Path-Integral Approach to Quantum Acoustics

TL;DR

This paper develops a path-integral framework for quantum acoustics, emphasizing wave phenomena in lattice vibrations and deriving a non-Markovian master equation applicable to complex quantum systems.

Contribution

It introduces a wave-based approach to quantum acoustics using path integrals and formulates a non-Markovian master equation within the coherent state picture.

Findings

Formulated a non-Markovian stochastic master equation for quantum acoustics.

Applied the framework to the Fröhlich model demonstrating its effectiveness.

Established a foundation linking quantum acoustics to quantum optics.

Abstract

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 but 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 eminent Fr\"ohlich 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-principle explorations of non-perturbative system dynamics driven by lattice vibrations.