[{"abstract":[{"lang":"eng","text":"Describing general quantum many-body dynamics is a challenging task due to the exponential growth of the Hilbert space with system size. The time-dependent variational principle (TDVP) provides a powerful tool to tackle this task by projecting quantum evolution onto a classical dynamical system within a variational manifold. In classical systems, periodic orbits play a crucial role in understanding the structure of the phase space and the long-term behavior of the system. However, finding periodic orbits is generally difficult, and their existence and properties in generic TDVP dynamics over matrix product states have remained largely unexplored. In this work, we develop an algorithm to systematically identify and characterize periodic orbits in TDVP dynamics. Applying our method to the periodically kicked Ising model, we uncover both stable and unstable periodic orbits. We characterize the Kolmogorov-Arnold-Moser tori in the vicinity of stable periodic orbits and track the change of the periodic orbits as we modify the Hamiltonian parameters. We observe that periodic orbits exist at any value of the coupling constant of the kicked Ising model between prethermal and fully thermalizing regimes, but their relevance to quantum dynamics and imprint on quantum eigenstates diminishes as the system leaves the prethermal regime. Our results demonstrate that periodic orbits provide valuable insights into the TDVP approximation of quantum many-body evolution and establish a closer connection between quantum and classical chaos."}],"date_updated":"2026-05-20T07:59:04Z","author":[{"first_name":"Elena","last_name":"Petrova","full_name":"Petrova, Elena","id":"0ac84990-897b-11ed-a09c-f5abb56a4ede"},{"orcid":"0000-0003-0038-7068","last_name":"Ljubotina","first_name":"Marko","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","full_name":"Ljubotina, Marko"},{"id":"66E74FA2-D8BF-11E9-8249-8DE2E5697425","full_name":"Yalniz, Gökhan","orcid":"0000-0002-8490-9312","first_name":"Gökhan","last_name":"Yalniz"},{"full_name":"Serbyn, Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","first_name":"Maksym","orcid":"0000-0002-2399-5827"}],"title":"Finding periodic orbits in projected quantum many-body dynamics","external_id":{"arxiv":["2504.12472"],"isi":["001616473700003"]},"date_created":"2025-11-14T09:40:52Z","project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","grant_number":"850899","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control","call_identifier":"H2020"},{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"}],"corr_author":"1","article_number":"040333","date_published":"2025-11-12T00:00:00Z","OA_type":"gold","publication":"PRX Quantum","file_date_updated":"2025-11-14T09:44:10Z","publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"American Physical Society","ddc":["539"],"quality_controlled":"1","citation":{"ama":"Petrova E, Ljubotina M, Yalniz G, Serbyn M. Finding periodic orbits in projected quantum many-body dynamics. <i>PRX Quantum</i>. 2025;6(4). doi:<a href=\"https://doi.org/10.1103/tldp-kvkd\">10.1103/tldp-kvkd</a>","apa":"Petrova, E., Ljubotina, M., Yalniz, G., &#38; Serbyn, M. (2025). Finding periodic orbits in projected quantum many-body dynamics. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/tldp-kvkd\">https://doi.org/10.1103/tldp-kvkd</a>","chicago":"Petrova, Elena, Marko Ljubotina, Gökhan Yalniz, and Maksym Serbyn. “Finding Periodic Orbits in Projected Quantum Many-Body Dynamics.” <i>PRX Quantum</i>. American Physical Society, 2025. <a href=\"https://doi.org/10.1103/tldp-kvkd\">https://doi.org/10.1103/tldp-kvkd</a>.","ista":"Petrova E, Ljubotina M, Yalniz G, Serbyn M. 2025. Finding periodic orbits in projected quantum many-body dynamics. PRX Quantum. 