Quantum fluctuations and particle dynamics test in harmonic confinement

Abstract

We investigate how a reservoir modifies the quantum Brownian motion of a particle by adopting a canonical quantization of the total system. Starting from a Lagrangian model describing a harmonically bound particle linearly coupled to a continuum of oscillators, we derive exact analytical solutions for the quantum correlations characterizing the system’s dynamics. This approach enables a complete, with no approximations, treatment of the quantum Brownian motion, including the late-time regime and the positivity of the particle’s kinetic energy. The generality of our formalism allows it to be extended to a broad class of coupling functions, offering a robust framework for exploring dissipative quantum dynamics and energy conservation mechanisms in open quantum systems.