[{"ec_funded":1,"issue":"6","volume":63,"publication_status":"published","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"d0d32c338c1896680174be88c70968fa","file_id":"11784","success":1,"date_updated":"2022-08-11T07:03:02Z","file_size":5957888,"creator":"dernst","date_created":"2022-08-11T07:03:02Z","file_name":"2022_JourMathPhysics_Bossmann.pdf"}],"scopus_import":"1","intvolume":" 63","month":"06","abstract":[{"text":"We consider a gas of N bosons with interactions in the mean-field scaling regime. We review the proof of an asymptotic expansion of its low-energy spectrum, eigenstates, and dynamics, which provides corrections to Bogoliubov theory to all orders in 1/ N. This is based on joint works with Petrat, Pickl, Seiringer, and Soffer. In addition, we derive a full asymptotic expansion of the ground state one-body reduced density matrix.","lang":"eng"}],"oa_version":"Published Version","department":[{"_id":"RoSe"}],"file_date_updated":"2022-08-11T07:03:02Z","date_updated":"2023-08-03T12:46:28Z","ddc":["530"],"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)"},"type":"journal_article","article_type":"original","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","_id":"11783","date_created":"2022-08-11T06:37:52Z","date_published":"2022-06-10T00:00:00Z","doi":"10.1063/5.0089983","year":"2022","isi":1,"has_accepted_license":"1","publication":"Journal of Mathematical Physics","day":"10","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","acknowledgement":"The author thanks Nataˇsa Pavlovic, Sören Petrat, Peter Pickl, Robert Seiringer, and Avy Soffer for the collaboration on Refs. 1, 2 and 21. Funding from the European Union’s Horizon 2020 Research and Innovation Programme under Marie Skℓodowska-Curie Grant Agreement\r\nNo. 754411 is gratefully acknowledged.","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2203.00730"],"isi":["000809648100002"]},"author":[{"full_name":"Bossmann, Lea","orcid":"0000-0002-6854-1343","last_name":"Bossmann","first_name":"Lea","id":"A2E3BCBE-5FCC-11E9-AA4B-76F3E5697425"}],"title":"Low-energy spectrum and dynamics of the weakly interacting Bose gas","citation":{"ama":"Bossmann L. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 2022;63(6). doi:10.1063/5.0089983","apa":"Bossmann, L. (2022). Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0089983","ieee":"L. Bossmann, “Low-energy spectrum and dynamics of the weakly interacting Bose gas,” Journal of Mathematical Physics, vol. 63, no. 6. AIP Publishing, 2022.","short":"L. Bossmann, Journal of Mathematical Physics 63 (2022).","mla":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics, vol. 63, no. 6, 061102, AIP Publishing, 2022, doi:10.1063/5.0089983.","ista":"Bossmann L. 2022. Low-energy spectrum and dynamics of the weakly interacting Bose gas. Journal of Mathematical Physics. 63(6), 061102.","chicago":"Bossmann, Lea. “Low-Energy Spectrum and Dynamics of the Weakly Interacting Bose Gas.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0089983."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"article_number":"061102"},{"date_created":"2022-08-18T07:23:26Z","doi":"10.1007/s10955-022-02940-4","date_published":"2022-07-01T00:00:00Z","year":"2022","isi":1,"has_accepted_license":"1","publication":"Journal of Statistical Physics","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"The authors thank Gérard Ben Arous for pointing out the question of a lower bound. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC Grant Agreement No. 694227 (R.S.) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (S.R.) is gratefully acknowledged.\r\nOpen access funding provided by IST Austria.","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000805175000001"]},"author":[{"first_name":"Simone Anna Elvira","id":"856966FE-A408-11E9-977E-802DE6697425","full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","last_name":"Rademacher"},{"last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"title":"Large deviation estimates for weakly interacting bosons","citation":{"ama":"Rademacher SAE, Seiringer R. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 2022;188. doi:10.1007/s10955-022-02940-4","apa":"Rademacher, S. A. E., & Seiringer, R. (2022). Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02940-4","short":"S.A.E. Rademacher, R. Seiringer, Journal of Statistical Physics 188 (2022).","ieee":"S. A. E. Rademacher and R. Seiringer, “Large deviation estimates for weakly interacting bosons,” Journal of Statistical Physics, vol. 188. Springer Nature, 2022.","mla":"Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics, vol. 188, 9, Springer Nature, 2022, doi:10.1007/s10955-022-02940-4.","ista":"Rademacher SAE, Seiringer R. 2022. Large deviation estimates for weakly interacting bosons. Journal of Statistical Physics. 