--- _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: '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: '51389' 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: C. full_name: Guillarmou, C. last_name: Guillarmou citation: ama: Hilgert J, Weich T, Guillarmou C. Classical and quantum resonances for hyperbolic surfaces. Math Ann. 2018;370:1231-1275. apa: Hilgert, J., Weich, T., & Guillarmou, C. (2018). Classical and quantum resonances for hyperbolic surfaces. Math. Ann., 370, 1231–1275. bibtex: '@article{Hilgert_Weich_Guillarmou_2018, title={Classical and quantum resonances for hyperbolic surfaces}, volume={370}, journal={Math. Ann.}, author={Hilgert, Joachim and Weich, Tobias and Guillarmou, C.}, year={2018}, pages={1231–1275} }' chicago: 'Hilgert, Joachim, Tobias Weich, and C. Guillarmou. “Classical and Quantum Resonances for Hyperbolic Surfaces.” Math. Ann. 370 (2018): 1231–75.' ieee: J. Hilgert, T. Weich, and C. Guillarmou, “Classical and quantum resonances for hyperbolic surfaces,” Math. Ann., vol. 370, pp. 1231–1275, 2018. mla: Hilgert, Joachim, et al. “Classical and Quantum Resonances for Hyperbolic Surfaces.” Math. Ann., vol. 370, 2018, pp. 1231–75. short: J. Hilgert, T. Weich, C. Guillarmou, Math. Ann. 370 (2018) 1231–1275. date_created: 2024-02-19T06:41:17Z date_updated: 2026-03-31T08:24:58Z department: - _id: '91' intvolume: ' 370' language: - iso: eng page: 1231-1275 publication: Math. Ann. publication_status: published status: public title: Classical and quantum resonances for hyperbolic surfaces type: journal_article user_id: '220' volume: 370 year: '2018' ... --- _id: '31268' author: - first_name: Frédéric full_name: Faure, Frédéric last_name: Faure - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Faure F, Weich T. Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. Communications in Mathematical Physics. 2017;356(3):755-822. doi:10.1007/s00220-017-3000-0 apa: Faure, F., & Weich, T. (2017). Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps. Communications in Mathematical Physics, 356(3), 755–822. https://doi.org/10.1007/s00220-017-3000-0 bibtex: '@article{Faure_Weich_2017, title={Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps}, volume={356}, DOI={10.1007/s00220-017-3000-0}, number={3}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Faure, Frédéric and Weich, Tobias}, year={2017}, pages={755–822} }' chicago: 'Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” Communications in Mathematical Physics 356, no. 3 (2017): 755–822. https://doi.org/10.1007/s00220-017-3000-0.' ieee: 'F. Faure and T. Weich, “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps,” Communications in Mathematical Physics, vol. 356, no. 3, pp. 755–822, 2017, doi: 10.1007/s00220-017-3000-0.' mla: Faure, Frédéric, and Tobias Weich. “Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps.” Communications in Mathematical Physics, vol. 356, no. 3, Springer Science and Business Media LLC, 2017, pp. 755–822, doi:10.1007/s00220-017-3000-0. short: F. Faure, T. Weich, Communications in Mathematical Physics 356 (2017) 755–822. date_created: 2022-05-17T12:11:13Z date_updated: 2022-05-19T10:14:36Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1007/s00220-017-3000-0 external_id: arxiv: - '1504.06728' intvolume: ' 356' issue: '3' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 755-822 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: Global Normal Form and Asymptotic Spectral Gap for Open Partially Expanding Maps type: journal_article user_id: '49178' volume: 356 year: '2017' ... --- _id: '31272' author: - first_name: Benjamin full_name: Harris, Benjamin last_name: Harris - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Harris B, Weich T. Wave front sets of reductive Lie group representations III. Advances in Mathematics. 