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We investigate the dynamics of the asymmetric simple exclusion process (ASEP)on a ring. The ASEP is equivalent to the derivative nonlinear Schr\"{o}dingerequation (DNLS), which is integrable quantum field theory, in the continuouslimit. We derive the Burgers equation with finite particle correction from theDNLS and numerically confirm that the obtained Burgers equation describes thedynamics of the ASEP at small numbers of particles better than the conventionalBurgers equation.

Burgers equation with finite particle correction of the asymmetric  simple exclusion process derived from the derivative nonlinear  Schr\"{o}dinger equation