188, 9.","chicago":"Rademacher, Simone Anna Elvira, and Robert Seiringer. “Large Deviation Estimates for Weakly Interacting Bosons.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02940-4."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"694227","name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"article_number":"9","ec_funded":1,"volume":188,"publication_status":"published","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"language":[{"iso":"eng"}],"file":[{"date_updated":"2022-08-18T08:09:00Z","file_size":483481,"creator":"dernst","date_created":"2022-08-18T08:09:00Z","file_name":"2022_JournalStatisticalPhysics_Rademacher.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"44418cb44f07fa21ed3907f85abf7f39","file_id":"11922","success":1}],"scopus_import":"1","intvolume":" 188","month":"07","abstract":[{"lang":"eng","text":"We study the many-body dynamics of an initially factorized bosonic wave function in the mean-field regime. We prove large deviation estimates for the fluctuations around the condensate. We derive an upper bound extending a recent result to more general interactions. Furthermore, we derive a new lower bound which agrees with the upper bound in leading order."}],"oa_version":"Published Version","department":[{"_id":"RoSe"}],"file_date_updated":"2022-08-18T08:09:00Z","date_updated":"2023-08-03T12:55:58Z","ddc":["510"],"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)"},"article_type":"original","type":"journal_article","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","_id":"11917"},{"department":[{"_id":"RoSe"}],"file_date_updated":"2022-09-12T07:35:34Z","date_updated":"2023-08-03T13:57:19Z","ddc":["510"],"type":"journal_article","article_type":"original","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)"},"status":"public","_id":"12083","volume":63,"issue":"8","ec_funded":1,"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12089","checksum":"e6fb0cf3f0327739c5e69a2cfc4020eb","success":1,"date_updated":"2022-09-12T07:35:34Z","file_size":4552261,"creator":"dernst","date_created":"2022-09-12T07:35:34Z","file_name":"2022_JourMathPhysics_Rademacher.pdf"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"08","intvolume":" 63","abstract":[{"lang":"eng","text":"We consider the many-body time evolution of weakly interacting bosons in the mean field regime for initial coherent states. We show that bounded k-particle operators, corresponding to dependent random variables, satisfy both a law of large numbers and a central limit theorem."}],"oa_version":"Published Version","author":[{"id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","full_name":"Rademacher, Simone Anna Elvira","orcid":"0000-0001-5059-4466","last_name":"Rademacher"}],"article_processing_charge":"No","external_id":{"isi":["000844402500001"],"arxiv":["2112.04817"]},"title":"Dependent random variables in quantum dynamics","citation":{"mla":"Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics, vol. 63, no. 8, 081902, AIP Publishing, 2022, doi:10.1063/5.0086712.","ama":"Rademacher SAE. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 2022;63(8). doi:10.1063/5.0086712","apa":"Rademacher, S. A. E. (2022). Dependent random variables in quantum dynamics. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0086712","short":"S.A.E. Rademacher, Journal of Mathematical Physics 63 (2022).","ieee":"S. A. E. Rademacher, “Dependent random variables in quantum dynamics,” Journal of Mathematical Physics, vol. 63, no. 8. AIP Publishing, 2022.","chicago":"Rademacher, Simone Anna Elvira. “Dependent Random Variables in Quantum Dynamics.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0086712.","ista":"Rademacher SAE. 2022. Dependent random variables in quantum dynamics. Journal of Mathematical Physics. 63(8), 081902."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"article_number":"081902","doi":"10.1063/5.0086712","date_published":"2022-08-25T00:00:00Z","date_created":"2022-09-11T22:01:56Z","isi":1,"has_accepted_license":"1","year":"2022","day":"25","publication":"Journal of Mathematical Physics","publisher":"AIP Publishing","quality_controlled":"1","oa":1,"acknowledgement":"S.R. would like to thank Robert Seiringer and Benedikt Stufler for helpful discussions. Funding from the European Union’s Horizon 2020 Research and Innovation Program under the ERC grant (Grant Agreement No. 694227) and under the Marie Skłodowska-Curie grant (Agreement No. 754411) is acknowledged."