Derivation of the Burgers equation with finite particle correction from the derivative nonlinear Schr\"{o}dinger equation

We investigate the dynamics of the asymmetric simple exclusion process (ASEP) in the continuous limit. We derive the Burgers equation with finite particle correction from the quantum derivative nonlinear Schr\"{o}dinger equation which is equivalent to the ASEP in the continuous limit. We numerically confirm that the obtained Burgers equation describes the dynamics of the ASEP with few particles better than the conventional one.