6(4), 040333.","mla":"Petrova, Elena, et al. “Finding Periodic Orbits in Projected Quantum Many-Body Dynamics.” <i>PRX Quantum</i>, vol. 6, no. 4, 040333, American Physical Society, 2025, doi:<a href=\"https://doi.org/10.1103/tldp-kvkd\">10.1103/tldp-kvkd</a>.","short":"E. Petrova, M. Ljubotina, G. Yalniz, M. Serbyn, PRX Quantum 6 (2025).","ieee":"E. Petrova, M. Ljubotina, G. Yalniz, and M. Serbyn, “Finding periodic orbits in projected quantum many-body dynamics,” <i>PRX Quantum</i>, vol. 6, no. 4. American Physical Society, 2025."},"oa_version":"Published Version","article_processing_charge":"Yes","_id":"20646","day":"12","department":[{"_id":"GradSch"},{"_id":"BjHo"},{"_id":"MaSe"}],"intvolume":"         6","article_type":"original","scopus_import":"1","DOAJ_listed":"1","arxiv":1,"isi":1,"month":"11","license":"https://creativecommons.org/licenses/by/4.0/","has_accepted_license":"1","related_material":{"link":[{"description":"News on ISTA website","relation":"press_release","url":"https://ista.ac.at/en/news/reaching-for-the-quantum-scars/"}]},"PlanS_conform":"1","issue":"4","doi":"10.1103/tldp-kvkd","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_id":"20647","success":1,"creator":"gyalniz","access_level":"open_access","relation":"main_file","date_created":"2025-11-14T09:44:10Z","file_size":2504713,"content_type":"application/pdf","checksum":"5d6d04ac518b4118405334e1ddc7a56d","file_name":"tldp-kvkd.pdf","date_updated":"2025-11-14T09:44:10Z"}],"language":[{"iso":"eng"}],"oa":1,"year":"2025","ec_funded":1,"status":"public","publication_identifier":{"eissn":["2691-3399"]},"OA_place":"publisher","volume":6,"type":"journal_article","acknowledgement":"We acknowledge useful discussions with C. Kollath, A. Green, and D. Huse. E.P., M.L., and M.S. acknowledge support by the European Research Council under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 850899). This research was funded in whole or in part by the Austrian Science Fund (FWF) (Grant No. 10.55776/COE1). For open access purposes, the author has applied a CC BY public copyright license to any author accepted manuscript version arising from this submission. M.L. acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111—390814868. This research was supported in part by National Science Foundation (NSF) Grant No. PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP) and by the Erwin Schrödinger International Institute for Mathematics and Physics (ESI).","APC_amount":"3599,50 EUR"},{"abstract":[{"lang":"eng","text":"The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum."}],"date_updated":"2025-09-08T14:26:29Z","title":"Tangent space generators of matrix product states and exact floquet quantum scars","author":[{"full_name":"Ljubotina, Marko","id":"F75EE9BE-5C90-11EA-905D-16643DDC885E","orcid":"0000-0003-0038-7068","first_name":"Marko","last_name":"Ljubotina"},{"id":"0ac84990-897b-11ed-a09c-f5abb56a4ede","full_name":"Petrova, Elena","last_name":"Petrova","first_name":"Elena"},{"full_name":"Schuch, Norbert","first_name":"Norbert","last_name":"Schuch"},{"full_name":"Serbyn, Maksym","id":"47809E7E-F248-11E8-B48F-1D18A9856A87","last_name":"Serbyn","first_name":"Maksym","orcid":"0000-0002-2399-5827"}],"external_id":{"arxiv":["2403.12325"],"isi":["001346198800001"]},"date_created":"2024-10-29T16:04:05Z","project":[{"_id":"23841C26-32DE-11EA-91FC-C7463DDC885E","call_identifier":"H2020","grant_number":"850899","name":"Non-Ergodic Quantum Matter: Universality, Dynamics and Control"}],"corr_author":"1","article_number":"040311","date_published":"2024-10-23T00:00:00Z","OA_type":"gold","file_date_updated":"2024-10-30T08:59:09Z","publication":"PRX Quantum","publication_status":"published","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"American Physical Society","ddc":["530"],"quality_controlled":"1","citation":{"chicago":"Ljubotina, Marko, Elena Petrova, Norbert Schuch, and Maksym Serbyn. “Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” <i>PRX Quantum</i>. American Physical Society, 2024. <a href=\"https://doi.org/10.1103/prxquantum.5.040311\">https://doi.org/10.1103/prxquantum.5.040311</a>.","ama":"Ljubotina M, Petrova E, Schuch N, Serbyn M. Tangent space generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>. 