},{"ddc":["500"],"date_updated":"2023-08-07T13:32:09Z","supervisor":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521"}],"file_date_updated":"2023-01-26T10:02:42Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"_id":"12390","status":"public","tmp":{"name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","image":"/images/cc_by_nc_sa.png","legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","short":"CC BY-NC-SA (4.0)"},"type":"dissertation","language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","file_size":3095225,"date_updated":"2023-01-26T10:02:34Z","file_name":"Brooks_Thesis.pdf","date_created":"2023-01-26T10:02:34Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"b31460e937f33b557abb40ebef02b567","file_id":"12391"},{"creator":"cchlebak","file_size":809842,"date_updated":"2023-01-26T10:02:42Z","file_name":"Brooks_Thesis.tex","date_created":"2023-01-26T10:02:42Z","relation":"source_file","access_level":"closed","content_type":"application/octet-stream","file_id":"12392","checksum":"9751869fa5e7981588ad4228f4fd4bd6"}],"publication_status":"published","degree_awarded":"PhD","publication_identifier":{"issn":["2663-337X"]},"ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","id":"9005","status":"public"}]},"oa_version":"Published Version","abstract":[{"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","lang":"eng"}],"month":"12","alternative_title":["ISTA Thesis"],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"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.","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.","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","ieee":"M. Brooks, “Translation-invariant quantum systems with effectively broken symmetry,” Institute of Science and Technology Austria, 2022.","short":"M. Brooks, Translation-Invariant Quantum Systems with Effectively Broken Symmetry, Institute of Science and Technology Austria, 2022."},"title":"Translation-invariant quantum systems with effectively broken symmetry","article_processing_charge":"No","author":[{"id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","first_name":"Morris","orcid":"0000-0002-6249-0928","full_name":"Brooks, Morris","last_name":"Brooks"}],"project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"day":"15","year":"2022","has_accepted_license":"1","date_created":"2023-01-26T10:00:42Z","date_published":"2022-12-15T00:00:00Z","doi":"10.15479/at:ista:12390","page":"196","oa":1,"publisher":"Institute of Science and Technology Austria"},{"intvolume":" 189","month":"07","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature."}],"ec_funded":1,"volume":189,"language":[{"iso":"eng"}],"file":[{"date_created":"2022-08-08T07:36:34Z","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","creator":"dernst","date_updated":"2022-08-08T07:36:34Z","file_size":419563,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","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)"},"article_type":"original","type":"journal_article","_id":"11732","file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"ddc":["530"],"date_updated":"2023-09-05T14:57:49Z","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","date_created":"2022-08-05T11:36:56Z","date_published":"2022-07-29T00:00:00Z","doi":"10.1007/s10955-022-02965-9","publication":"Journal of Statistical Physics","day":"29","year":"2022","isi":1,"has_accepted_license":"1","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"5","title":"The BCS energy gap at high density","external_id":{"isi":["000833007200002"]},"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","first_name":"Asbjørn Bækgaard"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022.","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5."}},{"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"M. Lewin, E.H. Lieb, R. Seiringer, Letters in Mathematical Physics 112 (2022).","ieee":"M. Lewin, E. H. Lieb, and R. Seiringer, “Improved Lieb–Oxford bound on the indirect and exchange energies,” Letters in Mathematical Physics, vol. 112, no. 5. Springer Nature, 2022.","apa":"Lewin, M., Lieb, E. H., & Seiringer, R. (2022). Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-022-01584-5","ama":"Lewin M, Lieb EH, Seiringer R. