--- _id: '31190' 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 $G/K$." author: - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Lasse Lennart full_name: Wolf, Lasse Lennart id: '45027' last_name: Wolf orcid: 0000-0001-8893-2045 citation: ama: Hilgert J, Weich T, Wolf LL. Higher rank quantum-classical correspondence. Analysis & PDE. 2023;16(10):2241–2265. doi:https://doi.org/10.2140/apde.2023.16.2241 apa: Hilgert, J., Weich, T., & Wolf, L. L. (2023). Higher rank quantum-classical correspondence. Analysis & PDE, 16(10), 2241–2265. https://doi.org/10.2140/apde.2023.16.2241 bibtex: '@article{Hilgert_Weich_Wolf_2023, title={Higher rank quantum-classical correspondence}, volume={16}, DOI={https://doi.org/10.2140/apde.2023.16.2241}, number={10}, journal={Analysis & PDE}, publisher={MSP}, author={Hilgert, Joachim and Weich, Tobias and Wolf, Lasse Lennart}, year={2023}, pages={2241–2265} }' chicago: 'Hilgert, Joachim, Tobias Weich, and Lasse Lennart Wolf. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE 16, no. 10 (2023): 2241–2265. https://doi.org/10.2140/apde.2023.16.2241.' ieee: 'J. Hilgert, T. Weich, and L. L. Wolf, “Higher rank quantum-classical correspondence,” Analysis & PDE, vol. 16, no. 10, pp. 2241–2265, 2023, doi: https://doi.org/10.2140/apde.2023.16.2241.' mla: Hilgert, Joachim, et al. “Higher Rank Quantum-Classical Correspondence.” Analysis & PDE, vol. 16, no. 10, MSP, 2023, pp. 2241–2265, doi:https://doi.org/10.2140/apde.2023.16.2241. short: J. Hilgert, T. Weich, L.L. Wolf, Analysis & PDE 16 (2023) 2241–2265. date_created: 2022-05-11T10:41:35Z date_updated: 2026-02-18T10:39:36Z department: - _id: '10' - _id: '548' - _id: '91' doi: https://doi.org/10.2140/apde.2023.16.2241 external_id: arxiv: - '2103.05667' intvolume: ' 16' issue: '10' language: - iso: eng page: 2241–2265 publication: Analysis & PDE publisher: MSP status: public title: Higher rank quantum-classical correspondence type: journal_article user_id: '49178' volume: 16 year: '2023' ... --- _id: '31059' abstract: - lang: eng 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. author: - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen citation: ama: Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. Communications in Mathematical Physics. 2023;398:655-678. doi:https://doi.org/10.1007/s00220-022-04538-z apa: Schütte, P., Weich, T., & Barkhofen, S. (2023). Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. Communications in Mathematical Physics, 398, 655–678. https://doi.org/10.1007/s00220-022-04538-z bibtex: '@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={https://doi.org/10.1007/s00220-022-04538-z}, journal={Communications in Mathematical Physics}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }' chicago: 'Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” Communications in Mathematical Physics 398 (2023): 655–78. https://doi.org/10.1007/s00220-022-04538-z.' ieee: 'P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” Communications in Mathematical Physics, vol. 398, pp. 655–678, 2023, doi: https://doi.org/10.1007/s00220-022-04538-z.' mla: Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” Communications in Mathematical Physics, vol. 398, 2023, pp. 655–78, doi:https://doi.org/10.1007/s00220-022-04538-z. short: P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics 398 (2023) 655–678. date_created: 2022-05-04T12:27:46Z date_updated: 2026-02-18T10:41:07Z department: - _id: '10' - _id: '548' - _id: '623' - _id: '15' doi: https://doi.org/10.1007/s00220-022-04538-z external_id: arxiv: - '2112.05791' intvolume: ' 398' language: - iso: eng page: 655-678 publication: Communications in Mathematical Physics status: public title: Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems type: journal_article user_id: '49178' volume: 398 year: '2023' ... --- _id: '31982' abstract: - lang: eng text: "AbstractWe show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold

$$\\Sigma $$

\r\n \ Σ\r\n with Betti number

$$b_1$$

\r\n \r\n \ b\r\n 1\r\n \ \r\n , the order of vanishing of the Ruelle zeta function at zero equals

$$4-b_1$$

\r\n \r\n \ 4\r\n -\r\n \ \r\n b\r\n \ 1\r\n \r\n \ \r\n , while in the hyperbolic case it is equal to

$$4-2b_1$$

\r\n \r\n \ 4\r\n -\r\n \ 2\r\n \r\n b\r\n \ 1\r\n \r\n \ \r\n . This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott–Ruelle resonant differential forms at 0 in the hyperbolic case and using first variation for the perturbation. To show that the first variation is generically nonzero we introduce a new identity relating pushforwards of products of resonant and coresonant 2-forms on the sphere bundle

$$S\\Sigma $$

