Abstract
A harmonic system coupled to a heat bath comprised of harmonic oscillators through a nonbilinear system-bath interaction ${q}^{2}{q}_{j}$ is considered, where $q$ and ${q}_{j}$ are the system and bath coordinates, respectively. The two-time correlation functions for the model are analytically obtained through a diagrammatic expansion. Numerical calculations of the analytical results are presented for the spontaneous (frequency-domain) Raman spectroscopy. Comparison with numerical results from the conventional linear-coupling model (the Brownian oscillator model) are made, which indicates experimentally distinguishable temperature dependences.
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