2017;313:176-236. doi:10.1016/j.aim.2017.03.025 apa: Harris, B., & Weich, T. (2017). Wave front sets of reductive Lie group representations III. Advances in Mathematics, 313, 176–236. https://doi.org/10.1016/j.aim.2017.03.025 bibtex: '@article{Harris_Weich_2017, title={Wave front sets of reductive Lie group representations III}, volume={313}, DOI={10.1016/j.aim.2017.03.025}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Harris, Benjamin and Weich, Tobias}, year={2017}, pages={176–236} }' chicago: 'Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” Advances in Mathematics 313 (2017): 176–236. https://doi.org/10.1016/j.aim.2017.03.025.' ieee: 'B. Harris and T. Weich, “Wave front sets of reductive Lie group representations III,” Advances in Mathematics, vol. 313, pp. 176–236, 2017, doi: 10.1016/j.aim.2017.03.025.' mla: Harris, Benjamin, and Tobias Weich. “Wave Front Sets of Reductive Lie Group Representations III.” Advances in Mathematics, vol. 313, Elsevier BV, 2017, pp. 176–236, doi:10.1016/j.aim.2017.03.025. short: B. Harris, T. Weich, Advances in Mathematics 313 (2017) 176–236. date_created: 2022-05-17T12:16:37Z date_updated: 2022-05-19T10:15:00Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1016/j.aim.2017.03.025 external_id: arxiv: - '1503.08431' intvolume: ' 313' keyword: - General Mathematics language: - iso: eng page: 176-236 publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier BV status: public title: Wave front sets of reductive Lie group representations III type: journal_article user_id: '49178' volume: 313 year: '2017' ... --- _id: '31267' 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. Classical and quantum resonances for hyperbolic surfaces. Mathematische Annalen. 2017;370(3-4):1231-1275. doi:10.1007/s00208-017-1576-5 apa: Guillarmou, C., Hilgert, J., & Weich, T. (2017). Classical and quantum resonances for hyperbolic surfaces. Mathematische Annalen, 370(3–4), 1231–1275. https://doi.org/10.1007/s00208-017-1576-5 bibtex: '@article{Guillarmou_Hilgert_Weich_2017, title={Classical and quantum resonances for hyperbolic surfaces}, volume={370}, DOI={10.1007/s00208-017-1576-5}, number={3–4}, journal={Mathematische Annalen}, publisher={Springer Science and Business Media LLC}, author={Guillarmou, Colin and Hilgert, Joachim and Weich, Tobias}, year={2017}, pages={1231–1275} }' chicago: 'Guillarmou, Colin, Joachim Hilgert, and Tobias Weich. “Classical and Quantum Resonances for Hyperbolic Surfaces.” Mathematische Annalen 370, no. 3–4 (2017): 1231–75. https://doi.org/10.1007/s00208-017-1576-5.' ieee: 'C. Guillarmou, J. Hilgert, and T. Weich, “Classical and quantum resonances for hyperbolic surfaces,” Mathematische Annalen, vol. 370, no. 3–4, pp. 1231–1275, 2017, doi: 10.1007/s00208-017-1576-5.' mla: Guillarmou, Colin, et al. “Classical and Quantum Resonances for Hyperbolic Surfaces.” Mathematische Annalen, vol. 370, no. 3–4, Springer Science and Business Media LLC, 2017, pp. 1231–75, doi:10.1007/s00208-017-1576-5. short: C. Guillarmou, J. Hilgert, T. Weich, Mathematische Annalen 370 (2017) 1231–1275. date_created: 2022-05-17T12:09:43Z date_updated: 2024-02-19T06:18:21Z department: - _id: '10' - _id: '623' - _id: '548' - _id: '91' doi: 10.1007/s00208-017-1576-5 external_id: arxiv: - '1605.08801' intvolume: ' 370' issue: 3-4 keyword: - General Mathematics language: - iso: eng page: 1231-1275 publication: Mathematische Annalen publication_identifier: issn: - 0025-5831 - 1432-1807 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Classical and quantum resonances for hyperbolic surfaces type: journal_article user_id: '49063' volume: 370 year: '2017' ... --- _id: '31377' article_type: original author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: Max full_name: Hoffmann, Max id: '32202' last_name: Hoffmann orcid: 0000-0002-6964-7123 citation: ama: 'Weich T, Hoffmann M. Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt. die hochschullehre. 2017;3.' apa: 'Weich, T., & Hoffmann, M. (2017). Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt. die hochschullehre, 3.' bibtex: '@article{Weich_Hoffmann_2017, title={Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.}, volume={3}, journal={die hochschullehre}, author={Weich, Tobias and Hoffmann, Max}, year={2017} }' chicago: 'Weich, Tobias, and Max Hoffmann. “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.” die hochschullehre 3 (2017).' ieee: 'T. Weich and M. Hoffmann, “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.,” die hochschullehre, vol. 3, 2017.' mla: 'Weich, Tobias, and Max Hoffmann. “Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.” die hochschullehre, vol. 3, 2017.' short: T. Weich, M. Hoffmann, die hochschullehre 3 (2017). date_created: 2022-05-22T15:00:35Z date_updated: 2023-07-19T13:59:03Z department: - _id: '97' intvolume: ' 3' language: - iso: ger main_file_link: - open_access: '1' url: http://www.hochschullehre.org/wp-content/files/diehochschullehre_2017_weich_hoffmann.pdf oa: '1' publication: die hochschullehre publication_status: published quality_controlled: '1' status: public title: 'Exkursinhalte in der fachmathematischen Lehramtsausbildung: Wie man das Wesen und die Rolle der Mathematik vermittelt.' type: journal_article user_id: '32202' volume: 3 year: '2017' ... --- _id: '31274' author: - 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: Borthwick D, Weich T. Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions. Journal of Spectral Theory. 2016;6(2):267-329. doi:10.4171/jst/125 apa: Borthwick, D., & Weich, T. (2016). Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions. Journal of Spectral Theory, 6(2), 267–329. https://doi.org/10.4171/jst/125 bibtex: '@article{Borthwick_Weich_2016, title={Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions}, volume={6}, DOI={10.4171/jst/125}, number={2}, journal={Journal of Spectral Theory}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Borthwick, David and Weich, Tobias}, year={2016}, pages={267–329} }' chicago: 'Borthwick, David, and Tobias Weich. “Symmetry Reduction of Holomorphic Iterated Function Schemes and Factorization of Selberg Zeta Functions.” Journal of Spectral Theory 6, no. 2 (2016): 267–329. https://doi.org/10.4171/jst/125.' ieee: 'D. Borthwick and T. Weich, “Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions,” Journal of Spectral Theory, vol. 6, no. 2, pp. 267–329, 2016, doi: 10.4171/jst/125.' mla: Borthwick, David, and Tobias Weich. “Symmetry Reduction of Holomorphic Iterated Function Schemes and Factorization of Selberg Zeta Functions.” Journal of Spectral Theory, vol. 6, no. 2, European Mathematical Society - EMS - Publishing House GmbH, 2016, pp. 267–329, doi:10.4171/jst/125. short: D. Borthwick, T. Weich, Journal of Spectral Theory 6 (2016) 267–329. date_created: 2022-05-17T12:18:22Z date_updated: 2022-05-19T10:15:17Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.4171/jst/125 external_id: arxiv: - '1407.6134 ' intvolume: ' 6' issue: '2' keyword: - Geometry and Topology - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 267-329 publication: Journal of Spectral Theory publication_identifier: issn: - 1664-039X publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Symmetry reduction of holomorphic iterated function schemes and factorization of Selberg zeta functions type: journal_article user_id: '49178' volume: 6 year: '2016' ... --- _id: '31289' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Weich T. On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows. Annales Henri Poincaré. 