page":"659-681","citation":{"ieee":"K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, pp. 659–681, 2022, doi: <a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","chicago":"Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i> 12, no. 2 (2022): 659–81. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>.","ama":"Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>. 2022;12(2):659-681. doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>","apa":"Bux, K.-U., Hilgert, J., &#38; Weich, T. (2022). Poisson transforms for trees of bounded degree. <i>Journal of Spectral Theory</i>, <i>12</i>(2), 659–681. <a href=\"https://doi.org/10.4171/jst/414\">https://doi.org/10.4171/jst/414</a>","bibtex":"@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, DOI={<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Bux, Kai-Uwe and Hilgert, Joachim and Weich, Tobias}, year={2022}, pages={659–681} }","mla":"Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>Journal of Spectral Theory</i>, vol. 12, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 659–81, doi:<a href=\"https://doi.org/10.4171/jst/414\">10.4171/jst/414</a>.","short":"K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681."},"date_updated":"2024-02-19T06:28:12Z","publisher":"European Mathematical Society - EMS - Publishing House GmbH","volume":12,"author":[{"first_name":"Kai-Uwe","full_name":"Bux, Kai-Uwe","last_name":"Bux"},{"full_name":"Hilgert, Joachim","id":"220","last_name":"Hilgert","first_name":"Joachim"},{"full_name":"Weich, Tobias","id":"49178","last_name":"Weich","orcid":"0000-0002-9648-6919","first_name":"Tobias"}],"date_created":"2023-01-06T08:49:06Z","title":"Poisson transforms for trees of bounded degree","doi":"10.4171/jst/414","publication":"Journal of Spectral Theory","type":"journal_article","status":"public","_id":"35322","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"user_id":"49063","keyword":["Geometry and Topology","Mathematical Physics","Statistical and Nonlinear Physics"],"language":[{"iso":"eng"}]},{"status":"public","type":"journal_article","publication":"J. of Spectral Theory","language":[{"iso":"eng"}],"user_id":"220","department":[{"_id":"91"}],"_id":"51385","citation":{"ama":"Hilgert J, Weich T, Bux K-U. Poisson transforms for trees of bounded degree. <i>J of Spectral Theory</i>. 2022;12:659-681.","chicago":"Hilgert, Joachim, Tobias Weich, and K.-U. Bux. “Poisson Transforms for Trees of Bounded Degree.” <i>J. of Spectral Theory</i> 12 (2022): 659–81.","ieee":"J. Hilgert, T. Weich, and K.-U. Bux, “Poisson transforms for trees of bounded degree,” <i>J. of Spectral Theory</i>, vol. 12, pp. 659–681, 2022.","short":"J. Hilgert, T. Weich, K.-U. Bux, J. of Spectral Theory 12 (2022) 659–681.","bibtex":"@article{Hilgert_Weich_Bux_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, journal={J. of Spectral Theory}, author={Hilgert, Joachim and Weich, Tobias and Bux, K.-U.}, year={2022}, pages={659–681} }","mla":"Hilgert, Joachim, et al. “Poisson Transforms for Trees of Bounded Degree.” <i>J. of Spectral Theory</i>, vol. 12, 2022, pp. 659–81.","apa":"Hilgert, J., Weich, T., &#38; Bux, K.-U. (2022). Poisson transforms for trees of bounded degree. <i>J. of Spectral Theory</i>, <i>12</i>, 659–681."},"page":"659-681","intvolume":"        12","year":"2022","publication_status":"published","title":"Poisson transforms for trees of bounded degree","date_created":"2024-02-19T06:36:17Z","author":[{"last_name":"Hilgert","full_name":"Hilgert, Joachim","id":"220","first_name":"Joachim"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"},{"full_name":"Bux, K.-U.","last_name":"Bux","first_name":"K.-U."