\r\n \ \r\n S\r\n Σ\r\n \ \r\n with harmonic 1-forms on

$$\\Sigma $$

\r\n \ Σ\r\n ." author: - first_name: Mihajlo full_name: Cekić, Mihajlo last_name: Cekić - first_name: Benjamin full_name: Delarue, Benjamin id: '70575' last_name: Delarue - first_name: Semyon full_name: Dyatlov, Semyon last_name: Dyatlov - first_name: Gabriel P. full_name: Paternain, Gabriel P. last_name: Paternain citation: ama: Cekić M, Delarue B, Dyatlov S, Paternain GP. The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones mathematicae. 2022;229(1):303-394. doi:10.1007/s00222-022-01108-x apa: Cekić, M., Delarue, B., Dyatlov, S., & Paternain, G. P. (2022). The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds. Inventiones Mathematicae, 229(1), 303–394. https://doi.org/10.1007/s00222-022-01108-x bibtex: '@article{Cekić_Delarue_Dyatlov_Paternain_2022, title={The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds}, volume={229}, DOI={10.1007/s00222-022-01108-x}, number={1}, journal={Inventiones mathematicae}, publisher={Springer Science and Business Media LLC}, author={Cekić, Mihajlo and Delarue, Benjamin and Dyatlov, Semyon and Paternain, Gabriel P.}, year={2022}, pages={303–394} }' chicago: 'Cekić, Mihajlo, Benjamin Delarue, Semyon Dyatlov, and Gabriel P. Paternain. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae 229, no. 1 (2022): 303–94. https://doi.org/10.1007/s00222-022-01108-x.' ieee: 'M. Cekić, B. Delarue, S. Dyatlov, and G. P. Paternain, “The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds,” Inventiones mathematicae, vol. 229, no. 1, pp. 303–394, 2022, doi: 10.1007/s00222-022-01108-x.' mla: Cekić, Mihajlo, et al. “The Ruelle Zeta Function at Zero for Nearly Hyperbolic 3-Manifolds.” Inventiones Mathematicae, vol. 229, no. 1, Springer Science and Business Media LLC, 2022, pp. 303–94, doi:10.1007/s00222-022-01108-x. short: M. Cekić, B. Delarue, S. Dyatlov, G.P. Paternain, Inventiones Mathematicae 229 (2022) 303–394. date_created: 2022-06-20T08:24:17Z date_updated: 2022-06-21T11:55:15Z department: - _id: '548' doi: 10.1007/s00222-022-01108-x intvolume: ' 229' issue: '1' keyword: - General Mathematics language: - iso: eng page: 303-394 publication: Inventiones mathematicae publication_identifier: issn: - 0020-9910 - 1432-1297 publication_status: published publisher: Springer Science and Business Media LLC status: public title: The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds type: journal_article user_id: '70575' volume: 229 year: '2022' ... --- _id: '35306' author: - first_name: Yannick full_name: Guedes Bonthonneau, Yannick last_name: Guedes Bonthonneau - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Guedes Bonthonneau Y, Weich T. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. Journal of the European Mathematical Society. 2022;24(3):851-923. doi:10.4171/jems/1103 apa: Guedes Bonthonneau, Y., & Weich, T. (2022). Ruelle–Pollicott resonances for manifolds with hyperbolic cusps. Journal of the European Mathematical Society, 24(3), 851–923. https://doi.org/10.4171/jems/1103 bibtex: '@article{Guedes Bonthonneau_Weich_2022, title={Ruelle–Pollicott resonances for manifolds with hyperbolic cusps}, volume={24}, DOI={10.4171/jems/1103}, 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} }' chicago: 'Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” Journal of the European Mathematical Society 24, no. 3 (2022): 851–923. https://doi.org/10.4171/jems/1103.' ieee: 'Y. Guedes Bonthonneau and T. Weich, “Ruelle–Pollicott resonances for manifolds with hyperbolic cusps,” Journal of the European Mathematical Society, vol. 24, no. 3, pp. 851–923, 2022, doi: 10.4171/jems/1103.' mla: Guedes Bonthonneau, Yannick, and Tobias Weich. “Ruelle–Pollicott Resonances for Manifolds with Hyperbolic Cusps.” Journal of the European Mathematical Society, vol. 24, no. 3, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 851–923, doi:10.4171/jems/1103. short: Y. Guedes Bonthonneau, T. Weich, Journal of the European Mathematical Society 24 (2022) 851–923. date_created: 2023-01-05T16:23:34Z date_updated: 2023-01-06T08:47:35Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.4171/jems/1103 intvolume: ' 24' issue: '3' keyword: - Applied Mathematics - General Mathematics language: - iso: eng page: 851-923 publication: Journal of the European Mathematical Society publication_identifier: issn: - 1435-9855 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Ruelle–Pollicott resonances for manifolds with hyperbolic cusps type: journal_article user_id: '49178' volume: 24 year: '2022' ... --- _id: '31057' abstract: - lang: eng 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. article_number: '244007' article_type: review author: - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: 'Barkhofen S, Schütte P, Weich T. Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical. 2022;55(24). doi:10.1088/1751-8121/ac6d2b' apa: 'Barkhofen, S., Schütte, P., & Weich, T. (2022). Semiclassical formulae For Wigner distributions. Journal of Physics A: Mathematical and Theoretical, 55(24), Article 244007. https://doi.org/10.1088/1751-8121/ac6d2b' bibtex: '@article{Barkhofen_Schütte_Weich_2022, title={Semiclassical formulae For Wigner distributions}, volume={55}, DOI={10.1088/1751-8121/ac6d2b}, 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} }' chicago: 'Barkhofen, Sonja, Philipp Schütte, and Tobias Weich. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical 55, no. 24 (2022). https://doi.org/10.1088/1751-8121/ac6d2b.' ieee: 'S. Barkhofen, P. Schütte, and T. Weich, “Semiclassical formulae For Wigner distributions,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, Art. no. 244007, 2022, doi: 10.1088/1751-8121/ac6d2b.' mla: 'Barkhofen, Sonja, et al. “Semiclassical Formulae For Wigner Distributions.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 24, 244007, IOP Publishing Ltd, 2022, doi:10.1088/1751-8121/ac6d2b.' short: 'S. Barkhofen, P. Schütte, T. Weich, Journal of Physics A: Mathematical and Theoretical 55 (2022).' date_created: 2022-05-04T12:23:11Z date_updated: 2024-02-06T20:40:45Z department: - _id: '623' - _id: '548' - _id: '10' doi: 10.1088/1751-8121/ac6d2b external_id: arxiv: - '2201.04892' intvolume: ' 55' issue: '24' language: - iso: eng publication: 'Journal of Physics A: Mathematical and Theoretical' publisher: IOP Publishing Ltd status: public title: Semiclassical formulae For Wigner distributions type: journal_article user_id: '49178' volume: 55 year: '2022' ... --- _id: '35322' author: - first_name: Kai-Uwe full_name: Bux, Kai-Uwe last_name: Bux - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Bux K-U, Hilgert J, Weich T. Poisson transforms for trees of bounded degree. Journal of Spectral Theory. 2022;12(2):659-681. doi:10.4171/jst/414 apa: Bux, K.-U., Hilgert, J., & Weich, T. (2022). Poisson transforms for trees of bounded degree. Journal of Spectral Theory, 12(2), 659–681. https://doi.org/10.4171/jst/414 bibtex: '@article{Bux_Hilgert_Weich_2022, title={Poisson transforms for trees of bounded degree}, volume={12}, DOI={10.4171/jst/414}, 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} }' chicago: 'Bux, Kai-Uwe, Joachim Hilgert, and Tobias Weich. “Poisson Transforms for Trees of Bounded Degree.” Journal of Spectral Theory 12, no. 2 (2022): 659–81. https://doi.org/10.4171/jst/414.' ieee: 'K.-U. Bux, J. Hilgert, and T. Weich, “Poisson transforms for trees of bounded degree,” Journal of Spectral Theory, vol. 12, no. 2, pp. 659–681, 2022, doi: 10.4171/jst/414.' mla: Bux, Kai-Uwe, et al. “Poisson Transforms for Trees of Bounded Degree.” Journal of Spectral Theory, vol. 12, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2022, pp. 659–81, doi:10.4171/jst/414. short: K.-U. Bux, J. Hilgert, T. Weich, Journal of Spectral Theory 12 (2022) 659–681. date_created: 2023-01-06T08:49:06Z date_updated: 2024-02-19T06:28:12Z department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' doi: 10.4171/jst/414 intvolume: ' 12' issue: '2' keyword: - Geometry and Topology - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 659-681 publication: Journal of Spectral Theory publication_identifier: issn: - 1664-039X publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Poisson transforms for trees of bounded degree type: journal_article user_id: '49063' volume: 12 year: '2022' ... --- _id: '64570' article_number: '9' author: - first_name: Martin full_name: Olbrich, Martin last_name: Olbrich - first_name: Guendalina full_name: Palmirotta, Guendalina id: '109467' last_name: Palmirotta citation: ama: Olbrich M, Palmirotta G. Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. Annals of Global Analysis and Geometry. 2022;63(1). doi:10.1007/s10455-022-09882-w apa: Olbrich, M., & Palmirotta, G. (2022). Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces. Annals of Global Analysis and Geometry, 63(1), Article 9. https://doi.org/10.1007/s10455-022-09882-w bibtex: '@article{Olbrich_Palmirotta_2022, title={Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces}, volume={63}, DOI={10.1007/s10455-022-09882-w}, number={19}, journal={Annals of Global Analysis and Geometry}, publisher={Springer Science and Business Media LLC}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022} }' chicago: Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” Annals of Global Analysis and Geometry 63, no. 1 (2022). https://doi.org/10.1007/s10455-022-09882-w. ieee: 'M. Olbrich and G. Palmirotta, “Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces,” Annals of Global Analysis and Geometry, vol. 63, no. 1, Art. no. 9, 2022, doi: 10.1007/s10455-022-09882-w.' mla: Olbrich, Martin, and Guendalina Palmirotta. “Delorme’s Intertwining Conditions for Sections of Homogeneous Vector Bundles on Two- and Three-Dimensional Hyperbolic Spaces.” Annals of Global Analysis and Geometry, vol. 63, no. 1, 9, Springer Science and Business Media LLC, 2022, doi:10.1007/s10455-022-09882-w. short: M. Olbrich, G. Palmirotta, Annals of Global Analysis and Geometry 63 (2022). date_created: 2026-02-20T20:02:50Z date_updated: 2026-02-20T20:03:38Z department: - _id: '10' - _id: '548' doi: 10.1007/s10455-022-09882-w extern: '1' intvolume: ' 63' issue: '1' language: - iso: eng publication: Annals of Global Analysis and Geometry publication_identifier: issn: - 0232-704X - 1572-9060 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Delorme’s intertwining conditions for sections of homogeneous vector bundles on two- and three-dimensional hyperbolic spaces type: journal_article user_id: '109467' volume: 63 year: '2022' ... --- _id: '64571' abstract: - lang: eng text: We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's Paley-Wiener theorem for compactly supported smooth functions on a real reductive group of Harish-Chandra class, we deduce topological Paley-Wiener and Paley-Wiener-Schwartz theorems for sections. author: - first_name: Martin full_name: Olbrich, Martin last_name: Olbrich - first_name: Guendalina full_name: Palmirotta, Guendalina id: '109467' last_name: Palmirotta citation: ama: Olbrich M, Palmirotta G. A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. Journal of Lie theory. 2022;34(2):53--384. apa: Olbrich, M., & Palmirotta, G. (2022). A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$. Journal of Lie Theory, 34(2), 53--384. bibtex: '@article{Olbrich_Palmirotta_2022, title={A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$}, volume={34}, number={2}, journal={Journal of Lie theory}, publisher={Heldermann Verlag}, author={Olbrich, Martin and Palmirotta, Guendalina}, year={2022}, pages={53--384} }' chicago: 'Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie Theory 34, no. 2 (2022): 53--384.' ieee: M. Olbrich and G. Palmirotta, “A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$,” Journal of Lie theory, vol. 34, no. 2, pp. 53--384, 2022. mla: Olbrich, Martin, and Guendalina Palmirotta. “A Topological Paley-Wiener-Schwartz Theorem for Sections of Homogeneous Vector Bundles on $G/K$.” Journal of Lie Theory, vol. 34, no. 2, Heldermann Verlag, 2022, pp. 53--384. short: M. Olbrich, G. Palmirotta, Journal of Lie Theory 34 (2022) 53--384. date_created: 2026-02-20T20:04:49Z date_updated: 2026-02-20T20:07:31Z department: - _id: '10' - _id: '548' extern: '1' external_id: arxiv: - '2202.06905' intvolume: ' 34' issue: '2' language: - iso: eng page: 53--384 publication: Journal of Lie theory publication_status: published publisher: Heldermann Verlag status: public title: A topological Paley-Wiener-Schwartz Theorem for sections of homogeneous vector bundles on $G/K$ type: journal_article user_id: '109467' volume: 34 year: '2022' ... --- _id: '32016' article_type: original author: - first_name: Benjamin full_name: Delarue, Benjamin id: '70575' last_name: Delarue - first_name: Pablo full_name: Ramacher, Pablo last_name: Ramacher citation: ama: Delarue B, Ramacher P. Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. Journal of Symplectic Geometry. 2021;19(6):1281-1337. doi:10.4310/JSG.2021.v19.n6.a1 apa: Delarue, B., & Ramacher, P. (2021). Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions. Journal of Symplectic Geometry, 19(6), 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1 bibtex: '@article{Delarue_Ramacher_2021, title={Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions}, volume={19}, DOI={10.4310/JSG.2021.v19.n6.a1}, number={6}, journal={Journal of Symplectic Geometry}, author={Delarue, Benjamin and Ramacher, Pablo}, year={2021}, pages={1281–1337} }' chicago: 'Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry 19, no. 6 (2021): 1281–1337. https://doi.org/10.4310/JSG.2021.v19.n6.a1.' ieee: 'B. Delarue and P. Ramacher, “Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions,” Journal of Symplectic Geometry, vol. 19, no. 6, pp. 1281–1337, 2021, doi: 10.4310/JSG.2021.v19.n6.a1.' mla: Delarue, Benjamin, and Pablo Ramacher. “Asymptotic Expansion of Generalized Witten Integrals for Hamiltonian Circle Actions.” Journal of Symplectic Geometry, vol. 19, no. 6, 