  We analyze dynamics of the infinite-dimensional Bose-Hubbard model with
spatially inhomogeneous dissipation in the hardcore boson limit by solving the
Lindblad master equation with use of the Gutzwiller variational method. We
consider dissipation processes that correspond to inelastic light scattering in
the case of Bose gases in optical lattices. We assume that the dissipation is
applied to a half of lattice sites in a spatially alternating manner. We focus
on steady states at which the system arrives after long-time evolution. We find
that when the average particle density is varied, the steady state exhibits a
transition between a state in which the sites without dissipation are vacuum
and that containing a finite number of particles at those sites. We associate
the transition with the tendency of the sites with dissipation towards a local
state at infinite temperature.
