School of Mathematics and Statistics - Research Publications

Permanent URI for this collection

http://hdl.handle.net/11343/294

Filters

2003 1
1
Reset filters

Settings
Statistics
Citations
Start date: 2001 × End date: 2004 × Author: Forrester, Peter × Subject: Difference and Integral Equations; Condensed Matter Physics - Other ; Mathematical Sciences; Physical Sciences ×

Search Results

Now showing 1 - 1 of 1
  • Item
    Thumbnail Image
    Painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons
    Forrester, PJ ; Frankel, NE ; Garoni, TM ; Witte, NS (SPRINGER, 2003)
    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.