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Duality relations for asymmetric exclusion processes

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Abstract

We derive duality relations for a class ofU q [SU(2)]-symmetric stochastic processes, including among others the asymmetric exclusion process in one dimension. Like the known duality relations for symmetric hopping processes, these relations express certainm-point correlation functions inN-particle systems (N≥m) in terms of sums of correlation functions of the same system but with onlym particles. For the totally asymmetric case we obtain exact expressions for some boundary density correlation functions. The dynamical exponent for these correlators isz=2, which is different from the dynamical exponent for bulk density correlations, which is known to bez=3/2.

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Schütz, G.M. Duality relations for asymmetric exclusion processes. J Stat Phys 86, 1265–1287 (1997). https://doi.org/10.1007/BF02183623

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