Nonlinear Response Functions in Model Dissipative Anharmonic Systems

We report the results of simulations of third order response functions ($R^{(3)}(\tau _3 ,0,\tau _1 )=\mbox{Tr}\left\{ {\hat {\alpha }(\tau _3 )[\hat {\alpha },[\hat {\alpha },[\hat {\alpha }(\tau _1 ),\rho _0 ]]]} \right\}$ where $\hat {\alpha }$ is the polarizability) for harmonic, Morse, and anharmonic model systems in a linearly dissipative environment. These simulations are carried out via the iterative path integral methodology developed earlier in our group which delivers efficient, numerically exact long time quantum dynamics. We find that even minor anharmonicity in the potential qualitatively changes the response function; rotating the pattern seen by 45$^{o}$ in the $\tau _1 -\tau _3 $ plane. We also observe that modulations in the $\tau _3 $ direction increase in frequency as we go to a more anharmonic potential. As the temperature is increased, these modulations also appear in the $\tau _1 $ direction. It is also found that asymmetry in the potential, at least at temperatures considered here, does not have a significant effect. Finally, in all three systems we notice that decay in the $\tau _3 $ direction is faster than in the $\tau _1 $ direction. The observed sensitivity of the response function to anharmonicities in the potential can be exploited to construct more accurate molecular potentials once the appropriate non-linear spectroscopic experiments have been performed.