Resumo:
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.
