{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,17]],"date-time":"2026-09-17T06:16:06Z","timestamp":1789625766031,"version":"build-2803163510"},"reference-count":82,"publisher":"AIP Publishing","issue":"3","license":[{"start":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T00:00:00Z","timestamp":1752537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["454252029"],"award-info":[{"award-number":["454252029"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Center for New Scientists at the Weizmann Institute of Science"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,7,21]]},"abstract":"<jats:p>In pulsed dynamic nuclear polarization (DNP), enhancement of bulk nuclear polarization requires the repeated application of a microwave pulse sequence. So far, analysis of a one-time transfer of electron spin polarization to a dipolar-coupled nuclear spin has guided the design of DNP pulse sequences. This has obvious shortcomings, such as the inability to predict the optimal repetition time. In an actual pulsed DNP experiment, a balance is reached between the polarization arriving from the unpaired electrons and nuclear relaxation. In this article, we explore three algorithms to compute this stroboscopic steady state: (1) explicit time evolution by propagator squaring, (2) generation of an effective propagator using the matrix logarithm, and (3) direct calculation of the steady state with the Newton\u2013Raphson method. Algorithm (2) is numerically unstable in dissipative DNP settings. Algorithms (1) and (3) are both stable; algorithm (3) is the most efficient. We compare the steady-state simulations to existing experimental results at 0.34 and 1.2\u00a0T and to the first experimental observation of X-inverse-X (XiX) DNP at 3.4\u00a0T. The agreement is good and improves further when electron\u2013proton distance and electron Rabi frequency distributions are accounted for. We demonstrate that the trajectory of the spin system during one-time application of a microwave pulse sequence differs from the steady orbit. This has implications for DNP pulse sequence design.<\/jats:p>","DOI":"10.1063\/5.0283196","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T10:05:47Z","timestamp":1752660347000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Simulation of pulsed dynamic nuclear polarization in the steady state"],"prefix":"10.1063","volume":"163","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8847-1939","authenticated-orcid":false,"given":"Shebha Anandhi","family":"Jegadeesan","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of Konstanz 1 , Konstanz,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5342-5702","authenticated-orcid":false,"given":"Yujie","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of St Andrews 2 , St Andrews,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6578-7412","authenticated-orcid":false,"given":"Graham M.","family":"Smith","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of St Andrews 2 , St Andrews,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0430-2682","authenticated-orcid":false,"given":"Ilya","family":"Kuprov","sequence":"additional","affiliation":[{"name":"Chemical and Biological Physics Department, Weizmann Institute of Science 3 , Rehovot,","place":["Israel"]},{"name":"School of Chemistry and Chemical Engineering, University of Southampton 4 , Southampton,","place":["United Kingdom"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2719-0743","authenticated-orcid":false,"given":"Guinevere","family":"Mathies","sequence":"additional","affiliation":[{"name":"Department of Chemistry, University of Konstanz 1 , Konstanz,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"issue":"2","key":"2025071606054249700_c1","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1103\/physrev.92.411","article-title":"Polarization of nuclei in metals","volume":"92","year":"1953","journal-title":"Phys. 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