TY - JOUR
AU - Forrester, PJ
AU - Frankel, NE
AU - Garoni, TM
AU - Witte, NS
Y2 - 2014/05/21
Y1 - 2003/01/01
SN - 0010-3616
UR - http://hdl.handle.net/11343/26326
AB - 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.
N1 - application/pdf
LA - English
PB - SPRINGER
KW - Differential
KW - Difference and Integral Equations; Condensed Matter Physics - Other ; Mathematical Sciences; Physical Sciences
T1 - Painleve transcendent evaluations of finite system density matrices for 1d impenetrable bosons
DO - 10.1007/s00220-003-0851-3
IS - COMMUNICATIONS IN MATHEMATICAL PHYSICS
VL - 238
IS - 1-2
SP - 257-285
L1 - /bitstream/handle/11343/26326/116101_5162.pdf?sequence=1&isAllowed=n
ER -