[{"date_published":"2022-04-08T00:00:00Z","_id":"11330","oa":1,"author":[{"full_name":"Wirth, Melchior","first_name":"Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth"}],"type":"journal_article","year":"2022","publisher":"Springer Nature","doi":"10.1007/s10955-022-02911-9","language":[{"iso":"eng"}],"volume":187,"article_type":"original","isi":1,"publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"quality_controlled":"1","month":"04","intvolume":"       187","file_date_updated":"2022-04-29T11:24:23Z","ddc":["510","530"],"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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).","department":[{"_id":"JaMa"}],"date_created":"2022-04-24T22:01:43Z","article_number":"19","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."}],"ec_funded":1,"day":"08","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication_status":"published","oa_version":"Published Version","license":"https://creativecommons.org/licenses/by/4.0/","status":"public","date_updated":"2023-08-03T06:37:49Z","file":[{"success":1,"date_updated":"2022-04-29T11:24:23Z","checksum":"f3e0b00884b7dde31347a3756788b473","file_id":"11338","date_created":"2022-04-29T11:24:23Z","file_size":362119,"file_name":"2022_JourStatisticalPhysics_Wirth.pdf","content_type":"application/pdf","relation":"main_file","access_level":"open_access","creator":"dernst"}],"title":"A dual formula for the noncommutative transport distance","external_id":{"isi":["000780305000001"]},"publication":"Journal of Statistical Physics","has_accepted_license":"1","scopus_import":"1","issue":"2","citation":{"ama":"Wirth M. A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. 2022;187(2). doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>","apa":"Wirth, M. (2022). A dual formula for the noncommutative transport distance. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>","ista":"Wirth M. 2022. A dual formula for the noncommutative transport distance. Journal of Statistical Physics. 187(2), 19.","short":"M. Wirth, Journal of Statistical Physics 187 (2022).","mla":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>, vol. 187, no. 2, 19, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02911-9\">10.1007/s10955-022-02911-9</a>.","ieee":"M. Wirth, “A dual formula for the noncommutative transport distance,” <i>Journal of Statistical Physics</i>, vol. 187, no. 2. Springer Nature, 2022.","chicago":"Wirth, Melchior. “A Dual Formula for the Noncommutative Transport Distance.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02911-9\">https://doi.org/10.1007/s10955-022-02911-9</a>."},"project":[{"_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2","name":"Taming Complexity in Partial Differential Systems","grant_number":"F6504"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","call_identifier":"H2020","grant_number":"716117"}]},{"ec_funded":1,"abstract":[{"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.","lang":"eng"}],"publication_status":"published","page":"448-464","oa_version":"Published Version","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"day":"01","date_updated":"2023-08-22T07:51:47Z","status":"public","external_id":{"arxiv":["2001.07144"],"isi":["000543030000002"]},"file":[{"creator":"dernst","relation":"main_file","content_type":"application/pdf","access_level":"open_access","file_size":404778,"file_name":"2020_JourStatPhysics_Seiringer.pdf","date_updated":"2020-11-25T15:05:04Z","success":1,"checksum":"5cbeef52caf18d0d952f17fed7b5545a","file_id":"8812","date_created":"2020-11-25T15:05:04Z"}],"title":"Emergence of Haldane pseudo-potentials in systems with short-range interactions","publication":"Journal of Statistical Physics","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"citation":{"ieee":"R. Seiringer and J. Yngvason, “Emergence of Haldane pseudo-potentials in systems with short-range interactions,” <i>Journal of Statistical Physics</i>, vol. 181. Springer, pp. 448–464, 2020.","chicago":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>.","ama":"Seiringer R, Yngvason J. Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. 2020;181:448-464. doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>","ista":"Seiringer R, Yngvason J. 2020. Emergence of Haldane pseudo-potentials in systems with short-range interactions. Journal of Statistical Physics. 181, 448–464.","apa":"Seiringer, R., &#38; Yngvason, J. (2020). Emergence of Haldane pseudo-potentials in systems with short-range interactions. <i>Journal of Statistical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s10955-020-02586-0\">https://doi.org/10.1007/s10955-020-02586-0</a>","short":"R. Seiringer, J. Yngvason, Journal of Statistical Physics 181 (2020) 448–464.","mla":"Seiringer, Robert, and Jakob Yngvason. “Emergence of Haldane Pseudo-Potentials in Systems with Short-Range Interactions.” <i>Journal of Statistical Physics</i>, vol. 181, Springer, 2020, pp. 448–64, doi:<a href=\"https://doi.org/10.1007/s10955-020-02586-0\">10.1007/s10955-020-02586-0</a>."},"arxiv":1,"has_accepted_license":"1","scopus_import":"1","oa":1,"_id":"8091","author":[{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"},{"first_name":"Jakob","full_name":"Yngvason, Jakob","last_name":"Yngvason"}],"date_published":"2020-10-01T00:00:00Z","publisher":"Springer","year":"2020","language":[{"iso":"eng"}],"doi":"10.1007/s10955-020-02586-0","type":"journal_article","quality_controlled":"1","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"month":"10","volume":181,"article_type":"original","isi":1,"department":[{"_id":"RoSe"}],"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. ","date_created":"2020-07-05T22:00:46Z","intvolume":"       181","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","ddc":["530"],"file_date_updated":"2020-11-25T15:05:04Z"},{"month":"12","quality_controlled":"1","publication_identifier":{"eissn":["15729613"],"issn":["00224715"]},"isi":1,"volume":181,"article_type":"original","date_created":"2020-11-15T23:01:18Z","department":[{"_id":"JaMa"}],"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","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["510"],"file_date_updated":"2021-02-04T10:29:11Z","intvolume":"       181","author":[{"id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","orcid":"0000-0002-0845-1338","first_name":"Jan","full_name":"Maas, Jan"},{"last_name":"Mielke","full_name":"Mielke, Alexander","first_name":"Alexander"}],"oa":1,"_id":"8758","date_published":"2020-12-01T00:00:00Z","language":[{"iso":"eng"}],"doi":"10.1007/s10955-020-02663-4","publisher":"Springer Nature","year":"2020","type":"journal_article","publication":"Journal of Statistical Physics","external_id":{"isi":["000587107200002"],"arxiv":["2004.02831"]},"file":[{"file_id":"9087","date_created":"2021-02-04T10:29:11Z","checksum":"bc2b63a90197b97cbc73eccada4639f5","success":1,"date_updated":"2021-02-04T10:29:11Z","file_name":"2020_JourStatPhysics_Maas.pdf","file_size":753596,"access_level":"open_access","content_type":"application/pdf","relation":"main_file","creator":"dernst"}],"title":"Modeling of chemical reaction systems with detailed balance using gradient structures","project":[{"grant_number":"716117","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","_id":"256E75B8-B435-11E9-9278-68D0E5697425"},{"grant_number":" F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems"}],"arxiv":1,"citation":{"ieee":"J. Maas and A. Mielke, “Modeling of chemical reaction systems with detailed balance using gradient structures,” <i>Journal of Statistical Physics</i>, vol. 181, no. 6. Springer Nature, pp. 2257–2303, 2020.","chicago":"Maas, Jan, and Alexander Mielke. “Modeling of Chemical Reaction Systems with Detailed Balance Using Gradient Structures.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>.","ama":"Maas J, Mielke A. Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. 