--- _id: '11330' abstract: - lang: eng text: In this article we study the noncommutative transport distance introduced by Carlen and Maas and its entropic regularization defined by Becker and Li. We prove a duality formula that can be understood as a quantum version of the dual Benamou–Brenier formulation of the Wasserstein distance in terms of subsolutions of a Hamilton–Jacobi–Bellmann equation. acknowledgement: "The author wants to thank Jan Maas for helpful comments. He also acknowledges financial support from the Austrian Science Fund (FWF) through Grant Number F65 and from the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (Grant Agreement No. 716117).\r\nOpen access funding provided by Institute of Science and Technology (IST Austria)." article_number: '19' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Melchior full_name: Wirth, Melchior id: 88644358-0A0E-11EA-8FA5-49A33DDC885E last_name: Wirth orcid: 0000-0002-0519-4241 citation: ama: Wirth M. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 2022;187(2). doi:10.1007/s10955-022-02911-9 apa: Wirth, M. (2022). A dual formula for the noncommutative transport distance. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02911-9 chicago: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02911-9. ieee: M. Wirth, “A dual formula for the noncommutative transport distance,” Journal of Statistical Physics, vol. 187, no. 2. Springer Nature, 2022. ista: Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19. mla: Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” Journal of Statistical Physics, vol. 187, no. 2, 19, Springer Nature, 2022, doi:10.1007/s10955-022-02911-9. short: M. Wirth, Journal of Statistical Physics 187 (2022). date_created: 2022-04-24T22:01:43Z date_published: 2022-04-08T00:00:00Z date_updated: 2023-08-03T06:37:49Z day: '08' ddc: - '510' - '530' department: - _id: JaMa doi: 10.1007/s10955-022-02911-9 ec_funded: 1 external_id: isi: - '000780305000001' file: - access_level: open_access checksum: f3e0b00884b7dde31347a3756788b473 content_type: application/pdf creator: dernst date_created: 2022-04-29T11:24:23Z date_updated: 2022-04-29T11:24:23Z file_id: '11338' file_name: 2022_JourStatisticalPhysics_Wirth.pdf file_size: 362119 relation: main_file success: 1 file_date_updated: 2022-04-29T11:24:23Z has_accepted_license: '1' intvolume: ' 187' isi: 1 issue: '2' language: - iso: eng month: '04' oa: 1 oa_version: Published Version project: - _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2 grant_number: F6504 name: Taming Complexity in Partial Differential Systems - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: A dual formula for the noncommutative transport distance 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: 187 year: '2022' ... --- _id: '8091' abstract: - lang: eng text: In the setting of the fractional quantum Hall effect we study the effects of strong, repulsive two-body interaction potentials of short range. We prove that Haldane’s pseudo-potential operators, including their pre-factors, emerge as mathematically rigorous limits of such interactions when the range of the potential tends to zero while its strength tends to infinity. In a common approach the interaction potential is expanded in angular momentum eigenstates in the lowest Landau level, which amounts to taking the pre-factors to be the moments of the potential. Such a procedure is not appropriate for very strong interactions, however, in particular not in the case of hard spheres. We derive the formulas valid in the short-range case, which involve the scattering lengths of the interaction potential in different angular momentum channels rather than its moments. Our results hold for bosons and fermions alike and generalize previous results in [6], which apply to bosons in the lowest angular momentum channel. Our main theorem asserts the convergence in a norm-resolvent sense of the Hamiltonian on the whole Hilbert space, after appropriate energy scalings, to Hamiltonians with contact interactions in the lowest Landau level. acknowledgement: "Open access funding provided by Institute of Science and Technology (IST Austria).\r\nThe work of R.S. was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No 694227). J.Y. gratefully acknowledges hospitality at the LPMMC Grenoble and valuable discussions with Alessandro Olgiati and Nicolas Rougerie. " article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Robert full_name: Seiringer, Robert id: 4AFD0470-F248-11E8-B48F-1D18A9856A87 last_name: Seiringer orcid: 0000-0002-6781-0521 - first_name: Jakob full_name: Yngvason, Jakob last_name: Yngvason citation: ama: Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 2020;181:448-464. doi:10.1007/s10955-020-02586-0 apa: Seiringer, R., & Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-020-02586-0 chicago: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics. Springer, 2020. https://doi.org/10.1007/s10955-020-02586-0. ieee: R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” Journal of Statistical Physics, vol. 181. Springer, pp. 448–464, 2020. ista: Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464. mla: Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” Journal of Statistical Physics, vol. 181, Springer, 2020, pp. 448–64, doi:10.1007/s10955-020-02586-0. short: R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464. date_created: 2020-07-05T22:00:46Z date_published: 2020-10-01T00:00:00Z date_updated: 2023-08-22T07:51:47Z day: '01' ddc: - '530' department: - _id: RoSe doi: 10.1007/s10955-020-02586-0 ec_funded: 1 external_id: arxiv: - '2001.07144' isi: - '000543030000002' file: - access_level: open_access checksum: 5cbeef52caf18d0d952f17fed7b5545a content_type: application/pdf creator: dernst date_created: 2020-11-25T15:05:04Z date_updated: 2020-11-25T15:05:04Z file_id: '8812' file_name: 2020_JourStatPhysics_Seiringer.pdf file_size: 404778 relation: main_file success: 1 file_date_updated: 2020-11-25T15:05:04Z has_accepted_license: '1' intvolume: ' 181' isi: 1 language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 448-464 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 25C6DC12-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '694227' name: Analysis of quantum many-body systems publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer