--- _id: '14441' abstract: - lang: eng text: We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation. acknowledgement: Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: 'Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 2023;404:287-337. doi:10.1007/s00220-023-04841-3' apa: 'Brooks, M., & Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04841-3' chicago: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04841-3.' ieee: 'M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” Communications in Mathematical Physics, vol. 404. Springer Nature, pp. 287–337, 2023.' ista: 'Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.' mla: 'Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” Communications in Mathematical Physics, vol. 404, Springer Nature, 2023, pp. 287–337, doi:10.1007/s00220-023-04841-3.' short: M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337. date_created: 2023-10-22T22:01:13Z date_published: 2023-11-01T00:00:00Z date_updated: 2023-10-31T12:22:51Z day: '01' ddc: - '510' department: - _id: RoSe doi: 10.1007/s00220-023-04841-3 ec_funded: 1 external_id: arxiv: - '2207.03156' file: - access_level: open_access checksum: 1ae49b39247cb6b40ff75997381581b8 content_type: application/pdf creator: dernst date_created: 2023-10-31T12:21:39Z date_updated: 2023-10-31T12:21:39Z file_id: '14477' file_name: 2023_CommMathPhysics_Brooks.pdf file_size: 832375 relation: main_file success: 1 file_date_updated: 2023-10-31T12:21:39Z has_accepted_license: '1' intvolume: ' 404' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '11' oa: 1 oa_version: Published Version page: 287-337 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: 'The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy' tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 404 year: '2023' ... --- _id: '12390' abstract: - lang: eng text: "The scope of this thesis is to study quantum systems exhibiting a continuous symmetry that\r\nis broken on the level of the corresponding effective theory. In particular we are going to\r\ninvestigate translation-invariant Bose gases in the mean field limit, effectively described by\r\nthe Hartree functional, and the Fröhlich Polaron in the regime of strong coupling, effectively\r\ndescribed by the Pekar functional. The latter is a model describing the interaction between a\r\ncharged particle and the optical modes of a polar crystal. Regarding the former, we assume in\r\naddition that the particles in the gas are unconfined, and typically we will consider particles\r\nthat are subject to an attractive interaction. In both cases the ground state energy of the\r\nHamiltonian is not a proper eigenvalue due to the underlying translation-invariance, while on\r\nthe contrary there exists a whole invariant orbit of minimizers for the corresponding effective\r\nfunctionals. Both, the absence of proper eigenstates and the broken symmetry of the effective\r\ntheory, make the study significantly more involved and it is the content of this thesis to\r\ndevelop a frameworks which allows for a systematic way to circumvent these issues.\r\nIt is a well-established result that the ground state energy of Bose gases in the mean field limit,\r\nas well as the ground state energy of the Fröhlich Polaron in the regime of strong coupling, is\r\nto leading order given by the minimal energy of the corresponding effective theory. As part\r\nof this thesis we identify the sub-leading term in the expansion of the ground state energy,\r\nwhich can be interpreted as the quantum correction to the classical energy, since the effective\r\ntheories under consideration can be seen as classical counterparts.\r\nWe are further going to establish an asymptotic expression for the energy-momentum relation\r\nof the Fröhlich Polaron in the strong coupling limit. In the regime of suitably small momenta,\r\nthis asymptotic expression agrees with the energy-momentum relation of a free particle having\r\nan effectively increased mass, and we find that this effectively increased mass agrees with the\r\nconjectured value in the physics literature.\r\nIn addition we will discuss two unrelated papers written by the author during his stay at ISTA\r\nin the appendix. The first one concerns the realization of anyons, which are quasi-particles\r\nacquiring a non-trivial phase under the exchange of two particles, as molecular impurities.\r\nThe second one provides a classification of those vector fields defined on a given manifold\r\nthat can be written as the gradient of a given functional with respect to a suitable metric,\r\nprovided that some mild smoothness assumptions hold. This classification is subsequently\r\nused to identify those quantum Markov semigroups that can be written as a gradient flow of\r\nthe relative entropy.\r\n" alternative_title: - ISTA Thesis article_processing_charge: No author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 citation: ama: Brooks M. Translation-invariant quantum systems with effectively broken symmetry. 2022. doi:10.15479/at:ista:12390 apa: Brooks, M. (2022). Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:12390 chicago: Brooks, Morris. “Translation-Invariant Quantum Systems with Effectively Broken Symmetry.