}],"volume":12,"date_updated":"2026-03-31T08:25:35Z"},{"language":[{"iso":"eng"}],"_id":"31058","external_id":{"arxiv":["2109.05907"]},"department":[{"_id":"10"},{"_id":"548"}],"user_id":"50168","abstract":[{"text":"We consider a geodesic billiard system consisting of a complete Riemannian manifold and an obstacle submanifold with boundary at which the trajectories of the geodesic flow experience specular reflections. We show that if the geodesic billiard system is hyperbolic on its trapped set and the latter is compact and non-grazing the techniques for open hyperbolic systems developed by Dyatlov and Guillarmou can be applied to a smooth model for the discontinuous flow defined by the non-grazing billiard trajectories. This allows us to obtain a meromorphic resolvent for the generator of the billiard flow. As an application we prove a meromorphic continuation of weighted zeta functions together with explicit residue formulae. In particular, our results apply to scattering by convex obstacles in the Euclidean plane.","lang":"eng"}],"status":"public","type":"preprint","title":"Resonances and weighted zeta functions for obstacle scattering via smooth models","date_updated":"2022-05-17T12:05:52Z","author":[{"first_name":"Philipp","full_name":"Schütte, Philipp","id":"50168","last_name":"Schütte"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"},{"first_name":"Benjamin","last_name":"Delarue","full_name":"Delarue, Benjamin"}],"date_created":"2022-05-04T12:25:58Z","year":"2021","citation":{"bibtex":"@article{Schütte_Weich_Delarue_2021, title={Resonances and weighted zeta functions for obstacle scattering via smooth models}, author={Schütte, Philipp and Weich, Tobias and Delarue, Benjamin}, year={2021} }","short":"P. Schütte, T. Weich, B. Delarue, (2021).","mla":"Schütte, Philipp, et al. <i>Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models</i>. 2021.","apa":"Schütte, P., Weich, T., &#38; Delarue, B. (2021). <i>Resonances and weighted zeta functions for obstacle scattering via smooth models</i>.","ieee":"P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions for obstacle scattering via smooth models.” 2021.","chicago":"Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” 2021.","ama":"Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle scattering via smooth models. Published online 2021."}},{"date_created":"2022-05-17T12:05:17Z","publisher":"Cellule MathDoc/CEDRAM","title":"High frequency limits for invariant Ruelle densities","year":"2021","external_id":{"arxiv":["1803.06717"]},"language":[{"iso":"eng"}],"publication":"Annales Henri Lebesgue","author":[{"last_name":"Guillarmou","full_name":"Guillarmou, Colin","first_name":"Colin"},{"first_name":"Joachim","last_name":"Hilgert","id":"220","full_name":"Hilgert, Joachim"},{"first_name":"Tobias","id":"49178","full_name":"Weich, Tobias","orcid":"0000-0002-9648-6919","last_name":"Weich"}],"volume":4,"date_updated":"2024-02-19T06:27:43Z","doi":"10.5802/ahl.67","publication_status":"published","publication_identifier":{"issn":["2644-9463"]},"citation":{"apa":"Guillarmou, C., Hilgert, J., &#38; Weich, T. (2021). High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>, <i>4</i>, 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>","mla":"Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i>, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119, doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>.","bibtex":"@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for invariant Ruelle densities}, volume={4}, DOI={<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>}, journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }","short":"C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119.","ieee":"C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant Ruelle densities,” <i>Annales Henri Lebesgue</i>, vol. 4, pp. 81–119, 2021, doi: <a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>.","chicago":"Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency Limits for Invariant Ruelle Densities.” <i>Annales Henri Lebesgue</i> 4 (2021): 81–119. <a href=\"https://doi.org/10.5802/ahl.67\">https://doi.org/10.5802/ahl.67</a>.","ama":"Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle densities. <i>Annales Henri Lebesgue</i>. 2021;4:81-119. doi:<a href=\"https://doi.org/10.5802/ahl.67\">10.5802/ahl.67</a>"},"page":"81-119","intvolume":"         4","user_id":"49063","department":[{"_id":"10"},{"_id":"623"},{"_id":"548"},{"_id":"91"}],"_id":"31263","type":"journal_article","status":"public"}]