We present an exact analytical solution of the Hu-Paz-Zhang master equation in a precise
Markovian limit for a system of two harmonically coupled harmonic oscillators interacting
with a common thermal bath of harmonic oscillators. The thermal bath is initially
considered to be at arbitrary temperatures and characterized by an Ohmic Lorentz-Drude
spectral density. In the examined system, couplings between the two harmonic oscillators
and the environment ensure a complete decoupling of the center-of-mass and relative
degrees of freedom, resulting in undamped dynamics in the relative coordinate. The
exact time evolution is used to analyze the system's entanglement dynamics, quantified
through logarithmic negativity and quantum mutual information, while ensuring the
positivity of the density operator to confirm the physical validity of the results.
We demonstrate that, under certain parameter regimes and initial conditions, the asymptotic
dynamics can give rise to periodic entanglement-disentanglement behavior. Furthermore,
numerical simulations reveal that for negative values of the direct coupling between
the oscillators, which are sufficiently close to a critical lower bound beyond which
the system becomes unstable, the system can maintain entanglement across a broad temperature
range and for arbitrarily long durations.
