Off-Equilibrium Dynamics of 1+1 dimensional Directed Polymer in Random Media

The relaxational dynamics of 1+1 dimensional directed polymer in random potential is studied by Monte Carlo simulation. A series of temperature quench experiments is performed changing waiting times. Clear crossover from quasi-equilibrium behavior to off-equilibrium behavior appears in the dynamical overlap function whose scaling properties are very similar to those found in the 3 dimensional spin-glass model. In the off-equilibrium part, the fluctuation dissipation theorem of the 1st kind which relates the response function to the tilt field with the conjugate correlation function, is found broken. These aging effects are brought about by the very slow growth of quasi-equilibrium domain driven by successive loop-excitations of various sizes, which form complex network structures.