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 2022;112(5). doi:10.1007/s11005-022-01584-5","mla":"Lewin, Mathieu, et al. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics, vol. 112, no. 5, 92, Springer Nature, 2022, doi:10.1007/s11005-022-01584-5.","ista":"Lewin M, Lieb EH, Seiringer R. 2022. Improved Lieb–Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics. 112(5), 92.","chicago":"Lewin, Mathieu, Elliott H. Lieb, and Robert Seiringer. “Improved Lieb–Oxford Bound on the Indirect and Exchange Energies.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-022-01584-5."},"title":"Improved Lieb–Oxford bound on the indirect and exchange energies","author":[{"first_name":"Mathieu","full_name":"Lewin, Mathieu","last_name":"Lewin"},{"first_name":"Elliott H.","last_name":"Lieb","full_name":"Lieb, Elliott H."},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"external_id":{"arxiv":["2203.12473"],"isi":["000854762600001"]},"article_processing_charge":"No","article_number":"92","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"day":"15","publication":"Letters in Mathematical Physics","isi":1,"year":"2022","date_published":"2022-09-15T00:00:00Z","doi":"10.1007/s11005-022-01584-5","date_created":"2023-01-16T09:53:54Z","acknowledgement":"We would like to thank David Gontier for useful advice on the numerical simulations. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreements MDFT No. 725528 of M.L. and AQUAMS No. 694227 of R.S.). We are thankful for the hospitality of the Institut Henri Poincaré in Paris, where part of this work was done.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"date_updated":"2023-09-05T15:17:34Z","department":[{"_id":"RoSe"}],"_id":"12246","status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","volume":112,"issue":"5","ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"The Lieb–Oxford inequality provides a lower bound on the Coulomb energy of a classical system of N identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree–Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.","lang":"eng"}],"month":"09","intvolume":" 112","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.12473","open_access":"1"}]},{"doi":"10.15479/at:ista:11473","date_published":"2022-07-01T00:00:00Z","date_created":"2022-06-30T12:15:03Z","page":"138","day":"01","has_accepted_license":"1","year":"2022","publisher":"Institute of Science and Technology Austria","oa":1,"title":"Polarons in Bose gases and polar crystals: Some rigorous energy estimates","author":[{"first_name":"Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","full_name":"Mysliwy, Krzysztof","last_name":"Mysliwy"}],"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Mysliwy, Krzysztof. Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates. Institute of Science and Technology Austria, 2022, doi:10.15479/at:ista:11473.","apa":"Mysliwy, K. (2022). Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:11473","ama":"Mysliwy K. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. 2022. doi:10.15479/at:ista:11473","ieee":"K. Mysliwy, “Polarons in Bose gases and polar crystals: Some rigorous energy estimates,” Institute of Science and Technology Austria, 2022.","short":"K. Mysliwy, Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates, Institute of Science and Technology Austria, 2022.","chicago":"Mysliwy, Krzysztof. “Polarons in Bose Gases and Polar Crystals: Some Rigorous Energy Estimates.” Institute of Science and Technology Austria, 2022. https://doi.org/10.15479/at:ista:11473.","ista":"Mysliwy K. 2022. Polarons in Bose gases and polar crystals: Some rigorous energy estimates. Institute of Science and Technology Austria."},"project":[{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"related_material":{"record":[{"status":"public","id":"10564","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"8705"}]},"ec_funded":1,"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"7970714a20a6052f75fb27a6c3e9976e","file_id":"11486","success":1,"date_updated":"2022-07-05T08:12:56Z","file_size":1830973,"creator":"kmysliwy","date_created":"2022-07-05T08:12:56Z","file_name":"thes1_no_isbn_2_1b.pdf"},{"file_size":5831060,"date_updated":"2022-07-05T08:17:12Z","creator":"kmysliwy","file_name":"thes_source.zip","date_created":"2022-07-05T08:15:52Z","content_type":"application/zip","relation":"source_file","access_level":"closed","file_id":"11487","checksum":"647a2011fdf56277096c9350fefe1097"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","month":"07","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","acknowledged_ssus":[{"_id":"SSU"}],"abstract":[{"text":"The polaron model is a basic model of quantum field theory describing a single particle\r\ninteracting with a bosonic field. It arises in many physical contexts. We are mostly concerned\r\nwith models applicable in the context of an impurity atom in a Bose-Einstein condensate as\r\nwell as the problem of electrons moving in polar crystals.