2024;5(4). doi:<a href=\"https://doi.org/10.1103/prxquantum.5.040311\">10.1103/prxquantum.5.040311</a>","apa":"Ljubotina, M., Petrova, E., Schuch, N., &#38; Serbyn, M. (2024). Tangent space generators of matrix product states and exact floquet quantum scars. <i>PRX Quantum</i>. American Physical Society. <a href=\"https://doi.org/10.1103/prxquantum.5.040311\">https://doi.org/10.1103/prxquantum.5.040311</a>","short":"M. Ljubotina, E. Petrova, N. Schuch, M. Serbyn, PRX Quantum 5 (2024).","mla":"Ljubotina, Marko, et al. “Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars.” <i>PRX Quantum</i>, vol. 5, no. 4, 040311, American Physical Society, 2024, doi:<a href=\"https://doi.org/10.1103/prxquantum.5.040311\">10.1103/prxquantum.5.040311</a>.","ieee":"M. Ljubotina, E. Petrova, N. Schuch, and M. Serbyn, “Tangent space generators of matrix product states and exact floquet quantum scars,” <i>PRX Quantum</i>, vol. 5, no. 4. American Physical Society, 2024.","ista":"Ljubotina M, Petrova E, Schuch N, Serbyn M. 2024. Tangent space generators of matrix product states and exact floquet quantum scars. PRX Quantum. 5(4), 040311."},"article_processing_charge":"Yes","oa_version":"Published Version","_id":"18488","day":"23","department":[{"_id":"MaSe"}],"intvolume":"         5","article_type":"original","scopus_import":"1","DOAJ_listed":"1","arxiv":1,"isi":1,"month":"10","has_accepted_license":"1","doi":"10.1103/prxquantum.5.040311","issue":"4","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"language":[{"iso":"eng"}],"file":[{"relation":"main_file","date_created":"2024-10-30T08:59:09Z","checksum":"2e057ba021744d0a74602517935326b3","content_type":"application/pdf","file_size":1151431,"file_name":"2024_PRXQuantum_Ljubotina.pdf","date_updated":"2024-10-30T08:59:09Z","file_id":"18489","success":1,"creator":"dernst","access_level":"open_access"}],"oa":1,"year":"2024","ec_funded":1,"status":"public","publication_identifier":{"eissn":["2691-3399"]},"OA_place":"publisher","volume":5,"type":"journal_article","acknowledgement":"We thank L. Piroli, S. Garratt, and A. Molnár for insightful discussions. This research was funded in part by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreements No. 850899 and No. 863476), the Austrian Science Fund (FWF) (Grant DOIs 10.55776/COE1, 10.55776/P36305, and 10.55776/F71), and the European Union (NextGenerationEU). This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation Grant PHY-2210452. This research was supported in part by NSF Grant PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).","APC_amount":"3711,01 EUR"},{"year":"2024","oa":1,"language":[{"iso":"eng"}],"issue":"5","doi":"10.1103/PhysRevLett.132.050401","month":"01","isi":1,"arxiv":1,"acknowledgement":"We thank A. Bargov, I. Khaymovich, and V. Tiunova for fruitful discussions and for useful comments. M. C. B. thanks S. Kühn for discussions about the phase structure of the model. A. K. F. thanks V. Gritsev and A. Garkun for insightful comments. E. V. P., E. S. T., and A. K. F. are\r\nsupported by the RSF Grant No. 20-42-05002 (studying the fractal Ansatz) and the Roadmap on Quantum Computing (Contract No. 868-1.3-15/15-2021, October 5, 2021; calculating on GS energies). A. K. F. thanks the Priority 2030 program at the NIST “MISIS” under the project No. K1-2022-027. M. C. B. was partly funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2111–390814868.","type":"journal_article","volume":132,"publication_identifier":{"eissn":["1079-7114"],"issn":["0031-9007"]},"status":"public","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publication_status":"published","pmid":1,"publication":"Physical Review Letters","date_published":"2024-01-30T00:00:00Z","article_number":"050401","date_created":"2024-02-18T23:01:00Z","external_id":{"pmid":["38364163"],"arxiv":["2201.10220"],"isi":["001179276700003"]},"author":[{"first_name":"Elena","last_name":"Petrova","full_name":"Petrova, Elena","id":"0ac84990-897b-11ed-a09c-f5abb56a4ede"},{"first_name":"Egor S.","last_name":"Tiunov","full_name":"Tiunov, Egor S."