--- _id: '8816' abstract: - lang: eng text: Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail. acknowledgement: The authors thank Yuki Arano, Nils Carqueville, Alexei Davydov, Reiner Lauterbach, Pau Enrique Moliner, Chris Heunen, André Henriques, Ehud Meir, Catherine Meusburger, Gregor Schaumann, Richard Szabo and Stefan Wagner for helpful discussions and comments. We also thank the referees for their detailed comments which significantly improved the exposition of this paper. LS is supported by the DFG Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. 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: Ingo full_name: Runkel, Ingo last_name: Runkel - first_name: Lorant full_name: Szegedy, Lorant id: 7943226E-220E-11EA-94C7-D59F3DDC885E last_name: Szegedy orcid: 0000-0003-2834-5054 citation: ama: Runkel I, Szegedy L. Area-dependent quantum field theory. Communications in Mathematical Physics. 2021;381(1):83–117. doi:10.1007/s00220-020-03902-1 apa: Runkel, I., & Szegedy, L. (2021). Area-dependent quantum field theory. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03902-1 chicago: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-020-03902-1. ieee: I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” Communications in Mathematical Physics, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021. ista: Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications in Mathematical Physics. 381(1), 83–117. mla: Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” Communications in Mathematical Physics, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117, doi:10.1007/s00220-020-03902-1. short: I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021) 83–117. date_created: 2020-11-29T23:01:17Z date_published: 2021-01-01T00:00:00Z date_updated: 2023-08-04T11:13:35Z day: '01' ddc: - '510' department: - _id: MiLe doi: 10.1007/s00220-020-03902-1 external_id: isi: - '000591139000001' file: - access_level: open_access checksum: 6f451f9c2b74bedbc30cf884a3e02670 content_type: application/pdf creator: dernst date_created: 2021-02-03T15:00:30Z date_updated: 2021-02-03T15:00:30Z file_id: '9081' file_name: 2021_CommMathPhys_Runkel.pdf file_size: 790526 relation: main_file success: 1 file_date_updated: 2021-02-03T15:00:30Z has_accepted_license: '1' intvolume: ' 381' isi: 1 issue: '1' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 83–117 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_identifier: eissn: - '14320916' issn: - '00103616' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Area-dependent quantum field theory 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 381 year: '2021' ... --- _id: '8325' abstract: - lang: eng text: "Let \U0001D439:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. " acknowledgement: We thank Andrea Sportiello for sharing his insights on perturbative regimes of the Abelian sandpile model which was the starting point of our work. We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who participated on the initial state of this project, when we had nothing except the computer simulation and pictures. We thank Mikhail Raskin for providing us the code on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak, Danila Cherkashin asked us a lot of questions and listened to us; not all of their questions found answers here, but we are going to treat them in subsequent papers. article_processing_charge: No article_type: original author: - first_name: Nikita full_name: Kalinin, Nikita last_name: Kalinin - first_name: Mikhail full_name: Shkolnikov, Mikhail id: 35084A62-F248-11E8-B48F-1D18A9856A87 last_name: Shkolnikov orcid: 0000-0002-4310-178X citation: ama: Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 2020;378(9):1649-1675. doi:10.1007/s00220-020-03828-8 apa: Kalinin, N., & Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-020-03828-8 chicago: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-020-03828-8. ieee: N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” Communications in Mathematical Physics, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020. ista: Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675. mla: Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” Communications in Mathematical Physics, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:10.1007/s00220-020-03828-8. short: N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675. date_created: 2020-08-30T22:01:13Z date_published: 2020-09-01T00:00:00Z date_updated: 2023-08-22T09:00:03Z day: '01' department: - _id: TaHa doi: 10.1007/s00220-020-03828-8 ec_funded: 1 external_id: arxiv: - '1711.04285' isi: - '000560620600001' intvolume: ' 378' isi: 1 issue: '9' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1711.04285 month: '09' oa: 1 oa_version: Preprint page: 1649-1675 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Communications in Mathematical Physics publication_identifier: eissn: - '14320916' issn: - '00103616' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Sandpile solitons via smoothing of superharmonic functions type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 378 year: '2020' ... --- _id: '554' abstract: - lang: eng text: We analyse the canonical Bogoliubov free energy functional in three dimensions at low temperatures in the dilute limit. We prove existence of a first-order phase transition and, in the limit (Formula presented.), we determine the critical temperature to be (Formula presented.) to leading order. Here, (Formula presented.) is the critical temperature of the free Bose gas, ρ is the density of the gas and a is the scattering length of the pair-interaction potential V. We also prove asymptotic expansions for the free energy. In particular, we recover the Lee–Huang–Yang formula in the limit (Formula presented.). author: - first_name: Marcin M full_name: Napiórkowski, Marcin M id: 4197AD04-F248-11E8-B48F-1D18A9856A87 last_name: Napiórkowski - first_name: Robin full_name: Reuvers, Robin last_name: Reuvers - first_name: Jan full_name: Solovej, Jan last_name: Solovej citation: ama: 'Napiórkowski MM, Reuvers R, Solovej J. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 2018;360(1):347-403. doi:10.1007/s00220-017-3064-x' apa: 'Napiórkowski, M. M., Reuvers, R., & Solovej, J. (2018). The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-017-3064-x' chicago: 'Napiórkowski, Marcin M, Robin Reuvers, and Jan Solovej. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” Communications in Mathematical Physics. Springer, 2018. https://doi.org/10.1007/s00220-017-3064-x.' ieee: 'M. M. Napiórkowski, R. Reuvers, and J. Solovej, “The Bogoliubov free energy functional II: The dilute Limit,” Communications in Mathematical Physics, vol. 360, no. 1. Springer, pp. 347–403, 2018.' ista: 'Napiórkowski MM, Reuvers R, Solovej J. 2018. The Bogoliubov free energy functional II: The dilute Limit. Communications in Mathematical Physics. 360(1), 347–403.' mla: 'Napiórkowski, Marcin M., et al. “The Bogoliubov Free Energy Functional II: The Dilute Limit.” Communications in Mathematical Physics, vol. 360, no. 1, Springer, 2018, pp. 347–403, doi:10.1007/s00220-017-3064-x.' short: M.M. Napiórkowski, R. Reuvers, J. Solovej, Communications in Mathematical Physics 360 (2018) 347–403. date_created: 2018-12-11T11:47:09Z date_published: 2018-05-01T00:00:00Z date_updated: 2021-01-12T08:02:35Z day: '01' department: - _id: RoSe doi: 10.1007/s00220-017-3064-x external_id: arxiv: - '1511.05953' intvolume: ' 360' issue: '1' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1511.05953 month: '05' oa: 1 oa_version: Submitted Version page: 347-403 project: - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Communications in Mathematical Physics publication_identifier: issn: - '00103616' publication_status: published publisher: Springer publist_id: '7260' quality_controlled: '1' scopus_import: 1 status: public title: 'The Bogoliubov free energy functional II: The dilute Limit' type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 360 year: '2018' ... --- _id: '1207' abstract: - lang: eng text: The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix. article_processing_charge: Yes (via OA deal) author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6 apa: Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2805-6 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017. ista: Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990. mla: Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:10.1007/s00220-016-2805-6. short: Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990. date_created: 2018-12-11T11:50:43Z date_published: 2017-02-01T00:00:00Z date_updated: 2023-09-20T11:16:57Z day: '01' ddc: - '530' department: - _id: LaEr doi: 10.1007/s00220-016-2805-6 ec_funded: 1 external_id: isi: - '000393696700005' file: - access_level: open_access checksum: ddff79154c3daf27237de5383b1264a9 content_type: application/pdf creator: system date_created: 2018-12-12T10:14:47Z date_updated: 2020-07-14T12:44:39Z file_id: '5102' file_name: IST-2016-722-v1+1_s00220-016-2805-6.pdf file_size: 1033743 relation: main_file file_date_updated: 2020-07-14T12:44:39Z has_accepted_license: '1' intvolume: ' 349' isi: 1 issue: '3' language: - iso: eng month: '02' oa: 1 oa_version: Published Version page: 947 - 990 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Communications in Mathematical Physics publication_identifier: issn: - '00103616' publication_status: published publisher: Springer publist_id: '6141' pubrep_id: '722' quality_controlled: '1' scopus_import: '1' status: public title: Local law of addition of random matrices on optimal scale 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 349 year: '2017' ... --- _id: '741' abstract: - lang: eng text: We prove that a system of N fermions interacting with an additional particle via point interactions is stable if the ratio of the mass of the additional particle to the one of the fermions is larger than some critical m*. The value of m* is independent of N and turns out to be less than 1. This fact has important implications for the stability of the unitary Fermi gas. We also characterize the domain of the Hamiltonian of this model, and establish the validity of the Tan relations for all wave functions in the domain. article_processing_charge: No author: - first_name: Thomas full_name: Moser, Thomas id: 2B5FC9A4-F248-11E8-B48F-1D18A9856A87 last_name: Moser - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 citation: ama: Moser T, Seiringer R. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 2017;356(1):329-355. doi:10.1007/s00220-017-2980-0 apa: Moser, T., & Seiringer, R. (2017). Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-017-2980-0 chicago: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-017-2980-0. ieee: T. Moser and R. Seiringer, “Stability of a fermionic N+1 particle system with point interactions,” Communications in Mathematical Physics, vol. 356, no. 1. Springer, pp. 329–355, 2017. ista: Moser T, Seiringer R. 2017. Stability of a fermionic N+1 particle system with point interactions. Communications in Mathematical Physics. 356(1), 329–355. mla: Moser, Thomas, and Robert Seiringer. “Stability of a Fermionic N+1 Particle System with Point Interactions.” Communications in Mathematical Physics, vol. 356, no. 1, Springer, 2017, pp. 329–55, doi:10.1007/s00220-017-2980-0. short: T. Moser, R. Seiringer, Communications in Mathematical Physics 356 (2017) 329–355. date_created: 2018-12-11T11:48:15Z date_published: 2017-11-01T00:00:00Z date_updated: 2023-09-27T12:34:15Z day: '01' ddc: - '539' department: - _id: RoSe doi: 10.1007/s00220-017-2980-0 ec_funded: 1 external_id: isi: - '000409821300010' file: - access_level: open_access checksum: 0fd9435400f91e9b3c5346319a2d24e3 content_type: application/pdf creator: system date_created: 2018-12-12T10:10:50Z date_updated: 2020-07-14T12:47:57Z file_id: '4841' file_name: IST-2017-880-v1+1_s00220-017-2980-0.pdf file_size: 952639 relation: main_file file_date_updated: 2020-07-14T12:47:57Z has_accepted_license: '1' intvolume: ' 356' isi: 1 issue: '1' language: - iso: eng month: '11' oa: 1 oa_version: Published Version page: 329 - 355 project: - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems - _id: 25C878CE-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P27533_N27 name: Structure of the Excitation Spectrum for Many-Body Quantum Systems publication: Communications in Mathematical Physics publication_identifier: issn: - '00103616' publication_status: published publisher: Springer publist_id: '6926' pubrep_id: '880' quality_controlled: '1' related_material: record: - id: '52' relation: dissertation_contains status: public scopus_import: '1' status: public title: Stability of a fermionic N+1 particle system with point interactions 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: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 356 year: '2017' ...