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dc.contributor.authorGondran, Michel
dc.contributor.authorLepaul, Sébastien
dc.date.accessioned2013-09-05T11:00:27Z
dc.date.available2013-09-05T11:00:27Z
dc.date.issued2012
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/11621
dc.language.isoenen
dc.subjectindiscernabilityen
dc.subjectGibbs paradoxen
dc.subjectmean fielden
dc.subjectmean field gameen
dc.subjectHamilton-Jacobi equationsen
dc.subject.ddc520en
dc.titleIndiscernability and Mean Field, a Base of Quantum Interactionen
dc.typeCommunication / Conférence
dc.description.abstractenWe study the convergence of the Schrödinger equation, when the Planck constant tends to 0. Our analysis leads us to introduce non-discerned particles in classical mechanics and discerned particles in quantum mechanics. These non-discerned particles in classical mechanics correspond to an action and a density which verify the statistical Hamilton-Jacobi equations. The indiscernability of classical particles provides a very simple and natural explanation to the Gibbs paradox. We then consider the case of a large number of identical non-discerned interacting particles modeled by a mean field. In classical mechanics these particles satisfy the mean field Hamilton-Jacobi equations. We show how the analysis of non-discerned particles in classical mechanics can be fruitfully applied to some other fields. In economics, we show that the theory of mean field games, where non-discerned agents are considered interacting with one another, is the analogue of mean field Hamilton-Jacobi equations.en
dc.identifier.citationpages218-226en
dc.relation.ispartofseriestitleLecture Notes in Computer Scienceen
dc.relation.ispartofseriesnumber7620en
dc.relation.ispartoftitleQuantum Interaction 6th International Symposium, QI 2012, Paris, June 27-29, 2012, Revised Selected Papersen
dc.relation.ispartofeditorBusemeyer, Jerome R.
dc.relation.ispartofeditorDubois, François
dc.relation.ispartofeditorLambert-Mogiliansky, Ariane
dc.relation.ispartofeditorMelucci, Massimo
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate2012
dc.relation.ispartofpages239en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-3-642-35659-9en
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.ispartofisbn978-3-642-35658-2en
dc.relation.conftitle6th International Symposium on Quantum Interaction, QI 2012en
dc.relation.confdate2012-06
dc.relation.confcityParisen
dc.relation.confcountryFranceen
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1007/978-3-642-35659-9_20en


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