[{"department":[{"_id":"GradSch"},{"_id":"RoSe"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","publisher":"Institute of Science and Technology Austria","article_processing_charge":"No","ec_funded":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc-sa/4.0/legalcode","image":"/images/cc_by_nc_sa.png","name":"Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)","short":"CC BY-NC-SA (4.0)"},"license":"https://creativecommons.org/licenses/by-nc-sa/4.0/","day":"30","file":[{"checksum":"ef039ffc3de2cb8dee5b14110938e9b6","date_updated":"2023-10-06T11:35:56Z","file_id":"14398","access_level":"open_access","date_created":"2023-10-06T11:35:56Z","file_name":"phd-thesis-draft_pdfa_acrobat.pdf","creator":"broos","relation":"main_file","content_type":"application/pdf","file_size":2365702},{"file_name":"Version5.zip","content_type":"application/x-zip-compressed","relation":"source_file","file_size":4691734,"creator":"broos","date_updated":"2023-10-06T11:38:01Z","file_id":"14399","checksum":"81dcac33daeefaf0111db52f41bb1fd0","date_created":"2023-10-06T11:38:01Z","access_level":"closed"}],"author":[{"last_name":"Roos","first_name":"Barbara","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara"}],"degree_awarded":"PhD","title":"Boundary superconductivity in BCS theory","project":[{"name":"Analysis of quantum many-body systems","call_identifier":"H2020","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","grant_number":"694227"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2663 - 337X"]},"doi":"10.15479/at:ista:14374","year":"2023","_id":"14374","abstract":[{"lang":"eng","text":"Superconductivity has many important applications ranging from levitating trains over qubits to MRI scanners. The phenomenon is successfully modeled by Bardeen-Cooper-Schrieffer (BCS) theory. From a mathematical perspective, BCS theory has been studied extensively for systems without boundary. However, little is known in the presence of boundaries. With the help of numerical methods physicists observed that the critical temperature may increase in the presence of a boundary. The goal of this thesis is to understand the influence of boundaries on the critical temperature in BCS theory and to give a first rigorous justification of these observations. On the way, we also study two-body Schrödinger operators on domains with boundaries and prove additional results for superconductors without boundary.\r\n\r\nBCS theory is based on a non-linear functional, where the minimizer indicates whether the system is superconducting or in the normal, non-superconducting state. By considering the Hessian of the BCS functional at the normal state, one can analyze whether the normal state is possibly a minimum of the BCS functional and estimate the critical temperature. The Hessian turns out to be a linear operator resembling a Schrödinger operator for two interacting particles, but with more complicated kinetic energy. As a first step, we study the two-body Schrödinger operator in the presence of boundaries.\r\nFor Neumann boundary conditions, we prove that the addition of a boundary can create new eigenvalues, which correspond to the two particles forming a bound state close to the boundary.\r\n\r\nSecond, we need to understand superconductivity in the translation invariant setting. While in three dimensions this has been extensively studied, there is no mathematical literature for the one and two dimensional cases. In dimensions one and two, we compute the weak coupling asymptotics of the critical temperature and the energy gap  in the translation invariant setting. We also prove that their ratio is independent of the microscopic details of the model in the weak coupling limit; this property is referred to as universality.\r\n\r\nIn the third part, we study the critical temperature of superconductors in the presence of boundaries. We start by considering the one-dimensional case of a half-line with contact interaction. Then, we generalize the results to generic interactions and half-spaces in one, two and three dimensions. Finally, we compare the critical temperature of a quarter space in two dimensions to the critical temperatures of a half-space and of the full space."