2021, pp. 1281–337, doi:10.4310/JSG.2021.v19.n6.a1. short: B. Delarue, P. Ramacher, Journal of Symplectic Geometry 19 (2021) 1281–1337. date_created: 2022-06-20T08:46:56Z date_updated: 2022-06-21T11:54:50Z department: - _id: '548' doi: 10.4310/JSG.2021.v19.n6.a1 intvolume: ' 19' issue: '6' language: - iso: eng page: 1281 - 1337 publication: Journal of Symplectic Geometry publication_identifier: unknown: - 1540-2347 - 1527-5256 publication_status: published status: public title: Asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions type: journal_article user_id: '70575' volume: 19 year: '2021' ... --- _id: '31058' abstract: - lang: eng 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. author: - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Benjamin full_name: Delarue, Benjamin last_name: Delarue citation: ama: Schütte P, Weich T, Delarue B. Resonances and weighted zeta functions for obstacle scattering via smooth models. Published online 2021. apa: Schütte, P., Weich, T., & Delarue, B. (2021). Resonances and weighted zeta functions for obstacle scattering via smooth models. 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} }' chicago: Schütte, Philipp, Tobias Weich, and Benjamin Delarue. “Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models,” 2021. ieee: P. Schütte, T. Weich, and B. Delarue, “Resonances and weighted zeta functions for obstacle scattering via smooth models.” 2021. mla: Schütte, Philipp, et al. Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models. 2021. short: P. Schütte, T. Weich, B. Delarue, (2021). date_created: 2022-05-04T12:25:58Z date_updated: 2022-05-17T12:05:52Z department: - _id: '10' - _id: '548' external_id: arxiv: - '2109.05907' language: - iso: eng status: public title: Resonances and weighted zeta functions for obstacle scattering via smooth models type: preprint user_id: '50168' year: '2021' ... --- _id: '31261' abstract: - lang: eng text: "Abstract\r\n 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." author: - first_name: Benjamin full_name: Küster, Benjamin last_name: Küster - first_name: Tobias full_name: Weich, Tobias last_name: Weich citation: ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices. 2021;2021(11):8225-8296. doi:10.1093/imrn/rnz068 apa: Küster, B., & Weich, T. (2021). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices, 2021(11), 8225–8296. https://doi.org/10.1093/imrn/rnz068 bibtex: '@article{Küster_Weich_2021, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={10.1093/imrn/rnz068}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2021}, pages={8225–8296} }' chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices 2021, no. 11 (2021): 8225–96. https://doi.org/10.1093/imrn/rnz068.' ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” International Mathematics Research Notices, vol. 2021, no. 11, pp. 8225–8296, 2021, doi: 10.1093/imrn/rnz068.' mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices, vol. 2021, no. 11, Oxford University Press (OUP), 2021, pp. 8225–96, doi:10.1093/imrn/rnz068. short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2021) 8225–8296. date_created: 2022-05-17T12:00:36Z date_updated: 2022-05-25T06:42:01Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1093/imrn/rnz068 external_id: arxiv: - '1710.04625' intvolume: ' 2021' issue: '11' keyword: - General Mathematics language: - iso: eng page: 8225-8296 publication: International Mathematics Research Notices publication_identifier: issn: - 1073-7928 - 1687-0247 publication_status: published publisher: Oxford University Press (OUP) status: public title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces type: journal_article user_id: '49178' volume: 2021 year: '2021' ... --- _id: '31263' author: - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Guillarmou C, Hilgert J, Weich T. High frequency limits for invariant Ruelle densities. Annales Henri Lebesgue. 2021;4:81-119. doi:10.5802/ahl.67 apa: Guillarmou, C., Hilgert, J., & Weich, T. (2021). High frequency limits for invariant Ruelle densities. Annales Henri Lebesgue, 4, 81–119. https://doi.org/10.5802/ahl.67 bibtex: '@article{Guillarmou_Hilgert_Weich_2021, title={High frequency limits for invariant Ruelle densities}, volume={4}, DOI={10.5802/ahl.67}, journal={Annales Henri Lebesgue}, publisher={Cellule MathDoc/CEDRAM}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2021}, pages={81–119} }' chicago: 'Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “High Frequency Limits for Invariant Ruelle Densities.” Annales Henri Lebesgue 4 (2021): 81–119. https://doi.org/10.5802/ahl.67.' ieee: 'C. Guillarmou, J. Hilgert, and T. Weich, “High frequency