Bath-induced stabilization of classical non-linear response in two-dimensional infrared spectroscopy

A characteristic feature of the nonlinear response of integrable classical systems is divergence at long times, a consequence of the continuous spectrum of oscillation frequencies possible in anharmonic classical systems. Although bath-induced dissipation and dephasing can eliminate such instabilities, little is known about the specific conditions on system-bath interactions needed to stabilize classical nonlinear response functions. Here, we address this gap by incorporating system-bath interactions into a diagrammatic expansion for classical nonlinear response recently developed for weakly anharmonic systems. The resulting expression for the weakly anharmonic response function is remarkably simple and exhibits a one-to-one correspondence with the quantum counterpart in the ℏ → 0 limit, offering potential computational advantages in extending the approach to large, multi-oscillator systems. We find that, to lowest order in anharmonicity, the bath-induced stabilization of both linear and nonlinear classical response functions depends sensitively on the nature of spectral density, particularly on the balance between low-frequency and high-frequency components. Application of this classical diagrammatic approach to 2D IR spectroscopy of the amide I band captures the characteristic population-time-dependent dynamics associated with spectral diffusion, suggesting that the approach may prove useful in describing real experimental systems at ambient temperatures.