Next: Construction of trial wave
Up: Three-dimensional wave functions
Previous: Trial wave function of
  Contents
To describe the lowest-lying gas-like state of the Hamiltonian (4.18), we
use for the one-body Bijl-Jastrow term an ansatz similar to (2.41):
|
|
|
(2.89) |
Here, and determine the Gaussian width of in the
longitudinal and transverse direction, respectively. These variational parameters
and are optimized in the course of the VMC calculation by
minimizing the energy expectation value. The two-body correlation factor
(2.37) is chosen to reproduce closely the scattering behavior of two bosons
at low energies. For the hard-sphere potential (1.48), we take
|
(2.90) |
The constraint for accounts for the boundary condition
imposed by the hard-sphere potential, it is exact even for the many-body system. For
the short-range potential (1.97), we use instead
|
(2.91) |
where and denote the lengths of the semi-axes of an ellipse. For two
particles under highly-elongated confinement, the nodal surface is to a good
approximation ellipticly shaped as will be discussed in Sec. 4.4.1.
Thus, the parameters and are determined by fitting the elliptical surface to
the nodal surface obtained by solving the Schrödinger equation for ,
Eqs. 4.7 and 4.8, by performing a B-spline basis set
calculation. In contrast to , the constraint in Eq. 2.91
parameterizes the many-body nodal surface for only approximately. We expect
that our parameterization leads to an accurate description of quasi-1D Bose gases if
the average distance between particles is much larger than the semi-axes of the
ellipse. The trial wave functions discussed here in the context of our VMC
calculations also enter our FN-DMC calculations.
Next: Construction of trial wave
Up: Three-dimensional wave functions
Previous: Trial wave function of
  Contents
G.E. Astrakharchik
15-th of December 2004