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.