2016;18(1):37-52. doi:10.1007/s00023-016-0514-5 apa: Weich, T. (2016). On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows. Annales Henri Poincaré, 18(1), 37–52. https://doi.org/10.1007/s00023-016-0514-5 bibtex: '@article{Weich_2016, title={On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows}, volume={18}, DOI={10.1007/s00023-016-0514-5}, number={1}, journal={Annales Henri Poincaré}, publisher={Springer Science and Business Media LLC}, author={Weich, Tobias}, year={2016}, pages={37–52} }' chicago: 'Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows.” Annales Henri Poincaré 18, no. 1 (2016): 37–52. https://doi.org/10.1007/s00023-016-0514-5.' ieee: 'T. Weich, “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows,” Annales Henri Poincaré, vol. 18, no. 1, pp. 37–52, 2016, doi: 10.1007/s00023-016-0514-5.' mla: Weich, Tobias. “On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows.” Annales Henri Poincaré, vol. 18, no. 1, Springer Science and Business Media LLC, 2016, pp. 37–52, doi:10.1007/s00023-016-0514-5. short: T. Weich, Annales Henri Poincaré 18 (2016) 37–52. date_created: 2022-05-17T12:53:51Z date_updated: 2022-05-19T10:15:36Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1007/s00023-016-0514-5 external_id: arxiv: - '1511.08338' intvolume: ' 18' issue: '1' keyword: - Mathematical Physics - Nuclear and High Energy Physics - Statistical and Nonlinear Physics language: - iso: eng page: 37-52 publication: Annales Henri Poincaré publication_identifier: issn: - 1424-0637 - 1424-0661 publication_status: published publisher: Springer Science and Business Media LLC status: public title: On the Support of Pollicott–Ruelle Resonanant States for Anosov Flows type: journal_article user_id: '49178' volume: 18 year: '2016' ... --- _id: '31291' abstract: - lang: eng text: We consider a simple model of an open partially expanding map. Its trapped set

${\mathcal{K}}$

in phase space is a fractal set. We first show that there is a well-defined discrete spectrum of Ruelle resonances which describes the asymptotic of correlation functions for large time and which is parametrized by the Fourier component

$\unicode[STIX]{x1D708}$

in the neutral direction of the dynamics. We introduce a specific hypothesis on the dynamics that we call ‘minimal captivity’. This hypothesis is stable under perturbations and means that the dynamics is univalued in a neighborhood of

${\mathcal{K}}$

. Under this hypothesis we show the existence of an asymptotic spectral gap and a fractal Weyl law for the upper bound of density of Ruelle resonances in the semiclassical limit

$\unicode[STIX]{x1D708}\rightarrow \infty$

. Some numerical computations with the truncated Gauss map and Bowen–Series maps illustrate these results. author: - first_name: JEAN FRANCOIS full_name: ARNOLDI, JEAN FRANCOIS last_name: ARNOLDI - first_name: FRÉDÉRIC full_name: FAURE, FRÉDÉRIC last_name: FAURE - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: ARNOLDI JF, FAURE F, Weich T. Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. Ergodic Theory and Dynamical Systems. 2015;37(1):1-58. doi:10.1017/etds.2015.34 apa: ARNOLDI, J. F., FAURE, F., & Weich, T. (2015). Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps. Ergodic Theory and Dynamical Systems, 37(1), 1–58. https://doi.org/10.1017/etds.2015.34 bibtex: '@article{ARNOLDI_FAURE_Weich_2015, title={Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps}, volume={37}, DOI={10.1017/etds.2015.34}, number={1}, journal={Ergodic Theory and Dynamical Systems}, publisher={Cambridge University Press (CUP)}, author={ARNOLDI, JEAN FRANCOIS and FAURE, FRÉDÉRIC and Weich, Tobias}, year={2015}, pages={1–58} }' chicago: 'ARNOLDI, JEAN FRANCOIS, FRÉDÉRIC FAURE, and Tobias Weich. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” Ergodic Theory and Dynamical Systems 37, no. 1 (2015): 1–58. https://doi.org/10.1017/etds.2015.34.' ieee: 'J. F. ARNOLDI, F. FAURE, and T. Weich, “Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps,” Ergodic Theory and Dynamical Systems, vol. 37, no. 1, pp. 1–58, 2015, doi: 10.1017/etds.2015.34.' mla: ARNOLDI, JEAN FRANCOIS, et al. “Asymptotic Spectral Gap and Weyl Law for Ruelle Resonances of Open Partially Expanding Maps.” Ergodic Theory and Dynamical Systems, vol. 37, no. 1, Cambridge University Press (CUP), 2015, pp. 1–58, doi:10.1017/etds.2015.34. short: J.F. ARNOLDI, F. FAURE, T. Weich, Ergodic Theory and Dynamical Systems 37 (2015) 1–58. date_created: 2022-05-17T12:55:26Z date_updated: 2022-05-19T10:15:54Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1017/etds.2015.34 external_id: arxiv: - '1302.3087' intvolume: ' 37' issue: '1' keyword: - Applied Mathematics - General Mathematics language: - iso: eng page: 1-58 publication: Ergodic Theory and Dynamical Systems publication_identifier: issn: - 0143-3857 - 1469-4417 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Asymptotic spectral gap and Weyl law for Ruelle resonances of open partially expanding maps type: journal_article user_id: '49178' volume: 37 year: '2015' ... --- _id: '31293' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Weich T. Resonance Chains and Geometric Limits on Schottky Surfaces. Communications in Mathematical Physics. 2015;337(2):727-765. doi:10.1007/s00220-015-2359-z apa: Weich, T. (2015). Resonance Chains and Geometric Limits on Schottky Surfaces. Communications in Mathematical Physics, 337(2), 727–765. https://doi.org/10.1007/s00220-015-2359-z bibtex: '@article{Weich_2015, title={Resonance Chains and Geometric Limits on Schottky Surfaces}, volume={337}, DOI={10.1007/s00220-015-2359-z}, number={2}, journal={Communications in Mathematical Physics}, publisher={Springer Science and Business Media LLC}, author={Weich, Tobias}, year={2015}, pages={727–765} }' chicago: 'Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” Communications in Mathematical Physics 337, no. 2 (2015): 727–65. https://doi.org/10.1007/s00220-015-2359-z.' ieee: 'T. Weich, “Resonance Chains and Geometric Limits on Schottky Surfaces,” Communications in Mathematical Physics, vol. 337, no. 2, pp. 727–765, 2015, doi: 10.1007/s00220-015-2359-z.' mla: Weich, Tobias. “Resonance Chains and Geometric Limits on Schottky Surfaces.” Communications in Mathematical Physics, vol. 337, no. 2, Springer Science and Business Media LLC, 2015, pp. 727–65, doi:10.1007/s00220-015-2359-z. short: T. Weich, Communications in Mathematical Physics 337 (2015) 727–765. date_created: 2022-05-17T12:56:21Z date_updated: 2022-05-19T10:16:21Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1007/s00220-015-2359-z external_id: arxiv: - '1403.7419 ' intvolume: ' 337' issue: '2' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 727-765 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: Resonance Chains and Geometric Limits on Schottky Surfaces type: journal_article user_id: '49178' volume: 337 year: '2015' ... --- _id: '31294' article_number: '101501' author: - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Weich T. Equivariant spectral asymptotics forh-pseudodifferential operators. Journal of Mathematical Physics. 