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:12390. ieee: M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022. ista: Brooks M. 2022. Translation-invariant quantum systems with effectively broken symmetry. Institute of Science and Technology Austria. mla: Brooks, Morris. Translation-Invariant Quantum Systems with Effectively Broken Symmetry. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:12390. short: M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022. date_created: 2023-01-26T10:00:42Z date_published: 2022-12-15T00:00:00Z date_updated: 2023-08-07T13:32:09Z day: '15' ddc: - '500' degree_awarded: PhD department: - _id: GradSch - _id: RoSe doi: 10.15479/at:ista:12390 ec_funded: 1 file: - access_level: open_access checksum: b31460e937f33b557abb40ebef02b567 content_type: application/pdf creator: cchlebak date_created: 2023-01-26T10:02:34Z date_updated: 2023-01-26T10:02:34Z file_id: '12391' file_name: Brooks_Thesis.pdf file_size: 3095225 relation: main_file success: 1 - access_level: closed checksum: 9751869fa5e7981588ad4228f4fd4bd6 content_type: application/octet-stream creator: cchlebak date_created: 2023-01-26T10:02:42Z date_updated: 2023-01-26T10:02:42Z file_id: '12392' file_name: Brooks_Thesis.tex file_size: 809842 relation: source_file file_date_updated: 2023-01-26T10:02:42Z has_accepted_license: '1' language: - iso: eng license: https://creativecommons.org/licenses/by-nc-sa/4.0/ month: '12' oa: 1 oa_version: Published Version page: '196' project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication_identifier: issn: - 2663-337X publication_status: published publisher: Institute of Science and Technology Austria related_material: record: - id: '9005' relation: part_of_dissertation status: public status: public supervisor: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 title: Translation-invariant quantum systems with effectively broken symmetry tmp: image: /images/cc_by_nc_sa.png legal_code_url: https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode name: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) short: CC BY-NC-SA (4.0) type: dissertation user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2022' ... --- _id: '10585' abstract: - lang: eng text: Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle acknowledgement: D. Lundholm acknowledges financial support from the Göran Gustafsson Foundation (grant no. 1804). article_number: '106' article_processing_charge: Yes article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: Douglas full_name: Lundholm, Douglas last_name: Lundholm - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 citation: ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 2021;9(4). doi:10.3390/atoms9040106 apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Emergence of anyons on the two-sphere in molecular impurities. Atoms. MDPI. https://doi.org/10.3390/atoms9040106 chicago: Brooks, Morris, Mikhail Lemeshko, Douglas Lundholm, and Enderalp Yakaboylu. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms. MDPI, 2021. https://doi.org/10.3390/atoms9040106. ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Emergence of anyons on the two-sphere in molecular impurities,” Atoms, vol. 9, no. 4. MDPI, 2021. ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Emergence of anyons on the two-sphere in molecular impurities. Atoms. 9(4), 106. mla: Brooks, Morris, et al. “Emergence of Anyons on the Two-Sphere in Molecular Impurities.” Atoms, vol. 9, no. 4, 106, MDPI, 2021, doi:10.3390/atoms9040106. short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Atoms 9 (2021). date_created: 2022-01-02T23:01:33Z date_published: 2021-12-02T00:00:00Z date_updated: 2023-06-15T14:51:49Z day: '02' ddc: - '530' department: - _id: MiLe - _id: RoSe doi: 10.3390/atoms9040106 external_id: arxiv: - '2108.06966' file: - access_level: open_access checksum: d0e44b95f36c9e06724f66832af0f8c3 content_type: application/pdf creator: alisjak date_created: 2022-01-03T10:15:05Z date_updated: 2022-01-03T10:15:05Z file_id: '10592' file_name: 2021_Atoms_Brooks.pdf file_size: 303070 relation: main_file success: 1 file_date_updated: 2022-01-03T10:15:05Z has_accepted_license: '1' intvolume: ' 9' issue: '4' keyword: - anyons - quasiparticles - Quantum Hall Effect - topological states of matter language: - iso: eng month: '12' oa: 1 oa_version: Published Version publication: Atoms publication_identifier: eissn: - 2218-2004 publication_status: published publisher: MDPI quality_controlled: '1' scopus_import: '1' status: public title: Emergence of anyons on the two-sphere in molecular impurities tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9 year: '2021' ... --- _id: '9005' abstract: - lang: eng text: Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field. acknowledgement: "We are grateful to A. Ghazaryan for valuable discussions and also thank the anonymous referees for comments. D.L. acknowledges financial support from the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully acknowledges financial support\r\nby the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770)." article_number: '015301' article_processing_charge: No article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Mikhail full_name: Lemeshko, Mikhail id: 37CB05FA-F248-11E8-B48F-1D18A9856A87 