},{"full_name":"Bañuls, Mari Carmen","first_name":"Mari Carmen","last_name":"Bañuls"},{"last_name":"Fedorov","first_name":"Aleksey K.","full_name":"Fedorov, Aleksey K."}],"title":"Fractal states of the Schwinger model","date_updated":"2025-09-04T12:02:33Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2201.10220"}],"abstract":[{"text":"The lattice Schwinger model, the discrete version of QED in \r\n1\r\n+\r\n1\r\n dimensions, is a well-studied test bench for lattice gauge theories. Here, we study the fractal properties of this model. We reveal the self-similarity of the ground state, which allows us to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We present the results of recurrently calculating ground-state wave functions using the fractal Ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground-state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.","lang":"eng"}],"scopus_import":"1","article_type":"original","intvolume":"       132","department":[{"_id":"MaSe"}],"day":"30","_id":"15002","oa_version":"Preprint","article_processing_charge":"No","quality_controlled":"1","citation":{"ista":"Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. 2024. Fractal states of the Schwinger model. Physical Review Letters. 132(5), 050401.","short":"E. Petrova, E.S. Tiunov, M.C. Bañuls, A.K. Fedorov, Physical Review Letters 132 (2024).","mla":"Petrova, Elena, et al. “Fractal States of the Schwinger Model.” <i>Physical Review Letters</i>, vol. 132, no. 5, 050401, American Physical Society, 2024, doi:<a href=\"https://doi.org/10.1103/PhysRevLett.132.050401\">10.1103/PhysRevLett.132.050401</a>.","ieee":"E. Petrova, E. S. Tiunov, M. C. Bañuls, and A. K. Fedorov, “Fractal states of the Schwinger model,” <i>Physical Review Letters</i>, vol. 132, no. 5. American Physical Society, 2024.","apa":"Petrova, E., Tiunov, E. S., Bañuls, M. C., &#38; Fedorov, A. K. (2024). Fractal states of the Schwinger model. <i>Physical Review Letters</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevLett.132.050401\">https://doi.org/10.1103/PhysRevLett.132.050401</a>","ama":"Petrova E, Tiunov ES, Bañuls MC, Fedorov AK. Fractal states of the Schwinger model. <i>Physical Review Letters</i>. 2024;132(5). doi:<a href=\"https://doi.org/10.1103/PhysRevLett.132.050401\">10.1103/PhysRevLett.132.050401</a>","chicago":"Petrova, Elena, Egor S. Tiunov, Mari Carmen Bañuls, and Aleksey K. Fedorov. “Fractal States of the Schwinger Model.” <i>Physical Review Letters</i>. American Physical Society, 2024. <a href=\"https://doi.org/10.1103/PhysRevLett.132.050401\">https://doi.org/10.1103/PhysRevLett.132.050401</a>."},"publisher":"American Physical Society"},{"publication":"Physical Review B","publication_status":"published","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_number":"184312","date_published":"2023-05-01T00:00:00Z","author":[{"full_name":"Orlov, Pavel","last_name":"Orlov","first_name":"Pavel"},{"full_name":"Tiutiakina, Anastasiia","first_name":"Anastasiia","last_name":"Tiutiakina"},{"full_name":"Sharipov, Rustem","last_name":"Sharipov","first_name":"Rustem"},{"first_name":"Elena","last_name":"Petrova","full_name":"Petrova, Elena","id":"0ac84990-897b-11ed-a09c-f5abb56a4ede"},{"full_name":"Gritsev, Vladimir","last_name":"Gritsev","first_name":"Vladimir"},{"full_name":"Kurlov, Denis V.","first_name":"Denis V.","last_name":"Kurlov"}],"title":"Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain","date_created":"2023-06-18T22:00:46Z","external_id":{"arxiv":["2303.00729"],"isi":["001003686900004"]},"abstract":[{"text":"We consider the spin-\r\n1\r\n2\r\n Heisenberg chain (XXX model) weakly perturbed away from integrability by an isotropic next-to-nearest neighbor exchange interaction. Recently, it was conjectured that this model possesses an infinite tower of quasiconserved integrals