\r\nThe model has a simple structure in which the interaction of the particle with the field is given\r\nby a term linear in the field’s creation and annihilation operators. In this work, we investigate\r\nthe properties of this model by providing rigorous estimates on various energies relevant to the\r\nproblem. The estimates are obtained, for the most part, by suitable operator techniques which\r\nconstitute the principal mathematical substance of the thesis.\r\nThe first application of these techniques is to derive the polaron model rigorously from first\r\nprinciples, i.e., from a full microscopic quantum-mechanical many-body problem involving an\r\nimpurity in an otherwise homogeneous system. We accomplish this for the N + 1 Bose gas\r\nin the mean-field regime by showing that a suitable polaron-type Hamiltonian arises at weak\r\ninteractions as a low-energy effective theory for this problem.\r\nIn the second part, we investigate rigorously the ground state of the model at fixed momentum\r\nand for large values of the coupling constant. Qualitatively, the system is expected to display\r\na transition from the quasi-particle behavior at small momenta, where the dispersion relation\r\nis parabolic and the particle moves through the medium dragging along a cloud of phonons, to\r\nthe radiative behavior at larger momenta where the polaron decelerates and emits free phonons.\r\nAt the same time, in the strong coupling regime, the bosonic field is expected to behave purely\r\nclassically. Accordingly, the effective mass of the polaron at strong coupling is conjectured to\r\nbe asymptotically equal to the one obtained from the semiclassical counterpart of the problem,\r\nfirst studied by Landau and Pekar in the 1940s. For polaron models with regularized form\r\nfactors and phonon dispersion relations of superfluid type, i.e., bounded below by a linear\r\nfunction of the wavenumbers for all phonon momenta as in the interacting Bose gas, we prove\r\nthat for a large window of momenta below the radiation threshold, the energy-momentum\r\nrelation at strong coupling is indeed essentially a parabola with semi-latus rectum equal to the\r\nLandau–Pekar effective mass, as expected.\r\nFor the Fröhlich polaron describing electrons in polar crystals where the dispersion relation is\r\nof the optical type and the form factor is formally UV–singular due to the nature of the point\r\ncharge-dipole interaction, we are able to give the corresponding upper bound. In contrast to\r\nthe regular case, this requires the inclusion of the quantum fluctuations of the phonon field,\r\nwhich makes the problem considerably more difficult.\r\nThe results are supplemented by studies on the absolute ground-state energy at strong coupling,\r\na proof of the divergence of the effective mass with the coupling constant for a wide class of\r\npolaron models, as well as the discussion of the apparent UV singularity of the Fröhlich model\r\nand the application of the techniques used for its removal for the energy estimates.\r\n","lang":"eng"}],"file_date_updated":"2022-07-05T08:17:12Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"ddc":["515","539"],"supervisor":[{"first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer"}],"date_updated":"2023-09-07T13:43:52Z","status":"public","type":"dissertation","_id":"11473"},{"oa_version":"Published Version","abstract":[{"text":"We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.","lang":"eng"}],"intvolume":" 186","month":"01","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"da03f6d293c4b9802091bce9471b1d29","file_id":"10716","success":1,"date_updated":"2022-02-02T14:24:41Z","file_size":434957,"creator":"cchlebak","date_created":"2022-02-02T14:24:41Z","file_name":"2022_JournalStatPhys_Myśliwy.pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"ec_funded":1,"issue":"1","related_material":{"record":[{"relation":"dissertation_contains","id":"11473","status":"public"}]},"volume":186,"_id":"10564","status":"public","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)"},"type":"journal_article","article_type":"original","ddc":["530"],"date_updated":"2023-09-07T13:43:51Z","file_date_updated":"2022-02-02T14:24:41Z","department":[{"_id":"RoSe"}],"acknowledgement":"Financial