}],"date_updated":"2023-10-27T10:37:30Z","oa_version":"Published Version","month":"09","type":"dissertation","page":"206","file_date_updated":"2023-10-06T11:38:01Z","date_created":"2023-09-28T14:23:04Z","status":"public","alternative_title":["ISTA Thesis"],"citation":{"chicago":"Roos, Barbara. “Boundary Superconductivity in BCS Theory.” Institute of Science and Technology Austria, 2023. <a href=\"https://doi.org/10.15479/at:ista:14374\">https://doi.org/10.15479/at:ista:14374</a>.","ieee":"B. Roos, “Boundary superconductivity in BCS theory,” Institute of Science and Technology Austria, 2023.","short":"B. Roos, Boundary Superconductivity in BCS Theory, Institute of Science and Technology Austria, 2023.","ama":"Roos B. Boundary superconductivity in BCS theory. 2023. doi:<a href=\"https://doi.org/10.15479/at:ista:14374\">10.15479/at:ista:14374</a>","apa":"Roos, B. (2023). <i>Boundary superconductivity in BCS theory</i>. Institute of Science and Technology Austria. <a href=\"https://doi.org/10.15479/at:ista:14374\">https://doi.org/10.15479/at:ista:14374</a>","mla":"Roos, Barbara. <i>Boundary Superconductivity in BCS Theory</i>. Institute of Science and Technology Austria, 2023, doi:<a href=\"https://doi.org/10.15479/at:ista:14374\">10.15479/at:ista:14374</a>.","ista":"Roos B. 2023. Boundary superconductivity in BCS theory. Institute of Science and Technology Austria."},"related_material":{"record":[{"id":"13207","status":"public","relation":"part_of_dissertation"},{"id":"10850","status":"public","relation":"part_of_dissertation"}]},"has_accepted_license":"1","publication_status":"published","oa":1,"supervisor":[{"first_name":"Robert","last_name":"Seiringer","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","full_name":"Seiringer, Robert"}],"date_published":"2023-09-30T00:00:00Z","ddc":["515","539"]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"World Scientific Publishing","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"publication":"Reviews in Mathematical Physics","ec_funded":1,"article_processing_charge":"Yes (in subscription journal)","scopus_import":"1","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)"},"author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha"},{"last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard"},{"full_name":"Roos, Barbara","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","last_name":"Roos","first_name":"Barbara"}],"day":"31","title":"Universality in low-dimensional BCS theory","arxiv":1,"article_number":"2360005 ","project":[{"grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"Mathematical Challenges in BCS Theory of Superconductivity","_id":"bda63fe5-d553-11ed-ba76-a16e3d2f256b","grant_number":"I06427"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1793-6659"],"issn":["0129-055X"]},"doi":"10.1142/s0129055x2360005x","quality_controlled":"1","acknowledgement":"We thank Robert Seiringer for comments on the paper. J. H. gratefully acknowledges  partial  financial  support  by  the  ERC  Advanced  Grant  “RMTBeyond”No. 101020331.This research was funded in part by the Austrian Science Fund (FWF) grantnumber I6427.","year":"2023","_id":"14542","date_updated":"2023-11-20T10:04:38Z","abstract":[{"lang":"eng","text":"It is a remarkable property of BCS theory that the ratio of the energy gap at zero temperature Ξ\r\n and the critical temperature Tc is (approximately) given by a universal constant, independent of the microscopic details of the fermionic interaction. This universality has rigorously been proven quite recently in three spatial dimensions and three different limiting regimes: weak coupling, low density and high density. The goal of this short note is to extend the universal behavior to lower dimensions d=1,2 and give an exemplary proof in the weak coupling limit."}],"month":"10","type":"journal_article","oa_version":"Published Version","date_created":"2023-11-15T23:48:14Z","status":"public","external_id":{"arxiv":["2301.05621"]},"citation":{"ama":"Henheik SJ, Lauritsen AB, Roos B. Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. 2023. doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>","apa":"Henheik, S. J., Lauritsen, A. B., &#38; Roos, B. (2023). Universality in low-dimensional BCS theory. <i>Reviews in Mathematical Physics</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>","ista":"Henheik SJ, Lauritsen AB, Roos B. 2023. Universality in low-dimensional BCS theory. Reviews in Mathematical Physics., 2360005.","mla":"Henheik, Sven Joscha, et al. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>, 2360005, World Scientific Publishing, 2023, doi:<a href=\"https://doi.org/10.1142/s0129055x2360005x\">10.1142/s0129055x2360005x</a>.","chicago":"Henheik, Sven Joscha, Asbjørn Bækgaard Lauritsen, and Barbara Roos. “Universality in Low-Dimensional BCS Theory.” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023. <a href=\"https://doi.org/10.1142/s0129055x2360005x\">https://doi.org/10.1142/s0129055x2360005x</a>.","ieee":"S. J. Henheik, A. B. Lauritsen, and B. Roos, “Universality in low-dimensional BCS theory,” <i>Reviews in Mathematical Physics</i>. World Scientific Publishing, 2023.","short":"S.J. Henheik, A.B. Lauritsen, B. Roos, Reviews in Mathematical Physics (2023)."},"oa":1,"publication_status":"epub_ahead","has_accepted_license":"1","date_published":"2023-10-31T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.1142/S0129055X2360005X","open_access":"1"}]},{"year":"2023","acknowledgement":"We thank Egor Babaev for encouraging us to study this problem, and Rupert Frank for many fruitful discussions. scussions. Funding. Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No. 694227 (Barbara Roos and Robert Seiringer) is gratefully acknowledged.","_id":"13207","type":"journal_article","month":"05","oa_version":"Published Version","abstract":[{"text":"We consider the linear BCS equation, determining the BCS critical temperature, in the presence of a boundary, where Dirichlet boundary conditions are imposed. In the one-dimensional case with point interactions, we prove that the critical temperature is strictly larger than the bulk value, at least at weak coupling. In particular, the Cooper-pair wave function localizes near the boundary, an effect that cannot be modeled by effective Neumann boundary conditions on the order parameter as often imposed in Ginzburg–Landau theory. We also show that the relative shift in critical temperature vanishes if the coupling constant either goes to zero or to infinity.","lang":"eng"}],"date_updated":"2023-10-27T10:37:29Z","page":"1507–1540","file_date_updated":"2023-07-11T08:19:15Z","date_created":"2023-07-10T16:35:45Z","volume":12,"status":"public","external_id":{"arxiv":["2201.08090"],"isi":["000997933500008"]},"citation":{"chicago":"Hainzl, Christian, Barbara Roos, and Robert Seiringer. “Boundary Superconductivity in the BCS Model.” <i>Journal of Spectral Theory</i>. EMS Press, 2023. <a href=\"https://doi.org/10.4171/JST/439\">https://doi.org/10.4171/JST/439</a>.","ieee":"C. Hainzl, B. Roos, and R. Seiringer, “Boundary superconductivity in the BCS model,” <i>Journal of Spectral Theory</i>, vol. 12, no. 4. EMS Press, pp. 1507–1540, 2023.","short":"C. Hainzl, B. Roos, R. Seiringer, Journal of Spectral Theory 12 (2023) 1507–1540.","ama":"Hainzl C, Roos B, Seiringer R. Boundary superconductivity in the BCS model. <i>Journal of Spectral Theory</i>. 2023;12(4):1507–1540. doi:<a href=\"https://doi.org/10.4171/JST/439\">10.4171/JST/439</a>","apa":"Hainzl, C., Roos, B., &#38; Seiringer, R. (2023). Boundary superconductivity in the BCS model. <i>Journal of Spectral Theory</i>. EMS Press. <a href=\"https://doi.org/10.4171/JST/439\">https://doi.org/10.4171/JST/439</a>","mla":"Hainzl, Christian, et al. “Boundary Superconductivity in the BCS Model.” <i>Journal of Spectral Theory</i>, vol. 12, no. 4, EMS Press, 2023, pp. 1507–1540, doi:<a href=\"https://doi.org/10.4171/JST/439\">10.4171/JST/439</a>.","ista":"Hainzl C, Roos B, Seiringer R. 2023. Boundary superconductivity in the BCS model. Journal of Spectral Theory. 12(4), 1507–1540."},"related_material":{"record":[{"id":"14374","status":"public","relation":"dissertation_contains"}]},"intvolume":"        12","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["530"],"date_published":"2023-05-18T00:00:00Z","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"publisher":"EMS Press","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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)"},"ec_funded":1,"article_processing_charge":"No","publication":"Journal of Spectral