quality_controlled: '1' scopus_import: '1' status: public title: Emergence of Haldane pseudo-potentials in systems with short-range 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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 181 year: '2020' ... --- _id: '8758' abstract: - lang: eng text: We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where the microscopic system satisfies the detailed-balance condition. The latter allows us to enrich the systems with a gradient structure, i.e. the evolution is given by a gradient-flow equation. We present the arising links between the associated gradient structures that are driven by the relative entropy of the detailed-balance steady state. The limit of large volumes is studied in the sense of evolutionary Γ-convergence of gradient flows. Moreover, we use the gradient structures to derive hybrid models for coupling different modeling levels. acknowledgement: The research of A.M. was partially supported by the Deutsche Forschungsgemeinschaft (DFG) via the Collaborative Research Center SFB 1114 Scaling Cascades in Complex Systems (Project No. 235221301), through the Subproject C05 Effective models for materials and interfaces with multiple scales. J.M. gratefully acknowledges support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 716117), and by the Austrian Science Fund (FWF), Project SFB F65. The authors thank Christof Schütte, Robert I. A. Patterson, and Stefanie Winkelmann for helpful and stimulating discussions. Open access funding provided by Austrian Science Fund (FWF). article_processing_charge: No article_type: original arxiv: 1 author: - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 - first_name: Alexander full_name: Mielke, Alexander last_name: Mielke citation: ama: Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 2020;181(6):2257-2303. doi:10.1007/s10955-020-02663-4 apa: Maas, J., & Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-020-02663-4 chicago: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-020-02663-4. ieee: J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” Journal of Statistical Physics, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020. ista: Maas J, Mielke A. 2020. Modeling of chemical reaction systems with detailed balance using gradient structures. Journal of Statistical Physics. 181(6), 2257–2303. mla: Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” Journal of Statistical Physics, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:10.1007/s10955-020-02663-4. short: J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303. date_created: 2020-11-15T23:01:18Z date_published: 2020-12-01T00:00:00Z date_updated: 2023-08-22T13:24:27Z day: '01' ddc: - '510' department: - _id: JaMa doi: 10.1007/s10955-020-02663-4 ec_funded: 1 external_id: arxiv: - '2004.02831' isi: - '000587107200002' file: - access_level: open_access checksum: bc2b63a90197b97cbc73eccada4639f5 content_type: application/pdf creator: dernst date_created: 2021-02-04T10:29:11Z date_updated: 2021-02-04T10:29:11Z file_id: '9087' file_name: 2020_JourStatPhysics_Maas.pdf file_size: 753596 relation: main_file success: 1 file_date_updated: 2021-02-04T10:29:11Z has_accepted_license: '1' intvolume: ' 181' isi: 1 issue: '6' language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 2257-2303 project: - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Modeling of chemical reaction systems with detailed balance using gradient structures 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: 181 year: '2020' ... --- _id: '6358' abstract: - lang: eng text: We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates. article_processing_charge: Yes (via OA deal) article_type: original arxiv: 1 author: - first_name: Eric A. full_name: Carlen, Eric A. last_name: Carlen - first_name: Jan full_name: Maas, Jan id: 4C5696CE-F248-11E8-B48F-1D18A9856A87 last_name: Maas orcid: 0000-0002-0845-1338 citation: ama: Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 2020;178(2):319-378. doi:10.1007/s10955-019-02434-w apa: Carlen, E. A., & Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-019-02434-w chicago: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics. Springer Nature, 2020. https://doi.org/10.1007/s10955-019-02434-w. ieee: E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” Journal of Statistical Physics, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020. ista: Carlen EA, Maas J. 2020. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. Journal of Statistical Physics. 178(2), 319–378. mla: Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” Journal of Statistical Physics, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:10.1007/s10955-019-02434-w. short: E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378. date_created: 2019-04-30T07:34:18Z date_published: 2020-01-01T00:00:00Z date_updated: 2023-08-17T13:49:40Z day: '01' ddc: - '500' department: - _id: JaMa doi: 10.1007/s10955-019-02434-w ec_funded: 1 external_id: arxiv: - '1811.04572' isi: - '000498933300001' file: - access_level: open_access checksum: 7b04befbdc0d4982c0ee945d25d19872 content_type: application/pdf creator: dernst date_created: 2019-12-23T12:03:09Z date_updated: 2020-07-14T12:47:28Z file_id: '7209' file_name: 2019_JourStatistPhysics_Carlen.pdf file_size: 905538 relation: main_file file_date_updated: 2020-07-14T12:47:28Z has_accepted_license: '1' intvolume: ' 178' isi: 1 issue: '2' language: - iso: eng month: '01' oa: 1 oa_version: Published Version page: 319-378 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund - _id: 256E75B8-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '716117' name: Optimal Transport and Stochastic Dynamics - _id: 260482E2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: ' F06504' name: Taming Complexity in Partial Di erential Systems publication: Journal of Statistical Physics publication_identifier: eissn: - '15729613' issn: - '00224715' publication_status: published publisher: Springer Nature quality_controlled: '1' related_material: link: - relation: erratum url: https://doi.org/10.1007/s10955-020-02671-4 scopus_import: '1' status: public title: Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems 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: 178 year: '2020' ...