limits for invariant Ruelle densities,” Annales Henri Lebesgue, vol. 4, pp. 81–119, 2021, doi: 10.5802/ahl.67.' mla: Guillarmou, Colin, et al. “High Frequency Limits for Invariant Ruelle Densities.” Annales Henri Lebesgue, vol. 4, Cellule MathDoc/CEDRAM, 2021, pp. 81–119, doi:10.5802/ahl.67. short: C. Guillarmou, J. Hilgert, T. Weich, Annales Henri Lebesgue 4 (2021) 81–119. date_created: 2022-05-17T12:05:17Z date_updated: 2024-02-19T06:27:43Z department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' doi: 10.5802/ahl.67 external_id: arxiv: - '1803.06717' intvolume: ' 4' language: - iso: eng page: 81-119 publication: Annales Henri Lebesgue publication_identifier: issn: - 2644-9463 publication_status: published publisher: Cellule MathDoc/CEDRAM status: public title: High frequency limits for invariant Ruelle densities type: journal_article user_id: '49063' volume: 4 year: '2021' ... --- _id: '32006' author: - first_name: Colin full_name: Guillarmou, Colin last_name: Guillarmou - first_name: Benjamin full_name: Küster, Benjamin last_name: Küster citation: ama: Guillarmou C, Küster B. Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. Annales Henri Poincaré. 2021;22(11):3565-3617. doi:10.1007/s00023-021-01068-7 apa: Guillarmou, C., & Küster, B. (2021). Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds. Annales Henri Poincaré, 22(11), 3565–3617. https://doi.org/10.1007/s00023-021-01068-7 bibtex: '@article{Guillarmou_Küster_2021, title={Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds}, volume={22}, DOI={10.1007/s00023-021-01068-7}, number={11}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Küster, Benjamin}, year={2021}, pages={3565–3617} }' chicago: 'Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” Annales Henri Poincaré 22, no. 11 (2021): 3565–3617. https://doi.org/10.1007/s00023-021-01068-7.' ieee: 'C. Guillarmou and B. Küster, “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds,” Annales Henri Poincaré, vol. 22, no. 11, pp. 3565–3617, 2021, doi: 10.1007/s00023-021-01068-7.' mla: Guillarmou, Colin, and Benjamin Küster. “Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds.” Annales Henri Poincaré, vol. 22, no. 11, Springer Science and Business Media LLC, 2021, pp. 3565–617, doi:10.1007/s00023-021-01068-7. short: C. Guillarmou, B. Küster, Annales Henri Poincaré 22 (2021) 3565–3617. date_created: 2022-06-20T08:37:52Z date_updated: 2024-04-11T12:39:23Z department: - _id: '548' doi: 10.1007/s00023-021-01068-7 intvolume: ' 22' issue: '11' keyword: - Mathematical Physics - Nuclear and High Energy Physics - Statistical and Nonlinear Physics language: - iso: eng page: 3565-3617 publication: Annales Henri Poincaré publication_identifier: issn: - 1424-0637 - 1424-0661 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Spectral Theory of the Frame Flow on Hyperbolic 3-Manifolds type: journal_article user_id: '70575' volume: 22 year: '2021' ... --- _id: '31264' abstract: - lang: eng text: "AbstractGiven a closed orientable hyperbolic manifold of dimension

$$\\ne 3$$

\r\n \ \r\n ≠\r\n 3\r\n \ \r\n we prove that the multiplicity of the Pollicott-Ruelle resonance of the geodesic flow on perpendicular one-forms at zero agrees with the first Betti number of the manifold. Additionally, we prove that this equality is stable under small perturbations of the Riemannian metric and simultaneous small perturbations of the geodesic vector field within the class of contact vector fields. For more general perturbations we get bounds on the multiplicity of the resonance zero on all one-forms in terms of the first and zeroth Betti numbers. Furthermore, we identify for hyperbolic manifolds further resonance spaces whose multiplicities are given by higher Betti numbers.\r\n" author: - first_name: Benjamin full_name: Küster, Benjamin last_name: Küster - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Küster B, Weich T. Pollicott-Ruelle Resonant States and Betti Numbers. Communications in Mathematical Physics. 