{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:29:59Z","timestamp":1760236199117,"version":"build-2065373602"},"reference-count":59,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,10,31]],"date-time":"2021-10-31T00:00:00Z","timestamp":1635638400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as N for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods.<\/jats:p>","DOI":"10.3390\/e23111441","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T22:21:08Z","timestamp":1635805268000},"page":"1441","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Dirac Spatial Search with Electric Fields"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7785-8246","authenticated-orcid":false,"given":"Julien","family":"Zylberman","sequence":"first","affiliation":[{"name":"Sorbonne Universit\u00e9, Observatoire de Paris, Universit\u00e9 PSL, CNRS, LERMA, F-75005 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabrice","family":"Debbasch","sequence":"additional","affiliation":[{"name":"Sorbonne Universit\u00e9, Observatoire de Paris, Universit\u00e9 PSL, CNRS, LERMA, F-75005 Paris, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,31]]},"reference":[{"key":"ref_1","unstructured":"Feynman, R.P., and Hibbs, A.R. 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