support through the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme Grant Agreement No. 694227 (R.S.) and the Maria Skłodowska-Curie Grant Agreement No. 665386 (K.M.) is gratefully acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","publication":"Journal of Statistical Physics","day":"01","year":"2022","isi":1,"has_accepted_license":"1","date_created":"2021-12-19T23:01:32Z","date_published":"2022-01-01T00:00:00Z","doi":"10.1007/s10955-021-02851-w","article_number":"5","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Mysliwy, K., & Seiringer, R. (2022). Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-021-02851-w","ama":"Mysliwy K, Seiringer R. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 2022;186(1). doi:10.1007/s10955-021-02851-w","short":"K. Mysliwy, R. Seiringer, Journal of Statistical Physics 186 (2022).","ieee":"K. Mysliwy and R. Seiringer, “Polaron models with regular interactions at strong coupling,” Journal of Statistical Physics, vol. 186, no. 1. Springer Nature, 2022.","mla":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics, vol. 186, no. 1, 5, Springer Nature, 2022, doi:10.1007/s10955-021-02851-w.","ista":"Mysliwy K, Seiringer R. 2022. Polaron models with regular interactions at strong coupling. Journal of Statistical Physics. 186(1), 5.","chicago":"Mysliwy, Krzysztof, and Robert Seiringer. “Polaron Models with Regular Interactions at Strong Coupling.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-021-02851-w."},"title":"Polaron models with regular interactions at strong coupling","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2106.09328"],"isi":["000726275600001"]},"author":[{"last_name":"Mysliwy","full_name":"Mysliwy, Krzysztof","id":"316457FC-F248-11E8-B48F-1D18A9856A87","first_name":"Krzysztof"},{"full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","last_name":"Seiringer","first_name":"Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}]},{"article_number":"109455","project":[{"name":"Analysis of quantum many-body systems","grant_number":"694227","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"citation":{"ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” Journal of Functional Analysis, vol. 282, no. 12. Elsevier, 2022.","short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).","apa":"Roos, B., & Seiringer, R. (2022). Two-particle bound states at interfaces and corners. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109455","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 2022;282(12). doi:10.1016/j.jfa.2022.109455","mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis, vol. 282, no. 12, 109455, Elsevier, 2022, doi:10.1016/j.jfa.2022.109455.","ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.","chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109455."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"author":[{"first_name":"Barbara","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","last_name":"Roos"},{"id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","last_name":"Seiringer"}],"title":"Two-particle bound states at interfaces and corners","acknowledgement":"We thank Rupert Frank for contributing Appendix B. Funding from the European Union's Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 is gratefully acknowledged.","oa":1,"quality_controlled":"1","publisher":"Elsevier","year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Functional Analysis","day":"15","date_created":"2022-03-16T08:41:53Z","date_published":"2022-06-15T00:00:00Z","doi":"10.1016/j.jfa.2022.109455","_id":"10850","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)"},"article_type":"original","type":"journal_article","keyword":["Analysis"],"status":"public","date_updated":"2023-10-27T10:37:29Z","ddc":["510"],"file_date_updated":"2022-08-02T10:37:55Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"abstract":[{"text":"We study two interacting quantum particles forming a bound state in d-dimensional free\r\nspace, and constrain the particles in k directions to (0, ∞)k ×Rd−k, with Neumann boundary\r\nconditions. First, we prove that the ground state energy strictly decreases upon going from k\r\nto k+1. This shows that the particles stick to the corner where all boundary planes intersect.