2020;378(2):917-941. doi:10.1007/s00220-020-03793-2 apa: Küster, B., & Weich, T. (2020). Pollicott-Ruelle Resonant States and Betti Numbers. Communications in Mathematical Physics, 378(2), 917–941. https://doi.org/10.1007/s00220-020-03793-2 bibtex: '@article{Küster_Weich_2020, title={Pollicott-Ruelle Resonant States and Betti Numbers}, volume={378}, DOI={10.1007/s00220-020-03793-2}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Küster, Benjamin and Weich, Tobias}, year={2020}, pages={917–941} }' chicago: 'Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” Communications in Mathematical Physics 378, no. 2 (2020): 917–41. https://doi.org/10.1007/s00220-020-03793-2.' ieee: 'B. Küster and T. Weich, “Pollicott-Ruelle Resonant States and Betti Numbers,” Communications in Mathematical Physics, vol. 378, no. 2, pp. 917–941, 2020, doi: 10.1007/s00220-020-03793-2.' mla: Küster, Benjamin, and Tobias Weich. “Pollicott-Ruelle Resonant States and Betti Numbers.” Communications in Mathematical Physics, vol. 378, no. 2, Springer Science and Business Media LLC, 2020, pp. 917–41, doi:10.1007/s00220-020-03793-2. short: B. Küster, T. Weich, Communications in Mathematical Physics 378 (2020) 917–941. date_created: 2024-04-11T12:33:03Z date_updated: 2024-04-11T12:36:53Z department: - _id: '548' doi: 10.1007/s00220-020-03793-2 intvolume: ' 378' issue: '2' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 917-941 publication: Communications in Mathematical Physics publication_identifier: issn: - 0010-3616 - 1432-0916 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Pollicott-Ruelle Resonant States and Betti Numbers type: journal_article user_id: '70575' volume: 378 year: '2020' ... --- _id: '31265' author: - first_name: Semyon full_name: Dyatlov, Semyon last_name: Dyatlov - first_name: David full_name: Borthwick, David last_name: Borthwick - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Dyatlov S, Borthwick D, Weich T. Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich. Journal of the European Mathematical Society. 2019;21(6):1595-1639. doi:10.4171/jems/867 apa: Dyatlov, S., Borthwick, D., & Weich, T. (2019). Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich. Journal of the European Mathematical Society, 21(6), 1595–1639. https://doi.org/10.4171/jems/867 bibtex: '@article{Dyatlov_Borthwick_Weich_2019, title={Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich}, volume={21}, DOI={10.4171/jems/867}, number={6}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Dyatlov, Semyon and Borthwick, David and Weich, Tobias}, year={2019}, pages={1595–1639} }' chicago: 'Dyatlov, Semyon, David Borthwick, and Tobias Weich. “Improved Fractal Weyl Bounds for Hyperbolic Manifolds. With an Appendix by David Borthwick, Semyon Dyatlov and Tobias Weich.” Journal of the European Mathematical Society 21, no. 6 (2019): 1595–1639. https://doi.org/10.4171/jems/867.' ieee: 'S. Dyatlov, D. Borthwick, and T. Weich, “Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich,” Journal of the European Mathematical Society, vol. 21, no. 6, pp. 1595–1639, 2019, doi: 10.4171/jems/867.' mla: Dyatlov, Semyon, et al. “Improved Fractal Weyl Bounds for Hyperbolic Manifolds. With an Appendix by David Borthwick, Semyon Dyatlov and Tobias Weich.” Journal of the European Mathematical Society, vol. 21, no. 6, European Mathematical Society - EMS - Publishing House GmbH, 2019, pp. 1595–639, doi:10.4171/jems/867. short: S. Dyatlov, D. Borthwick, T. Weich, Journal of the European Mathematical Society 21 (2019) 1595–1639. date_created: 2022-05-17T12:06:41Z date_updated: 2022-05-19T10:12:59Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.4171/jems/867 external_id: arxiv: - '1512.00836' intvolume: ' 21' issue: '6' keyword: - Applied Mathematics - General Mathematics language: - iso: eng page: 1595-1639 publication: Journal of the European Mathematical Society publication_identifier: issn: - 1435-9855 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Improved fractal Weyl bounds for hyperbolic manifolds. With an appendix by David Borthwick, Semyon Dyatlov and Tobias Weich type: journal_article user_id: '49178' volume: 21 year: '2019' ... --- _id: '31191' abstract: - lang: eng 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 $SL_2(\\mathbb{R})$." author: - first_name: Martin full_name: Kolb, Martin last_name: Kolb - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Lasse Lennart full_name: Wolf, Lasse Lennart id: '45027' last_name: Wolf citation: ama: Kolb M, Weich T, Wolf LL. Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. arXiv:190906183. Published online 2019. apa: Kolb, M., Weich, T., & Wolf, L. L. (2019). Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces. In arXiv:1909.06183. 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} }' chicago: Kolb, Martin, Tobias Weich, and Lasse Lennart Wolf. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” ArXiv:1909.06183, 2019. ieee: M. Kolb, T. Weich, and L. L. Wolf, “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces,” arXiv:1909.06183. 