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dc.contributor.authorColin, Samuel
dc.date.accessioned2017-05-03T11:43:20Z
dc.date.available2017-05-03T11:43:20Z
dc.date.issued2012
dc.date.modified2013-06-17T02:59:28Z
dc.identifier.issn1471-2946
dc.identifier.doi10.1098/rspa.2011.0549
dc.identifier.urihttp://hdl.handle.net/10072/48642
dc.description.abstractNumerical simulations indicate that the Born rule does not need to be postulated in the de Broglie-Bohm pilot-wave theory, but tends to arise dynamically (relaxation to quantum equilibrium). These simulations were done for a particle in a two-dimensional box whose wave function obeys the non-relativistic Schr椩nger equation and is therefore scalar. The chaotic nature of the de Broglie-Bohm trajectories, thanks to the nodes of the wave function which yield to vortices, is crucial for a fast relaxation to quantum equilibrium. For spinors, we typically do not expect any node. However, in the case of the Dirac equation, the de Broglie-Bohm velocity field has vorticity even in the absence of nodes. This observation raises the question of the origin of relaxation to quantum equilibrium for fermions. In this article, we provide numerical evidence to show that Dirac particles also undergo relaxation, by simulating the evolution of various non-equilibrium distributions for two-dimensional systems (the two-dimensional Dirac oscillator and the Dirac particle in a two-dimensional spherical step potential).
dc.description.peerreviewedYes
dc.description.publicationstatusYes
dc.languageEnglish
dc.language.isoeng
dc.publisherThe Royal Society Publishing
dc.publisher.placeUnited Kingdom
dc.relation.ispartofstudentpublicationN
dc.relation.ispartofpagefrom1116
dc.relation.ispartofpageto1135
dc.relation.ispartofissue2140
dc.relation.ispartofjournalProceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences
dc.relation.ispartofvolume468
dc.rights.retentionY
dc.subject.fieldofresearchQuantum Physics not elsewhere classified
dc.subject.fieldofresearchMathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
dc.subject.fieldofresearchMathematical Sciences
dc.subject.fieldofresearchPhysical Sciences
dc.subject.fieldofresearchEngineering
dc.subject.fieldofresearchcode020699
dc.subject.fieldofresearchcode010503
dc.subject.fieldofresearchcode01
dc.subject.fieldofresearchcode02
dc.subject.fieldofresearchcode09
dc.titleRelaxation to quantum equilibrium for Dirac fermions in the de Broglie–Bohm pilot-wave theory
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyGriffith Sciences, School of Natural Sciences
gro.date.issued2012
gro.hasfulltextNo Full Text
gro.griffith.authorColin, Samuel


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