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The one body density matrix (OBDM) of a homogeneous system described by the
many body wave function
according to (1.18) is equal
to
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(2.139) |
Since in DMC calculation does not sample directly the ground-state probability
distribution , but instead the mixed probability (2.12)
one obtains the mixed one-body density matrix as the output
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(2.140) |
This formula can be rewritten in a way convenient for the Monte Carlo sampling:
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(2.141) |
where we have used the asymptotic formula (2.19) and have taken into
account that in a homogeneous system depends only on the module of the
relative distance between two particles. If the trial wave function is chosen as a
product of pair functions (2.37) then using the notation (2.38)
) and one has
. Then the ratio of the trial wave function
appearing in (2.141) becomes
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(2.142) |
In order to gain better statistics it is convenient to average over all possible
pairs of particles
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(2.143) |
The asymptotic limit of the OBDM gives the condensate density
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(2.144) |
and the condensate fraction is obtained by the calculating the asymptotic ratio
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(2.145) |
Next: One body density matrix
Up: Measured quantities
Previous: Static structure factor
  Contents
G.E. Astrakharchik
15-th of December 2004