2014;55(10). doi:10.1063/1.4896698 apa: Weich, T. (2014). Equivariant spectral asymptotics forh-pseudodifferential operators. Journal of Mathematical Physics, 55(10), Article 101501. https://doi.org/10.1063/1.4896698 bibtex: '@article{Weich_2014, title={Equivariant spectral asymptotics forh-pseudodifferential operators}, volume={55}, DOI={10.1063/1.4896698}, number={10101501}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Weich, Tobias}, year={2014} }' chicago: Weich, Tobias. “Equivariant Spectral Asymptotics forh-Pseudodifferential Operators.” Journal of Mathematical Physics 55, no. 10 (2014). https://doi.org/10.1063/1.4896698. ieee: 'T. Weich, “Equivariant spectral asymptotics forh-pseudodifferential operators,” Journal of Mathematical Physics, vol. 55, no. 10, Art. no. 101501, 2014, doi: 10.1063/1.4896698.' mla: Weich, Tobias. “Equivariant Spectral Asymptotics forh-Pseudodifferential Operators.” Journal of Mathematical Physics, vol. 55, no. 10, 101501, AIP Publishing, 2014, doi:10.1063/1.4896698. short: T. Weich, Journal of Mathematical Physics 55 (2014). date_created: 2022-05-17T12:57:00Z date_updated: 2022-05-19T10:16:38Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1063/1.4896698 external_id: arxiv: - '1311.2436 ' intvolume: ' 55' issue: '10' keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng publication: Journal of Mathematical Physics publication_identifier: issn: - 0022-2488 - 1089-7658 publication_status: published publisher: AIP Publishing status: public title: Equivariant spectral asymptotics forh-pseudodifferential operators type: journal_article user_id: '49178' volume: 55 year: '2014' ... --- _id: '31296' author: - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen - first_name: F full_name: Faure, F last_name: Faure - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 citation: ama: Barkhofen S, Faure F, Weich T. Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum. Nonlinearity. 2014;27(8):1829-1858. doi:10.1088/0951-7715/27/8/1829 apa: Barkhofen, S., Faure, F., & Weich, T. (2014). Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum. Nonlinearity, 27(8), 1829–1858. https://doi.org/10.1088/0951-7715/27/8/1829 bibtex: '@article{Barkhofen_Faure_Weich_2014, title={Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum}, volume={27}, DOI={10.1088/0951-7715/27/8/1829}, number={8}, journal={Nonlinearity}, publisher={IOP Publishing}, author={Barkhofen, Sonja and Faure, F and Weich, Tobias}, year={2014}, pages={1829–1858} }' chicago: 'Barkhofen, Sonja, F Faure, and Tobias Weich. “Resonance Chains in Open Systems, Generalized Zeta Functions and Clustering of the Length Spectrum.” Nonlinearity 27, no. 8 (2014): 1829–58. https://doi.org/10.1088/0951-7715/27/8/1829.' ieee: 'S. Barkhofen, F. Faure, and T. Weich, “Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum,” Nonlinearity, vol. 27, no. 8, pp. 1829–1858, 2014, doi: 10.1088/0951-7715/27/8/1829.' mla: Barkhofen, Sonja, et al. “Resonance Chains in Open Systems, Generalized Zeta Functions and Clustering of the Length Spectrum.” Nonlinearity, vol. 27, no. 8, IOP Publishing, 2014, pp. 1829–58, doi:10.1088/0951-7715/27/8/1829. short: S. Barkhofen, F. Faure, T. Weich, Nonlinearity 27 (2014) 1829–1858. date_created: 2022-05-17T12:58:25Z date_updated: 2023-01-19T08:56:12Z department: - _id: '10' - _id: '548' - _id: '288' doi: 10.1088/0951-7715/27/8/1829 external_id: arxiv: - '1403.7771 ' intvolume: ' 27' issue: '8' keyword: - Applied Mathematics - General Physics and Astronomy - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng page: 1829-1858 publication: Nonlinearity publication_identifier: issn: - 0951-7715 - 1361-6544 publication_status: published publisher: IOP Publishing status: public title: Resonance chains in open systems, generalized zeta functions and clustering of the length spectrum type: journal_article user_id: '48188' volume: 27 year: '2014' ... --- _id: '31297' article_number: '033029' author: - 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 - first_name: U full_name: Kuhl, U last_name: Kuhl - first_name: C full_name: Poli, C last_name: Poli - first_name: H full_name: Schomerus, H last_name: Schomerus citation: ama: Weich T, Barkhofen S, Kuhl U, Poli C, Schomerus H. Formation and interaction of resonance chains in the open three-disk system. New Journal of Physics. 