{"title":"Koopman analysis of quantum systems","status":"public","oa":"1","publisher":"IOP Publishing Ltd.","publication_status":"published","abstract":[{"text":"Koopman operator theory has been successfully applied to problems from various research areas such as fluid dynamics, molecular dynamics, climate science, engineering, and biology. Applications include detecting metastable or coherent sets, coarse-graining, system identification, and control. There is an intricate connection between dynamical systems driven by stochastic differential equations and quantum mechanics. In this paper, we compare the ground-state transformation and Nelson's stochastic mechanics and demonstrate how data-driven methods developed for the approximation of the Koopman operator can be used to analyze quantum physics problems. Moreover, we exploit the relationship between Schrödinger operators and stochastic control problems to show that modern data-driven methods for stochastic control can be used to solve the stationary or imaginary-time Schrödinger equation. Our findings open up a new avenue towards solving Schrödinger's equation using recently developed tools from data science.","lang":"eng"}],"type":"journal_article","page":"314002","year":"2022","issue":"31","doi":"10.1088/1751-8121/ac7d22","intvolume":"        55","_id":"29673","volume":55,"author":[{"first_name":"Stefan","last_name":"Klus","full_name":"Klus, Stefan"},{"orcid":"0000-0003-2444-7889","full_name":"Nüske, Feliks","id":"81513","last_name":"Nüske","first_name":"Feliks"},{"full_name":"Peitz, Sebastian","orcid":"0000-0002-3389-793X","id":"47427","last_name":"Peitz","first_name":"Sebastian"}],"citation":{"mla":"Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, IOP Publishing Ltd., 2022, p. 314002, doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>.","apa":"Klus, S., Nüske, F., &#38; Peitz, S. (2022). Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>, <i>55</i>(31), 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>","short":"S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical 55 (2022) 314002.","bibtex":"@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems}, volume={55}, DOI={<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>}, number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian}, year={2022}, pages={314002} }","ama":"Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. <i>Journal of Physics A: Mathematical and Theoretical</i>. 2022;55(31):314002. doi:<a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>","chicago":"Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of Quantum Systems.” <i>Journal of Physics A: Mathematical and Theoretical</i> 55, no. 31 (2022): 314002. <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">https://doi.org/10.1088/1751-8121/ac7d22</a>.","ieee":"S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” <i>Journal of Physics A: Mathematical and Theoretical</i>, vol. 55, no. 31, p. 314002, 2022, doi: <a href=\"https://doi.org/10.1088/1751-8121/ac7d22\">10.1088/1751-8121/ac7d22</a>."},"department":[{"_id":"655"},{"_id":"101"}],"publication":"Journal of Physics A: Mathematical and Theoretical","external_id":{"arxiv":["2201.12062"]},"date_updated":"2022-07-18T14:26:41Z","main_file_link":[{"open_access":"1","url":"https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf"}],"user_id":"47427","language":[{"iso":"eng"}],"date_created":"2022-01-31T09:49:40Z"}