
Teitel Group Theoretical Statistical and Condensed Matter Physics
Lattice Gas Models for NonEquilibrium Steady States: Application to a Driven Two Dimensional Vortex LatticeWhen a time independent force, with non zero spatial average, is applied to a system of interacting particles, a time independent nonequilibrium state with a finite current will in general result. While the theory of phase transitions between equilibrium states is well developed, the phase transitions between such driven nonequilibrium steady states are less well understood. Numerical studies of such problems often involve the simulation of continuous time stochastic equations of motion for particles moving in a spatial continuum ("molecular dynamics"). In contrast, in the theory of equilibrium transitions, significant progress was achieved by the introduction of lattice models, in which degrees of freedom are restricted to a discrete lattice of spatial sites. In addition to the analytical simplifications introducted, the great reduction of phase space in such lattice models means that numerical simulations can often be more efficient and accurate. We are seeking to develop similar lattice models for nonequilibrium states, in which particles will be restricted to discrete hops between spatially discrete lattice sites.

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