2019. mla: Kolb, Martin, et al. “Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces.” ArXiv:1909.06183, 2019. short: M. Kolb, T. Weich, L.L. Wolf, ArXiv:1909.06183 (2019). date_created: 2022-05-11T10:42:11Z date_updated: 2022-05-24T13:06:58Z department: - _id: '548' external_id: arxiv: - '1909.06183' language: - iso: eng publication: arXiv:1909.06183 status: public title: Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces type: preprint user_id: '45027' year: '2019' ... --- _id: '31302' author: - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte citation: ama: Schütte P. Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces.; 2019. apa: Schütte, P. (2019). Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces. bibtex: '@book{Schütte_2019, title={Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces}, author={Schütte, Philipp}, year={2019} }' chicago: Schütte, Philipp. Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces, 2019. ieee: P. Schütte, Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces. 2019. mla: Schütte, Philipp. Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces. 2019. short: P. Schütte, Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces, 2019. date_created: 2022-05-17T13:41:53Z date_updated: 2024-02-19T06:21:23Z department: - _id: '548' language: - iso: eng status: public supervisor: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Joachim full_name: Hilgert, Joachim id: '220' last_name: Hilgert title: Numerically Investigating Residues of Weighted Zeta Functions on Schottky Surfaces type: mastersthesis user_id: '49063' year: '2019' ... --- _id: '53416' abstract: - lang: eng text: "Abstract\r\n 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." author: - first_name: Benjamin full_name: Küster, Benjamin last_name: Küster - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Küster B, Weich T. Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices. 2019;2021(11):8225-8296. doi:10.1093/imrn/rnz068 apa: Küster, B., & Weich, T. (2019). Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces. International Mathematics Research Notices, 2021(11), 8225–8296. https://doi.org/10.1093/imrn/rnz068 bibtex: '@article{Küster_Weich_2019, title={Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces}, volume={2021}, DOI={10.1093/imrn/rnz068}, number={11}, journal={International Mathematics Research Notices}, publisher={Oxford University Press (OUP)}, author={Küster, Benjamin and Weich, Tobias}, year={2019}, pages={8225–8296} }' chicago: 'Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices 2021, no. 11 (2019): 8225–96. https://doi.org/10.1093/imrn/rnz068.' ieee: 'B. Küster and T. Weich, “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces,” International Mathematics Research Notices, vol. 2021, no. 11, pp. 8225–8296, 2019, doi: 10.1093/imrn/rnz068.' mla: Küster, Benjamin, and Tobias Weich. “Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces.” International Mathematics Research Notices, vol. 2021, no. 11, Oxford University Press (OUP), 2019, pp. 8225–96, doi:10.1093/imrn/rnz068. short: B. Küster, T. Weich, International Mathematics Research Notices 2021 (2019) 8225–8296. date_created: 2024-04-11T12:33:46Z date_updated: 2024-04-11T12:36:33Z department: - _id: '548' doi: 10.1093/imrn/rnz068 intvolume: ' 2021' issue: '11' keyword: - General Mathematics language: - iso: eng page: 8225-8296 publication: International Mathematics Research Notices publication_identifier: issn: - 1073-7928 - 1687-0247 publication_status: published publisher: Oxford University Press (OUP) status: public title: Quantum-Classical Correspondence on Associated Vector Bundles Over Locally Symmetric Spaces type: journal_article user_id: '70575' volume: 2021 year: '2019' ... --- _id: '31301' author: - first_name: Philipp full_name: Schütte, Philipp id: '50168' last_name: Schütte citation: ama: Schütte P. Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks.; 2017. apa: Schütte, P. (2017). Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks. bibtex: '@book{Schütte_2017, title={Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks}, author={Schütte, Philipp}, year={2017} }' chicago: Schütte, Philipp. Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks, 2017. ieee: P. Schütte, Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks. 2017. mla: Schütte, Philipp. Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks. 2017. short: P. Schütte, Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks, 2017. date_created: 2022-05-17T13:40:30Z date_updated: 2022-05-17T13:42:20Z department: - _id: '548' - _id: '288' language: - iso: eng status: public supervisor: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Christine full_name: Silberhorn, Christine id: '26263' last_name: Silberhorn title: Identifying and Realizing Symmetries in Quantum Walks - Symmetry Classes and Quantum Walks type: bachelorsthesis user_id: '50168' year: '2017' ...