The effect of boundaries and impurity on a system with non-local hop dynamics

We study a one-dimensional lattice model of particles which interact with each other via hard-core
repulsion, and which can make long hops in addition to the usual nearest neighbour hopping dynamics.
The parameter p gives the probability for long hops and the p   =  0 limit leads to the well studied
totally asymmetric simple exclusion process (TASEP). The first part of this study describes the
combined effect of open boundaries and long hops on the steady state of the system. Apart from the
usual low density (LD), high density (HD) and maximum current (MC) phases, the introduction of a
finite p leads to a new possibility-an empty road (ER) phase with particles clearing out faster than
they enter. The variation in the phase diagram with p is interesting, with the LD and MC phases
vanishing at large values of p while the ER and HD phases divide the parameter space into 1/2. In
the second part of this study, we look at the combined effect of long h...

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