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In this paper we study a system of $N$ coupled quantum oscillatorsinteracting with each other directly with varying coupling strengths andindirectly through linear couplings to a scalar massless quantum field as itsenvironment. The influence of the quantum field on the system is calculatedwith the use of the influence functional formalism. We take the direct route ofseeking solutions to the evolutionary operator of the reduced density matrixfor the derivation of the correlation functions. They are then used toconstruct the covariance matrix which we use to perform an analysis of thestructure of quantum entanglement in the open system at a stationary state. Tosee the physical features more explicitly we specialize to a system of threequantum coupled oscillators placed at the vertices of a equilateral triangleand allowed to have disparate pairwise couplings. We analyze the entanglementbetween one oscillator and the other two with equal (symmetric) and unequal(asymmetric) coupling strengths. As an illustration we use the results forthese two different configurations to address two representative issues inmacroscopic quantum phenomena. We also mention possible extensions of our workand applications of our analysis and results to issues in some current areas ofresearch in quantum thermodynamics and mesoscopic quantum systems.

Entanglement Structure of an Open System of $N$ Quantum Oscillators: II. Strong Disparate Couplings N=3