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