  A disordered version of the one dimensional asymmetric exclusion model where
the particle hopping rates are quenched random variables is studied. The steady
state is solved exactly by use of a matrix product. It is shown how the
phenomenon of Bose condensation whereby a finite fraction of the empty sites
are condensed in front of the slowest particle may occur. Above a critical
density of particles a phase transition occurs out of the low density phase
(Bose condensate) to a high density phase. An exponent describing the decrease
of the steady state velocity as the density of particles goes above the
critical value is calculated analytically and shown to depend on the
distribution of hopping rates. The relation to traffic flow models is
discussed.

Condensed Matter