\r\nSecond, we show that for all k the resulting Hamiltonian, after removing the free part of the\r\nkinetic energy, has only finitely many eigenvalues below the essential spectrum. This paper\r\ngeneralizes the work of Egger, Kerner and Pankrashkin (J. Spectr. Theory 10(4):1413–1444,\r\n2020) to dimensions d > 1.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 282","month":"06","publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"language":[{"iso":"eng"}],"file":[{"file_size":631391,"date_updated":"2022-08-02T10:37:55Z","creator":"dernst","file_name":"2022_JourFunctionalAnalysis_Roos.pdf","date_created":"2022-08-02T10:37:55Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"63efcefaa1f2717244ef5407bd564426","file_id":"11720"}],"ec_funded":1,"issue":"12","related_material":{"record":[{"relation":"dissertation_contains","id":"14374","status":"public"}]},"volume":282},{"ec_funded":1,"volume":55,"issue":"1","related_material":{"record":[{"status":"public","id":"9791","relation":"earlier_version"}]},"language":[{"iso":"eng"}],"file":[{"date_created":"2022-02-14T08:20:19Z","file_name":"2022_JournalPhysicsA_Feliciangeli.pdf","creator":"dernst","date_updated":"2022-02-14T08:20:19Z","file_size":1132380,"file_id":"10757","checksum":"0875e562705563053d6dd98fba4d8578","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1751-8121"],"issn":["1751-8113"]},"intvolume":" 55","month":"01","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We provide a definition of the effective mass for the classical polaron described by the Landau–Pekar (LP) equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by LP (1948 J. Exp. Theor. Phys. 18 419–423)."}],"department":[{"_id":"RoSe"}],"file_date_updated":"2022-02-14T08:20:19Z","ddc":["510"],"date_updated":"2024-03-06T12:30:44Z","status":"public","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)"},"type":"journal_article","article_type":"original","_id":"10755","date_created":"2022-02-13T23:01:35Z","date_published":"2022-01-19T00:00:00Z","doi":"10.1088/1751-8121/ac3947","publication":"Journal of Physics A: Mathematical and Theoretical","day":"19","year":"2022","has_accepted_license":"1","oa":1,"publisher":"IOP Publishing","quality_controlled":"1","acknowledgement":"We thank Herbert Spohn for helpful comments. Funding from the European Union’s Horizon\r\n2020 research and innovation programme under the ERC Grant Agreement No. 694227\r\n(DF and RS) and under the Marie Skłodowska-Curie Grant Agreement No. 754411 (SR) is\r\ngratefully acknowledged.","title":"The effective mass problem for the Landau-Pekar equations","article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2107.03720"]},"author":[{"orcid":"0000-0003-0754-8530","full_name":"Feliciangeli, Dario","last_name":"Feliciangeli","id":"41A639AA-F248-11E8-B48F-1D18A9856A87","first_name":"Dario"},{"id":"856966FE-A408-11E9-977E-802DE6697425","first_name":"Simone Anna Elvira","last_name":"Rademacher","orcid":"0000-0001-5059-4466","full_name":"Rademacher, Simone Anna Elvira"},{"last_name":"Seiringer","orcid":"0000-0002-6781-0521","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","first_name":"Robert"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Feliciangeli, D., Rademacher, S. A. E., & Seiringer, R. (2022). The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. IOP Publishing. https://doi.org/10.1088/1751-8121/ac3947","ama":"Feliciangeli D, Rademacher SAE, Seiringer R. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 2022;55(1). doi:10.1088/1751-8121/ac3947","ieee":"D. Feliciangeli, S. A. E. Rademacher, and R. Seiringer, “The effective mass problem for the Landau-Pekar equations,” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1. IOP Publishing, 2022.","short":"D. Feliciangeli, S.A.E. Rademacher, R. Seiringer, Journal of Physics A: Mathematical and Theoretical 55 (2022).","mla":"Feliciangeli, Dario, et al. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical, vol. 55, no. 1, 015201, IOP Publishing, 2022, doi:10.1088/1751-8121/ac3947.","ista":"Feliciangeli D, Rademacher SAE, Seiringer R. 2022. The effective mass problem for the Landau-Pekar equations. Journal of Physics A: Mathematical and Theoretical. 55(1), 015201.","chicago":"Feliciangeli, Dario, Simone Anna Elvira Rademacher, and Robert Seiringer. “The Effective Mass Problem for the Landau-Pekar Equations.” Journal of Physics A: Mathematical and Theoretical. IOP Publishing, 2022. https://doi.org/10.1088/1751-8121/ac3947."},"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems"},{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"015201"}]