dc.contributor.author Forrester, PJ dc.contributor.author Frankel, NE dc.contributor.author Garoni, TM dc.contributor.author Witte, NS dc.date.available 2014-05-21T19:28:01Z dc.date.issued 2003-01-01 dc.identifier http://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.citation Forrester, 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.issn 0010-3616 dc.identifier.uri http://hdl.handle.net/11343/26326 dc.description C1 - Journal Articles Refereed dc.description.abstract The 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.format application/pdf dc.language English dc.publisher SPRINGER dc.subject Differential dc.subject Difference and Integral Equations; Condensed Matter Physics - Other ; Mathematical Sciences; Physical Sciences dc.title Painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons dc.type Journal Article dc.identifier.doi 10.1007/s00220-003-0851-3 melbourne.peerreview Peer Reviewed melbourne.affiliation The University of Melbourne melbourne.affiliation.department Mathematics And Statistics melbourne.source.title COMMUNICATIONS IN MATHEMATICAL PHYSICS melbourne.source.volume 238 melbourne.source.issue 1-2 melbourne.source.pages 257-285 dc.research.coderfcd 230107 dc.research.coderfcd 240204 dc.research.codeseo1998 780101 dc.research.codeseo1998 780102 melbourne.publicationid 19052 melbourne.elementsid 257547 melbourne.contributor.author Forrester, Peter melbourne.contributor.author Frankel, Norman melbourne.contributor.author Garoni, Timothy melbourne.contributor.author WITTE, NICHOLAS melbourne.internal.ingestnote Abstract bulk upload (2017-07-20) dc.identifier.eissn 1432-0916 melbourne.accessrights This item is currently not available from this repository
﻿

Files in this item

FilesSizeFormatView

There are no files associated with this item.