Theory","day":"18","file":[{"date_created":"2023-07-11T08:19:15Z","access_level":"open_access","date_updated":"2023-07-11T08:19:15Z","file_id":"13208","checksum":"5501da33be010b5c81440438287584d5","relation":"main_file","content_type":"application/pdf","file_size":304619,"creator":"alisjak","success":1,"file_name":"2023_EMS_Hainzl.pdf"}],"author":[{"last_name":"Hainzl","first_name":"Christian","full_name":"Hainzl, Christian"},{"first_name":"Barbara","last_name":"Roos","orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara"},{"full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521","first_name":"Robert","last_name":"Seiringer"}],"arxiv":1,"title":"Boundary superconductivity in the BCS model","project":[{"name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"694227"}],"issue":"4","language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eissn":["1664-0403"],"issn":["1664-039X"]},"quality_controlled":"1","doi":"10.4171/JST/439"},{"volume":282,"date_created":"2022-03-16T08:41:53Z","file_date_updated":"2022-08-02T10:37:55Z","abstract":[{"lang":"eng","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."}],"date_updated":"2023-10-27T10:37:29Z","type":"journal_article","oa_version":"Published Version","month":"06","_id":"10850","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.","year":"2022","date_published":"2022-06-15T00:00:00Z","ddc":["510"],"publication_status":"published","oa":1,"has_accepted_license":"1","intvolume":"       282","related_material":{"record":[{"id":"14374","status":"public","relation":"dissertation_contains"}]},"citation":{"short":"B. Roos, R. Seiringer, Journal of Functional Analysis 282 (2022).","ieee":"B. Roos and R. Seiringer, “Two-particle bound states at interfaces and corners,” <i>Journal of Functional Analysis</i>, vol. 282, no. 12. Elsevier, 2022.","chicago":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>.","ista":"Roos B, Seiringer R. 2022. Two-particle bound states at interfaces and corners. Journal of Functional Analysis. 282(12), 109455.","mla":"Roos, Barbara, and Robert Seiringer. “Two-Particle Bound States at Interfaces and Corners.” <i>Journal of Functional Analysis</i>, vol. 282, no. 12, 109455, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>.","apa":"Roos, B., &#38; Seiringer, R. (2022). Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">https://doi.org/10.1016/j.jfa.2022.109455</a>","ama":"Roos B, Seiringer R. Two-particle bound states at interfaces and corners. <i>Journal of Functional Analysis</i>. 2022;282(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109455\">10.1016/j.jfa.2022.109455</a>"},"external_id":{"isi":["000795160200009"],"arxiv":["2105.04874"]},"status":"public","arxiv":1,"title":"Two-particle bound states at interfaces and corners","article_number":"109455","author":[{"id":"5DA90512-D80F-11E9-8994-2E2EE6697425","orcid":"0000-0002-9071-5880","full_name":"Roos, Barbara","first_name":"Barbara","last_name":"Roos"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87"}],"file":[{"success":1,"file_name":"2022_JourFunctionalAnalysis_Roos.pdf","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_size":631391,"checksum":"63efcefaa1f2717244ef5407bd564426","date_updated":"2022-08-02T10:37:55Z","file_id":"11720","access_level":"open_access","date_created":"2022-08-02T10:37:55Z"}],"day":"15","publication":"Journal of Functional Analysis","article_processing_charge":"Yes (via OA deal)","ec_funded":1,"scopus_import":"1","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)"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Elsevier","department":[{"_id":"GradSch"},{"_id":"RoSe"}],"doi":"10.1016/j.jfa.2022.109455","quality_controlled":"1","publication_identifier":{"issn":["0022-1236"]},"isi":1,"keyword":["Analysis"],"language":[{"iso":"eng"}],"issue":"12","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}]},{"publication_identifier":{"eissn":["2691-3399"]},"quality_controlled":"1","doi":"10.1103/prxquantum.3.030343","project":[{"grant_number":"850899","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020","_id":"23841C26-32DE-11EA-91FC-C7463DDC885E"}],"language":[{"iso":"eng"}],"issue":"3","keyword":["General