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Particle-Number-Projected HFB
In the context of HFB
theory [1], the particle-number-projected (PNP) state
is given by the standard expression
![\begin{displaymath}
\displaystyle
\vert\Psi_N\rangle \equiv {\hat P}_N \vert\P...
...{0}^{2\pi} {\rm d}\phi\,e^{i\phi(\hat{N}-N)}\vert\Phi\rangle ,
\end{displaymath}](img30.png) |
(1) |
where
is the PN operator,
is the gauge angle,
is the projection
operator for
particles, and
is the HFB wave function (generalized product state)
which does not have well-defined
particle number. This expression, after the integral
is discretized, is most often used
in practical calculations. However, it only constitutes a specific
realization of a more general form [35] given by the contour integral,
![\begin{displaymath}
\displaystyle
\vert\Psi_N\rangle \equiv {\hat P}_N \vert\P...
...{1}{2\pi i}\oint_C {\rm d}z\,z^{\hat{N}-N-1}\vert\Phi\rangle ,
\end{displaymath}](img36.png) |
(2) |
where C is an arbitrary closed contour encircling the origin
of the complex plane.
Subsections
Jacek Dobaczewski
2007-08-08