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dc.contributor.authorForrester, PJ
dc.contributor.authorFrankel, NE
dc.contributor.authorGaroni, TM
dc.contributor.authorWitte, NS
dc.date.available2014-05-21T19:28:01Z
dc.date.issued2003-01-01
dc.identifierhttp://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000183774800011&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=d4d813f4571fa7d6246bdc0dfeca3a1c
dc.identifier.citationForrester, P. J., Frankel, N. E., Garoni, T. M. & Witte, N. S. (2003). Painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 238 (1-2), pp.257-285. https://doi.org/10.1007/s00220-003-0851-3.
dc.identifier.issn0010-3616
dc.identifier.urihttp://hdl.handle.net/11343/26326
dc.descriptionC1 - Journal Articles Refereed
dc.description.abstractThe recent experimental realisation of a one-dimensional Bose gas of ultra cold alkali atoms has renewed attention on the theoretical properties of the impenetrable Bose gas. Of primary concern is the ground state occupation of effective single particle states in the finite system, and thus the tendency for Bose-Einstein condensation. This requires the computation of the density matrix. For the impenetrable Bose gas on a circle we evaluate the density matrix in terms of a particular Painlev\'e VI transcendent in $\sigma$-form, and furthermore show that the density matrix satisfies a recurrence relation in the number of particles. For the impenetrable Bose gas in a harmonic trap, and with Dirichlet or Neumann boundary conditions, we give a determinant form for the density matrix, a form as an average over the eigenvalues of an ensemble of random matrices, and in special cases an evaluation in terms of a transcendent related to Painlev\'e V and VI. We discuss how our results can be used to compute the ground state occupations.
dc.formatapplication/pdf
dc.languageEnglish
dc.publisherSPRINGER
dc.subjectDifferential
dc.subjectDifference and Integral Equations; Condensed Matter Physics - Other ; Mathematical Sciences; Physical Sciences
dc.titlePainleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons
dc.typeJournal Article
dc.identifier.doi10.1007/s00220-003-0851-3
melbourne.peerreviewPeer Reviewed
melbourne.affiliationThe University of Melbourne
melbourne.affiliation.departmentMathematics And Statistics
melbourne.source.titleCOMMUNICATIONS IN MATHEMATICAL PHYSICS
melbourne.source.volume238
melbourne.source.issue1-2
melbourne.source.pages257-285
dc.research.coderfcd230107
dc.research.coderfcd240204
dc.research.codeseo1998780101
dc.research.codeseo1998780102
melbourne.publicationid19052
melbourne.elementsid257547
melbourne.contributor.authorForrester, Peter
melbourne.contributor.authorFrankel, Norman
melbourne.contributor.authorGaroni, Timothy
melbourne.contributor.authorWITTE, NICHOLAS
melbourne.internal.ingestnoteAbstract bulk upload (2017-07-20)
dc.identifier.eissn1432-0916
melbourne.accessrightsThis item is currently not available from this repository


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