Medicine"],"day":"23","file":[{"file_name":"2022_PRXQuantum_Ljubotina.pdf","success":1,"file_size":7661905,"content_type":"application/pdf","relation":"main_file","creator":"dernst","file_id":"12457","date_updated":"2023-01-30T11:02:50Z","checksum":"ef8f0a1b5a019b3958009162de0fa4c3","date_created":"2023-01-30T11:02:50Z","access_level":"open_access"}],"author":[{"id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","full_name":"Ljubotina, Marko","last_name":"Ljubotina","first_name":"Marko"},{"orcid":"0000-0002-9071-5880","id":"5DA90512-D80F-11E9-8994-2E2EE6697425","full_name":"Roos, Barbara","last_name":"Roos","first_name":"Barbara"},{"full_name":"Abanin, Dmitry A.","first_name":"Dmitry A.","last_name":"Abanin"},{"last_name":"Serbyn","first_name":"Maksym","orcid":"0000-0002-2399-5827","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","full_name":"Serbyn, Maksym"}],"title":"Optimal steering of matrix product states and quantum many-body scars","arxiv":1,"article_number":"030343","department":[{"_id":"MaSe"},{"_id":"RoSe"}],"publisher":"American Physical Society","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","ec_funded":1,"article_processing_charge":"No","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)"},"publication":"PRX Quantum","has_accepted_license":"1","oa":1,"publication_status":"published","date_published":"2022-09-23T00:00:00Z","ddc":["530"],"external_id":{"arxiv":["2204.02899"]},"status":"public","citation":{"short":"M. Ljubotina, B. Roos, D.A. Abanin, M. Serbyn, PRX Quantum 3 (2022).","chicago":"Ljubotina, Marko, Barbara Roos, Dmitry A. Abanin, and Maksym Serbyn. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” <i>PRX Quantum</i>. American Physical Society, 2022. <a href=\"https://doi.org/10.1103/prxquantum.3.030343\">https://doi.org/10.1103/prxquantum.3.030343</a>.","ieee":"M. Ljubotina, B. Roos, D. A. Abanin, and M. Serbyn, “Optimal steering of matrix product states and quantum many-body scars,” <i>PRX Quantum</i>, vol. 3, no. 3. American Physical Society, 2022.","apa":"Ljubotina, M., Roos, B., Abanin, D. A., &#38; Serbyn, M. (2022). Optimal steering of matrix product states and quantum many-body scars. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/prxquantum.3.030343\">https://doi.org/10.1103/prxquantum.3.030343</a>","ista":"Ljubotina M, Roos B, Abanin DA, Serbyn M. 2022. Optimal steering of matrix product states and quantum many-body scars. PRX Quantum. 3(3), 030343.","mla":"Ljubotina, Marko, et al. “Optimal Steering of Matrix Product States and Quantum Many-Body Scars.” <i>PRX Quantum</i>, vol. 3, no. 3, 030343, American Physical Society, 2022, doi:<a href=\"https://doi.org/10.1103/prxquantum.3.030343\">10.1103/prxquantum.3.030343</a>.","ama":"Ljubotina M, Roos B, Abanin DA, Serbyn M. Optimal steering of matrix product states and quantum many-body scars. <i>PRX Quantum</i>. 2022;3(3). doi:<a href=\"https://doi.org/10.1103/prxquantum.3.030343\">10.1103/prxquantum.3.030343</a>"},"intvolume":"         3","abstract":[{"text":"Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of nontrivial quantum states. Here we formulate an approach to control quantum systems based on matrix product states (MPSs). We compare counterdiabatic and leakage minimization approaches to the so-called local steering problem that consists in finding the best value of the control parameters for generating a unitary evolution of the specific MPS in a given direction. In order to benchmark the different approaches, we apply them to the generalization of the PXP model known to exhibit coherent quantum dynamics due to quantum many-body scars. We find that the leakage-based approach generally outperforms the counterdiabatic framework and use it to construct a Floquet model with quantum scars. We perform the first steps towards global trajectory optimization and demonstrate entanglement steering capabilities in the generalized PXP model. Finally, we apply our leakage minimization approach to construct quantum scars in the periodically driven nonintegrable Ising model.","lang":"eng"}],"date_updated":"2023-01-30T11:05:23Z","oa_version":"Published Version","month":"09","type":"journal_article","date_created":"2023-01-16T10:01:56Z","file_date_updated":"2023-01-30T11:02:50Z","volume":3,"year":"2022","acknowledgement":"We thank A. A. Michailidis for insightful discussions. M.L. and M.S. acknowledge support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 850899). D.A. is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 864597) and by the Swiss National Science Foundation. The infinite TEBD simulations were performed using the ITensor library [67].","_id":"12276"}]