Multitime response functions and nonlinear spectra for model quantum dissipative systems

Using iterative evaluation of the real-time path integral expression, we calculate four-time correlation functions for one-dimensional systems coupled to model dissipative environments. We use these correlation functions to calculate response functions relevant to third order infrared or seventh order Raman experiments for harmonic, Morse, and quadratic-quartic potentials interacting with harmonic and two-level-system dissipative baths. Our calculations reveal the role of potential features (anharmonicity and eigenvalue spectrum), both on short and long time scales, on the response function. Further, thermal excitation causes dramatic changes in the appearance of the response function, introducing symmetry with respect to the main diagonal. Finally, coupling to harmonic dissipative baths leads to decay of the response function (primarily along the $τ3$ direction) and a broadening of the peaks in its Fourier transform. At high temperatures two-level-system baths are less efficient in destroying coherence than harmonic baths of similar parameters.