2014;16(3). doi:10.1088/1367-2630/16/3/033029 apa: Weich, T., Barkhofen, S., Kuhl, U., Poli, C., & Schomerus, H. (2014). Formation and interaction of resonance chains in the open three-disk system. New Journal of Physics, 16(3), Article 033029. https://doi.org/10.1088/1367-2630/16/3/033029 bibtex: '@article{Weich_Barkhofen_Kuhl_Poli_Schomerus_2014, title={Formation and interaction of resonance chains in the open three-disk system}, volume={16}, DOI={10.1088/1367-2630/16/3/033029}, number={3033029}, journal={New Journal of Physics}, publisher={IOP Publishing}, author={Weich, Tobias and Barkhofen, Sonja and Kuhl, U and Poli, C and Schomerus, H}, year={2014} }' chicago: Weich, Tobias, Sonja Barkhofen, U Kuhl, C Poli, and H Schomerus. “Formation and Interaction of Resonance Chains in the Open Three-Disk System.” New Journal of Physics 16, no. 3 (2014). https://doi.org/10.1088/1367-2630/16/3/033029. ieee: 'T. Weich, S. Barkhofen, U. Kuhl, C. Poli, and H. Schomerus, “Formation and interaction of resonance chains in the open three-disk system,” New Journal of Physics, vol. 16, no. 3, Art. no. 033029, 2014, doi: 10.1088/1367-2630/16/3/033029.' mla: Weich, Tobias, et al. “Formation and Interaction of Resonance Chains in the Open Three-Disk System.” New Journal of Physics, vol. 16, no. 3, 033029, IOP Publishing, 2014, doi:10.1088/1367-2630/16/3/033029. short: T. Weich, S. Barkhofen, U. Kuhl, C. Poli, H. Schomerus, New Journal of Physics 16 (2014). date_created: 2022-05-17T12:59:49Z date_updated: 2023-01-24T08:07:57Z department: - _id: '10' - _id: '548' doi: 10.1088/1367-2630/16/3/033029 external_id: arxiv: - '1311.5128 ' intvolume: ' 16' issue: '3' keyword: - General Physics and Astronomy language: - iso: eng publication: New Journal of Physics publication_identifier: issn: - 1367-2630 publication_status: published publisher: IOP Publishing status: public title: Formation and interaction of resonance chains in the open three-disk system type: journal_article user_id: '48188' volume: 16 year: '2014' ... --- _id: '31298' article_number: '164102' author: - first_name: Sonja full_name: Barkhofen, Sonja id: '48188' last_name: Barkhofen - first_name: Tobias full_name: Weich, Tobias id: '49178' last_name: Weich orcid: 0000-0002-9648-6919 - first_name: A. full_name: Potzuweit, A. last_name: Potzuweit - first_name: H.-J. full_name: Stöckmann, H.-J. last_name: Stöckmann - first_name: U. full_name: Kuhl, U. last_name: Kuhl - first_name: M. full_name: Zworski, M. last_name: Zworski citation: ama: Barkhofen S, Weich T, Potzuweit A, Stöckmann H-J, Kuhl U, Zworski M. Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. Physical Review Letters. 2013;110(16). doi:10.1103/physrevlett.110.164102 apa: Barkhofen, S., Weich, T., Potzuweit, A., Stöckmann, H.-J., Kuhl, U., & Zworski, M. (2013). Experimental Observation of the Spectral Gap in Microwave n-Disk Systems. Physical Review Letters, 110(16), Article 164102. https://doi.org/10.1103/physrevlett.110.164102 bibtex: '@article{Barkhofen_Weich_Potzuweit_Stöckmann_Kuhl_Zworski_2013, title={Experimental Observation of the Spectral Gap in Microwave n-Disk Systems}, volume={110}, DOI={10.1103/physrevlett.110.164102}, number={16164102}, journal={Physical Review Letters}, publisher={American Physical Society (APS)}, author={Barkhofen, Sonja and Weich, Tobias and Potzuweit, A. and Stöckmann, H.-J. and Kuhl, U. and Zworski, M.