{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T07:54:22Z","timestamp":1764402862109,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,7,9]],"date-time":"2018-07-09T00:00:00Z","timestamp":1531094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004007","name":"Instituto Nazionale di Fisica Nucleare","doi-asserted-by":"publisher","award":["VIP"],"award-info":[{"award-number":["VIP"]}],"id":[{"id":"10.13039\/501100004007","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002428","name":"Austrian Science Fund","doi-asserted-by":"publisher","award":["P25529-N20"],"award-info":[{"award-number":["P25529-N20"]}],"id":[{"id":"10.13039\/501100002428","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000921","name":"European Cooperation in Science and Technology","doi-asserted-by":"publisher","award":["CA15220"],"award-info":[{"award-number":["CA15220"]}],"id":[{"id":"10.13039\/501100000921","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014144","name":"Centro Fermi","doi-asserted-by":"publisher","award":["Problemi aperti nella meccanica quantistica"],"award-info":[{"award-number":["Problemi aperti nella meccanica quantistica"]}],"id":[{"id":"10.13039\/501100014144","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000925","name":"John Templeton Foundation","doi-asserted-by":"publisher","award":["ID 58158"],"award-info":[{"award-number":["ID 58158"]}],"id":[{"id":"10.13039\/100000925","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The VIolation of Pauli (VIP) experiment (and its upgraded version, VIP-2) uses the Ramberg and Snow (RS) method (Phys. Lett. B 1990, 238, 438) to search for violations of the Pauli exclusion principle in the Gran Sasso underground laboratory. The RS method consists of feeding a copper conductor with a high direct current, so that the large number of newly-injected conduction electrons can interact with the copper atoms and possibly cascade electromagnetically to an already occupied atomic ground state if their wavefunction has the wrong symmetry with respect to the atomic electrons, emitting characteristic X-rays as they do so. In their original data analysis, RS considered a very simple path for each electron, which is sure to return a bound, albeit a very weak one, because it ignores the meandering random walks of the electrons as they move from the entrance to the exit of the copper sample. These complex walks bring the electrons close to many more atoms than in the RS calculation. Here, we consider the full description of these walks and show that this leads to a nontrivial and nonlinear X-ray emission rate. Finally, we obtain an improved bound, which sets much tighter constraints on the violation of the Pauli exclusion principle for electrons.<\/jats:p>","DOI":"10.3390\/e20070515","type":"journal-article","created":{"date-parts":[[2018,7,9]],"date-time":"2018-07-09T11:18:53Z","timestamp":1531135133000},"page":"515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["On the Importance of Electron Diffusion in a Bulk-Matter Test of the Pauli Exclusion Principle"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7348-9765","authenticated-orcid":false,"given":"Edoardo","family":"Milotti","sequence":"first","affiliation":[{"name":"Dipartimento di Fisica, Universit\u00e0 di Trieste and INFN-Sezione di Trieste, 34127 Trieste, Italy"}]},{"given":"Sergio","family":"Bartalucci","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Sergio","family":"Bertolucci","sequence":"additional","affiliation":[{"name":"Dipartimento di Fisica e Astronomia, Universit\u00e0 di Bologna, 40126 Bologna, Italy"}]},{"given":"Massimiliano","family":"Bazzi","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Mario","family":"Bragadireanu","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei, 077125 M\u00e2gurele, Romania"}]},{"given":"Michael","family":"Cargnelli","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, 1090 Vienna, Austria"}]},{"given":"Alberto","family":"Clozza","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Catalina","family":"Curceanu","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei, 077125 M\u00e2gurele, Romania"},{"name":"Centro Fermi, Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, 00184 Roma, Italy"}]},{"given":"Luca","family":"De Paolis","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Jean-Pierre","family":"Egger","sequence":"additional","affiliation":[{"name":"Institut de Physique, Universit\u00e9 de Neuch\u00e2tel, 2000 Neuch\u00e2tel, Switzerland"}]},{"given":"Carlo","family":"Guaraldo","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Mihail","family":"Iliescu","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5390-4343","authenticated-orcid":false,"given":"Matthias","family":"Laubenstein","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali del Gran Sasso, Istituto Nazionale di Fisica Nucleare, 67100 Assergi, Italy"}]},{"given":"Johann","family":"Marton","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, 1090 Vienna, Austria"}]},{"given":"Marco","family":"Miliucci","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Andreas","family":"Pichler","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, 1090 Vienna, Austria"}]},{"given":"Dorel","family":"Pietreanu","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei, 077125 M\u00e2gurele, Romania"}]},{"given":"Kristian","family":"Piscicchia","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"Centro Fermi, Museo Storico della Fisica e Centro Studi e Ricerche \u201cEnrico Fermi\u201d, 00184 Roma, Italy"}]},{"given":"Alessandro","family":"Scordo","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"}]},{"given":"Hexi","family":"Shi","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Hochenergiephysik der \u00d6sterreichischen Akademie der Wissenschaften, 1050 Vienna, Austria"}]},{"given":"Diana Laura","family":"Sirghi","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"IFIN-HH, Institutul National pentru Fizica si Inginerie Nucleara Horia Hulubei, 077125 M\u00e2gurele, Romania"}]},{"given":"Florin","family":"Sirghi","sequence":"additional","affiliation":[{"name":"Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, 00044 Frascati, Italy"},{"name":"IFIN-HH, 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