A diagrammatic theory is developed for the classical description of nonlinear response functions of weakly anharmonic oscillators. The expansion employs a harmonic basis of contributions to the phase-space probability density that exactly describes the response properties of harmonic systems and is directly analogous to the expansion of the quantum-mechanical density matrix into coherence and population terms. Introducing weak anharmonicity into the system potential leads to nonvanishing response functions that have a simple diagrammatic description in terms of transitions between these classical coherences and populations. The theory is used to explicitly calculate two-dimensional (2D) infrared (IR) spectra both with and without static disorder. Significantly, it is demonstrated that, to first order in the anharmonicity, the classical and quantum third-order response functions are identical, supporting the utility of classical methods for describing 2D IR spectra in weakly anharmonic systems.

• Received 31 May 2021
• Revised 19 August 2021
• Accepted 19 August 2021

DOI:https://doi.org/10.1103/PhysRevA.104.033519