Steady states and phase transitions in heterogeneous asymmetric exclusion processes

Abstract

We study the nonequilibrium steady states in totally asymmetric exclusion processes (TASEP) with open boundary conditions having spatially inhomogeneous hopping rates. Considering smoothly varying hopping rates, we show that the steady states are in general classified by the steady state currents in direct analogy with open TASEPs having uniform hopping rates. We calculate the steady state bulk density profiles, which are now spatially nonuniform. We also obtain the phase diagrams in the plane of the control parameters, which though have phase boundaries that are in general curved lines, have the same topology as their counterparts for conventional open TASEPs, independent of the form of the hopping rate functions. This reveals a type of universality, not encountered in critical phenomena. Surprisingly and in contrast to the phase transitions in an open TASEP with uniform hopping, our studies on the phase transitions in the model reveal that all the three transitions are {\em first order} in nature. { We also demonstrate that this model admits delocalised domain walls (DDWs) on the phase boundaries demarcating the generalised low and high density phases in this model. However, in contrast to the DDWs observed in an open TASEP with uniform hopping, the envelopes of the DDWs in the present model are generally curved lines.}

14 pages, 11 figures

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Cited by in corpus (4)

• Nonequilibrium steady states in coupled asymmetric and symmetric exclusion processes
• Defect versus defect: stationary states of single file marching in periodic landscapes with road blocks
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process
• Symmetry Breaking of Current Response in Disordered Exclusion Processes