A path-integral approach to quantum acoustics is developed here. In contrast to the commonly utilized particle perspective, this emerging field brings forth a long-neglected yet essential wave paradigm for lattice vibrations. Within the coherent state picture, we formulate a non-Markovian stochastic master equation that captures the exact dynamics of any system with coupling linear in the bath coordinates and nonlinear in the system coordinates. We further demonstrate the capability of the presented master equation by applying the corresponding procedure to the well-known Fröhlich model. In general, we establish a solid foundation for quantum acoustics as a kindred framework to quantum optics, while paving the way for deeper first-principles explorations of nonperturbative system dynamics driven by lattice vibrations.

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• Lattice dynamics
• Path integrals
• Phonons