2020;181(6):2257-2303. doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>","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.” <i>Journal of Statistical Physics</i>, vol. 181, no. 6, Springer Nature, 2020, pp. 2257–303, doi:<a href=\"https://doi.org/10.1007/s10955-020-02663-4\">10.1007/s10955-020-02663-4</a>.","short":"J. Maas, A. Mielke, Journal of Statistical Physics 181 (2020) 2257–2303.","apa":"Maas, J., &#38; Mielke, A. (2020). Modeling of chemical reaction systems with detailed balance using gradient structures. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-020-02663-4\">https://doi.org/10.1007/s10955-020-02663-4</a>"},"issue":"6","scopus_import":"1","has_accepted_license":"1","publication_status":"published","oa_version":"Published Version","page":"2257-2303","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ec_funded":1,"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."}],"date_updated":"2023-08-22T13:24:27Z","status":"public"},{"type":"journal_article","doi":"10.1007/s10955-019-02434-w","language":[{"iso":"eng"}],"year":"2020","publisher":"Springer Nature","date_published":"2020-01-01T00:00:00Z","author":[{"first_name":"Eric A.","full_name":"Carlen, Eric A.","last_name":"Carlen"},{"orcid":"0000-0002-0845-1338","id":"4C5696CE-F248-11E8-B48F-1D18A9856A87","last_name":"Maas","full_name":"Maas, Jan","first_name":"Jan"}],"_id":"6358","oa":1,"file_date_updated":"2020-07-14T12:47:28Z","article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","ddc":["500"],"intvolume":"       178","date_created":"2019-04-30T07:34:18Z","department":[{"_id":"JaMa"}],"isi":1,"article_type":"original","volume":178,"month":"01","publication_identifier":{"issn":["00224715"],"eissn":["15729613"]},"quality_controlled":"1","status":"public","date_updated":"2023-08-17T13:49:40Z","day":"01","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"oa_version":"Published Version","publication_status":"published","page":"319-378","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"scopus_import":"1","issue":"2","has_accepted_license":"1","citation":{"ama":"Carlen EA, Maas J. Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. 2020;178(2):319-378. doi:<a href=\"https://doi.org/10.1007/s10955-019-02434-w\">10.1007/s10955-019-02434-w</a>","short":"E.A. Carlen, J. Maas, Journal of Statistical Physics 178 (2020) 319–378.","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.","apa":"Carlen, E. A., &#38; Maas, J. (2020). Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-019-02434-w\">https://doi.org/10.1007/s10955-019-02434-w</a>","mla":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” <i>Journal of Statistical Physics</i>, vol. 178, no. 2, Springer Nature, 2020, pp. 319–78, doi:<a href=\"https://doi.org/10.1007/s10955-019-02434-w\">10.1007/s10955-019-02434-w</a>.","ieee":"E. A. Carlen and J. Maas, “Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems,” <i>Journal of Statistical Physics</i>, vol. 178, no. 2. Springer Nature, pp. 319–378, 2020.","chicago":"Carlen, Eric A., and Jan Maas. “Non-Commutative Calculus, Optimal Transport and Functional Inequalities  in Dissipative Quantum Systems.” <i>Journal of Statistical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s10955-019-02434-w\">https://doi.org/10.1007/s10955-019-02434-w</a>."},"arxiv":1,"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"H2020","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics"},{"grant_number":" F06504","call_identifier":"FWF","_id":"260482E2-B435-11E9-9278-68D0E5697425","name":"Taming Complexity in Partial Di erential Systems"}],"publication":"Journal of Statistical Physics","file":[{"relation":"main_file","content_type":"application/pdf","access_level":"open_access","creator":"dernst","date_updated":"2020-07-14T12:47:28Z","checksum":"7b04befbdc0d4982c0ee945d25d19872","file_id":"7209","date_created":"2019-12-23T12:03:09Z","file_size":905538,"file_name":"2019_JourStatistPhysics_Carlen.pdf"}],"title":"Non-commutative calculus, optimal transport and functional inequalities  in dissipative quantum systems","external_id":{"isi":["000498933300001"],"arxiv":["1811.04572"]},"related_material":{"link":[{"url":"https://doi.org/10.1007/s10955-020-02671-4","relation":"erratum"}]}}]