{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T16:31:57Z","timestamp":1772641917650,"version":"3.50.1"},"reference-count":65,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spain\u2019s Ministerio de Ciencia, Innovacion y Universidades","award":["PID2021-127840NB-I00"],"award-info":[{"award-number":["PID2021-127840NB-I00"]}]},{"name":"Spain\u2019s Ministerio de Ciencia, Innovacion y Universidades","award":["MICINN\/AEI\/FEDER, UE"],"award-info":[{"award-number":["MICINN\/AEI\/FEDER, UE"]}]},{"name":"Spain\u2019s Ministerio de Ciencia, Innovacion y Universidades","award":["881603"],"award-info":[{"award-number":["881603"]}]},{"name":"MICINN\/AEI\/FEDER, UE","award":["PID2021-127840NB-I00"],"award-info":[{"award-number":["PID2021-127840NB-I00"]}]},{"name":"MICINN\/AEI\/FEDER, UE","award":["MICINN\/AEI\/FEDER, UE"],"award-info":[{"award-number":["MICINN\/AEI\/FEDER, UE"]}]},{"name":"MICINN\/AEI\/FEDER, UE","award":["881603"],"award-info":[{"award-number":["881603"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["PID2021-127840NB-I00"],"award-info":[{"award-number":["PID2021-127840NB-I00"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["MICINN\/AEI\/FEDER, UE"],"award-info":[{"award-number":["MICINN\/AEI\/FEDER, UE"]}]},{"name":"European Union\u2019s Horizon 2020 research and innovation program","award":["881603"],"award-info":[{"award-number":["881603"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>It is certain that electrical properties\u2014whether slow (sec) or fast (nsec), even optical (fsec)\u2014are described by Maxwell\u2019s equations, and there are terms that depend on the rate of the change of the electric and magnetic fields. In particular, Maxwell\u2019s equation for the curl of the magnetic field contains both the steady-state conduction current and a term depending upon the temporal derivative of the electric displacement field. The latter is referred to as the displacement current and is generally believed to have been included originally by Maxwell himself, although there is evidence it was earlier considered by Kirchhoff. Maxwell\u2019s equations and Kirchoff\u2019s circuit laws both are important over the wide range of frequencies with which electronics traditionally deal. Additionally, the displacement current is an important contribution to these in both classical and quantum mechanics. Here, the development of the displacement current, its importance in both classical and quantum mechanics, and some applications are provided to illustrate the fundamental role that it plays in the dynamics of a wide range of systems.<\/jats:p>","DOI":"10.3390\/computation13020045","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T09:02:42Z","timestamp":1738918962000},"page":"45","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Displacement Current in Classical and Quantum Systems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0942-8033","authenticated-orcid":false,"given":"David K.","family":"Ferry","sequence":"first","affiliation":[{"name":"School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2181-4284","authenticated-orcid":false,"given":"Xavier","family":"Oriols","sequence":"additional","affiliation":[{"name":"Departament d\u2019Enginyeria Electro\u00f2nica, Universitat Aut\u00f2noma de Barcelona, 08193 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4860-5434","authenticated-orcid":false,"given":"Robert","family":"Eisenberg","sequence":"additional","affiliation":[{"name":"Department of Physiology and Biophysics, Rush University Medical Center, Chicago, IL 60607, USA"},{"name":"Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60607, USA"},{"name":"Department of Biomedical Engineering, University of Illinois Chicago, Chicago, IL 60607, USA"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"key":"ref_1","first-page":"155","article-title":"On Faraday\u2019s Lines of Force","volume":"10","author":"Maxwell","year":"1855","journal-title":"Trans. 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