last_name: Lemeshko orcid: 0000-0002-6990-7802 - first_name: D. full_name: Lundholm, D. last_name: Lundholm - first_name: Enderalp full_name: Yakaboylu, Enderalp id: 38CB71F6-F248-11E8-B48F-1D18A9856A87 last_name: Yakaboylu orcid: 0000-0001-5973-0874 citation: ama: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301 apa: Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301 chicago: Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301. ieee: M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities as a realization of anyons on the two-sphere,” Physical Review Letters, vol. 126, no. 1. American Physical Society, 2021. ista: Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 126(1), 015301. mla: Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301. short: M. Brooks, M. Lemeshko, D. Lundholm, E. Yakaboylu, Physical Review Letters 126 (2021). date_created: 2021-01-17T23:01:10Z date_published: 2021-01-08T00:00:00Z date_updated: 2023-08-07T13:32:10Z day: '08' department: - _id: MiLe - _id: RoSe doi: 10.1103/PhysRevLett.126.015301 ec_funded: 1 external_id: arxiv: - '2009.05948' isi: - '000606325000003' intvolume: ' 126' isi: 1 issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2009.05948 month: '01' oa: 1 oa_version: Preprint project: - _id: 2688CF98-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '801770' name: 'Angulon: physics and applications of a new quasiparticle' publication: Physical Review Letters publication_identifier: eissn: - '10797114' issn: - '00319007' publication_status: published publisher: American Physical Society quality_controlled: '1' related_material: link: - description: News on IST Homepage relation: press_release url: https://ist.ac.at/en/news/dancing-molecules-and-two-dimensional-particles/ record: - id: '12390' relation: dissertation_contains status: public scopus_import: '1' status: public title: Molecular impurities as a realization of anyons on the two-sphere type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 126 year: '2021' ... --- _id: '9348' abstract: - lang: eng text: We consider the stochastic quantization of a quartic double-well energy functional in the semiclassical regime and derive optimal asymptotics for the exponentially small splitting of the ground state energy. Our result provides an infinite-dimensional version of some sharp tunneling estimates known in finite dimensions for semiclassical Witten Laplacians in degree zero. From a stochastic point of view it proves that the L2 spectral gap of the stochastic one-dimensional Allen-Cahn equation in finite volume satisfies a Kramers-type formula in the limit of vanishing noise. We work with finite-dimensional lattice approximations and establish semiclassical estimates which are uniform in the dimension. Our key estimate shows that the constant separating the two exponentially small eigenvalues from the rest of the spectrum can be taken independently of the dimension. acknowledgement: GDG gratefully acknowledges the financial support of HIM Bonn in the framework of the 2019 Junior Trimester Programs “Kinetic Theory” and “Randomness, PDEs and Nonlinear Fluctuations” and the hospitality at the University of Rome La Sapienza during his frequent visits. article_number: '109029' article_processing_charge: No article_type: original author: - first_name: Morris full_name: Brooks, Morris id: B7ECF9FC-AA38-11E9-AC9A-0930E6697425 last_name: Brooks orcid: 0000-0002-6249-0928 - first_name: Giacomo full_name: Di Gesù, Giacomo last_name: Di Gesù citation: ama: Brooks M, Di Gesù G. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 2021;281(3). doi:10.1016/j.jfa.2021.109029 apa: Brooks, M., & Di Gesù, G. (2021). Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2021.109029 chicago: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” Journal of Functional Analysis. Elsevier, 2021. https://doi.org/10.1016/j.jfa.2021.109029. ieee: M. Brooks and G. Di Gesù, “Sharp tunneling estimates for a double-well model in infinite dimension,” Journal of Functional Analysis, vol. 281, no. 3. Elsevier, 2021. ista: Brooks M, Di Gesù G. 2021. Sharp tunneling estimates for a double-well model in infinite dimension. Journal of Functional Analysis. 281(3), 109029. mla: Brooks, Morris, and Giacomo Di Gesù. “Sharp Tunneling Estimates for a Double-Well Model in Infinite Dimension.” Journal of Functional Analysis, vol. 281, no. 3, 109029, Elsevier, 2021, doi:10.1016/j.jfa.2021.109029. short: M. Brooks, G. Di Gesù, Journal of Functional Analysis 281 (2021). date_created: 2021-04-25T22:01:29Z date_published: 2021-04-07T00:00:00Z date_updated: 2023-08-08T13:15:11Z day: '07' department: - _id: RoSe doi: 10.1016/j.jfa.2021.109029 external_id: arxiv: - '1911.03187' isi: - '000644702800005' intvolume: ' 281' isi: 1 issue: '3' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1911.03187 month: '04' oa: 1 oa_version: Preprint publication: Journal of Functional Analysis publication_identifier: eissn: - 1096-0783 issn: - 0022-1236 publication_status: published publisher: Elsevier quality_controlled: '1' scopus_import: '1' status: public title: Sharp tunneling estimates for a double-well model in infinite dimension type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 281 year: '2021' ...