  We perform a numerical study of ghost condensation -- in the so-called
Overhauser channel -- for SU(2) lattice gauge theory in minimal Landau gauge.
The off-diagonal components of the momentum-space ghost propagator G^{cd}(p)
are evaluated for lattice volumes V = 8^4, 12^4, 16^4, 20^4, 24^4 and for three
values of the lattice coupling: \beta = 2.2, 2.3, 2.4. Our data show that the
quantity \phi^b(p) = \epsilon^{bcd} G^{cd}(p) / 2 is zero within error bars,
being characterized by very large statistical fluctuations. On the contrary,
|\phi^b(p)| has relatively small error bars and behaves at small momenta as
L^{-2} p^{-z}, where L is the lattice side in physical units and z \approx 4.
We argue that the large fluctuations for \phi^b(p) come from spontaneous
breaking of a global symmetry and are associated with ghost condensation. It
may thus be necessary (in numerical simulations at finite volume) to consider
|\phi^b(p)| instead of \phi^b(p), to avoid a null average due to tunneling
between different broken vacua. Also, we show that \phi^b(p) is proportional to
the Fourier-transformed gluon field components {\widetilde A}_{\mu}^b(q). This
explains the L^{-2} dependence of |\phi^b(p)|, as induced by the behavior of |
{\widetilde A}_{\mu}^b(q) |. We fit our data for |\phi^b(p)| to the theoretical
prediction (r / L^2 + v) / (p^4 + v^2), obtaining for the ghost condensate v an
upper bound of about 0.058 GeV^2. In order to check if v is nonzero in the
continuum limit, one probably needs numerical simulations at much larger
physical volumes than the ones we consider. As a by-product of our analysis, we
perform a careful study of the color structure of the inverse Faddeev-Popov
matrix in momentum space.