of motion (charges) [D. Kurlov et al., Phys. Rev. B 105, 104302 (2022)]. In this work we first test this conjecture by investigating how the norm of the adiabatic gauge potential (AGP) scales with the system size, which is known to be a remarkably accurate measure of chaos. We find that for the perturbed XXX chain the behavior of the AGP norm corresponds to neither an integrable nor a chaotic regime, which supports the conjectured quasi-integrability of the model. We then prove the conjecture and explicitly construct the infinite set of quasiconserved charges. Our proof relies on the fact that the XXX chain perturbed by next-to-nearest exchange interaction can be viewed as a truncation of an integrable long-range deformation of the Heisenberg spin chain.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2303.00729"}],"date_updated":"2023-08-02T06:16:02Z","department":[{"_id":"GradSch"}],"intvolume":"       107","article_type":"original","scopus_import":"1","article_processing_charge":"No","oa_version":"Preprint","_id":"13138","day":"01","citation":{"chicago":"Orlov, Pavel, Anastasiia Tiutiakina, Rustem Sharipov, Elena Petrova, Vladimir Gritsev, and Denis V. Kurlov. “Adiabatic Eigenstate Deformations and Weak Integrability Breaking of Heisenberg Chain.” <i>Physical Review B</i>. American Physical Society, 2023. <a href=\"https://doi.org/10.1103/PhysRevB.107.184312\">https://doi.org/10.1103/PhysRevB.107.184312</a>.","ama":"Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain. <i>Physical Review B</i>. 2023;107(18). doi:<a href=\"https://doi.org/10.1103/PhysRevB.107.184312\">10.1103/PhysRevB.107.184312</a>","apa":"Orlov, P., Tiutiakina, A., Sharipov, R., Petrova, E., Gritsev, V., &#38; Kurlov, D. V. (2023). Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain. <i>Physical Review B</i>. American Physical Society. <a href=\"https://doi.org/10.1103/PhysRevB.107.184312\">https://doi.org/10.1103/PhysRevB.107.184312</a>","ieee":"P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, and D. V. Kurlov, “Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain,” <i>Physical Review B</i>, vol. 107, no. 18. American Physical Society, 2023.","short":"P. Orlov, A. Tiutiakina, R. Sharipov, E. Petrova, V. Gritsev, D.V. Kurlov, Physical Review B 107 (2023).","mla":"Orlov, Pavel, et al. “Adiabatic Eigenstate Deformations and Weak Integrability Breaking of Heisenberg Chain.” <i>Physical Review B</i>, vol. 107, no. 18, 184312, American Physical Society, 2023, doi:<a href=\"https://doi.org/10.1103/PhysRevB.107.184312\">10.1103/PhysRevB.107.184312</a>.","ista":"Orlov P, Tiutiakina A, Sharipov R, Petrova E, Gritsev V, Kurlov DV. 2023. Adiabatic eigenstate deformations and weak integrability breaking of Heisenberg chain. Physical Review B. 107(18), 184312."},"quality_controlled":"1","publisher":"American Physical Society","language":[{"iso":"eng"}],"oa":1,"year":"2023","issue":"18","doi":"10.1103/PhysRevB.107.184312","month":"05","arxiv":1,"isi":1,"acknowledgement":"The numerical computations in this work were performed using QuSpin [83, 84]. We acknowledge useful discussions with Igor Aleiner, Boris Altshuler, Jacopo de Nardis, Anatoli Polkovnikov, and Gora Shlyapnikov. We thank Piotr Sierant and Dario Rosa for drawing our attention to Refs. [31, 42, 46] and Ref. [47], respectively. We are grateful to an anonymous referee for very useful comments and for drawing our attention to Refs. [80, 81]. The work of VG is part of the DeltaITP consortium, a program of the Netherlands Organization for Scientific\r\nResearch (NWO) funded by the Dutch Ministry of Education, Culture and Science (OCW). VG is also partially supported by RSF 19-71-10092. The work of AT was supported by the ERC Starting Grant 101042293 (HEPIQ). RS acknowledges support from Slovenian Research Agency (ARRS) - research programme P1-0402. ","type":"journal_article","volume":107,"status":"public","publication_identifier":{"eissn":["2469-9969"],"issn":["2469-9950"]}}]