}, year={2013} }' chicago: Barkhofen, Sonja, Tobias Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” Physical Review Letters 110, no. 16 (2013). https://doi.org/10.1103/physrevlett.110.164102. ieee: 'S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, and M. Zworski, “Experimental Observation of the Spectral Gap in Microwave n-Disk Systems,” Physical Review Letters, vol. 110, no. 16, Art. no. 164102, 2013, doi: 10.1103/physrevlett.110.164102.' mla: Barkhofen, Sonja, et al. “Experimental Observation of the Spectral Gap in Microwave N-Disk Systems.” Physical Review Letters, vol. 110, no. 16, 164102, American Physical Society (APS), 2013, doi:10.1103/physrevlett.110.164102. short: S. Barkhofen, T. Weich, A. Potzuweit, H.-J. Stöckmann, U. Kuhl, M. Zworski, Physical Review Letters 110 (2013). date_created: 2022-05-17T13:00:47Z date_updated: 2023-01-19T08:49:01Z department: - _id: '10' - _id: '548' - _id: '288' doi: 10.1103/physrevlett.110.164102 external_id: arxiv: - '1212.5897 ' intvolume: ' 110' issue: '16' keyword: - General Physics and Astronomy language: - iso: eng publication: Physical Review Letters publication_identifier: issn: - 0031-9007 - 1079-7114 publication_status: published publisher: American Physical Society (APS) status: public title: Experimental Observation of the Spectral Gap in Microwave n-Disk Systems type: journal_article user_id: '48188' volume: 110 year: '2013' ... --- _id: '31300' article_number: '066205' author: - first_name: A. full_name: Potzuweit, A. last_name: Potzuweit - 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 - first_name: U. full_name: Kuhl, U. last_name: Kuhl - first_name: H.-J. full_name: Stöckmann, H.-J. last_name: Stöckmann - first_name: M. full_name: Zworski, M. last_name: Zworski citation: ama: 'Potzuweit A, Weich T, Barkhofen S, Kuhl U, Stöckmann H-J, Zworski M. Weyl asymptotics: From closed to open systems. Physical Review E. 2012;86(6). doi:10.1103/physreve.86.066205' apa: 'Potzuweit, A., Weich, T., Barkhofen, S., Kuhl, U., Stöckmann, H.-J., & Zworski, M. (2012). Weyl asymptotics: From closed to open systems. Physical Review E, 86(6), Article 066205. https://doi.org/10.1103/physreve.86.066205' bibtex: '@article{Potzuweit_Weich_Barkhofen_Kuhl_Stöckmann_Zworski_2012, title={Weyl asymptotics: From closed to open systems}, volume={86}, DOI={10.1103/physreve.86.066205}, number={6066205}, journal={Physical Review E}, publisher={American Physical Society (APS)}, author={Potzuweit, A. and Weich, Tobias and Barkhofen, Sonja and Kuhl, U. and Stöckmann, H.-J. and Zworski, M.}, year={2012} }' chicago: 'Potzuweit, A., Tobias Weich, Sonja Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski. “Weyl Asymptotics: From Closed to Open Systems.” Physical Review E 86, no. 6 (2012). https://doi.org/10.1103/physreve.86.066205.' ieee: 'A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, and M. Zworski, “Weyl asymptotics: From closed to open systems,” Physical Review E, vol. 86, no. 6, Art. no. 066205, 2012, doi: 10.1103/physreve.86.066205.' mla: 'Potzuweit, A., et al. “Weyl Asymptotics: From Closed to Open Systems.” Physical Review E, vol. 86, no. 6, 066205, American Physical Society (APS), 2012, doi:10.1103/physreve.86.066205.' short: A. Potzuweit, T. Weich, S. Barkhofen, U. Kuhl, H.-J. Stöckmann, M. Zworski, Physical Review E 86 (2012). date_created: 2022-05-17T13:01:39Z date_updated: 2022-05-19T10:18:57Z department: - _id: '10' - _id: '623' - _id: '548' doi: 10.1103/physreve.86.066205 external_id: arxiv: - '1209.2304' intvolume: ' 86' issue: '6' keyword: - Industrial and Manufacturing Engineering - Metals and Alloys - Strategy and Management - Mechanical Engineering language: - iso: eng publication: Physical Review E publication_identifier: issn: - 1539-3755 - 1550-2376 publication_status: published publisher: American Physical Society (APS) status: public title: 'Weyl asymptotics: From closed to open systems' type: journal_article user_id: '49178' volume: 86 year: '2012' ...