Finite one-dimensional impenetrable Bose systems: Occupation numbers

P. J. Forrester, N. E. Frankel, T. M. Garoni, and N. S. Witte
Phys. Rev. A 67, 043607 – Published 17 April 2003
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Abstract

Bosons in the form of ultracold alkali-metal atoms can be confined to a one-dimensional (1D) domain by the use of harmonic traps. This motivates the study of the ground-state occupations λi of effective single-particle states φi, in the theoretical 1D impenetrable Bose gas. Both the system on a circle and the harmonically trapped system are considered. The λi and φi are the eigenvalues and eigenfunctions, respectively, of the one-body density matrix. We present a detailed numerical and analytic study of this problem. Our main results are the explicit scaled forms of the density matrices, from which it is deduced that for fixed i the occupations λi are asymptotically proportional to N in both the circular and harmonically trapped cases.

  • Received 5 November 2002

DOI:https://doi.org/10.1103/PhysRevA.67.043607

©2003 American Physical Society

Authors & Affiliations

P. J. Forrester1,*, N. E. Frankel2,†, T. M. Garoni2,‡, and N. S. Witte1,2,§

  • 1Department of Mathematics and Statistics, University of Melbourne, Victoria 3010, Australia
  • 2School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia

  • *Email address: P.Forrester@ms.unimelb.edu.au
  • Email address: n.frankel@physics.unimelb.edu.au
  • Email address: t.garoni@physics.unimelb.edu.au
  • §Email address: N.Witte@ms.unimelb.edu.au

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Vol. 67, Iss. 4 — April 2003

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