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The influence of the environment in the thermal equilibrium properties of abipartite continuous variable quantum system is studied. The problem is treatedwithin a system-plus-reservoir approach. The considered model reproduces theconventional Brownian motion when the two particles are far apart and inducesan effective interaction between them, depending on the choice of the spectralfunction of the bath. The coupling between the system and the environmentguarantees the translational invariance of the system in the absence of anexternal potential. The entanglement between the particles is measured by thelogarithmic negativity, which is shown to monotonically decrease with theincrease of the temperature. A range of finite temperatures is found in whichentanglement is still induced by the reservoir.

Thermal equilibrium of two quantum Brownian particles