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.

中文翻译：

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经典相干二维红外光谱的图解方法

为弱非谐振荡器的非线性响应函数的经典描述开发了图解理论。扩展采用对相空间概率密度的贡献的谐波基，它准确地描述了谐波系统的响应特性，并且直接类似于将量子力学密度矩阵扩展为相干项和布居项。将弱非谐性引入系统势会导致非零响应函数在这些经典相干和种群之间的转换方面具有简单的图解描述。该理论用于明确计算有和没有静态无序的二维 (2D) 红外 (IR) 光谱。重要的是，它证明了，对于非谐性的一阶，