Dynamics of entanglement among the environment oscillators of a many-body system

In this work, we extend the discussion that began in Ref. 16 [A. L. de Paula, Jr., J. G. G. de Oliveira, Jr., J. G. P. de Faria, D. S. Freitas and M. C. Nemes, Phys. Rev. A 89 (2014) 022303] to deal with the dynamics of the concurrence of a many-body system. In that previous paper, the discussion was focused on the residual entanglement between the partitions of the system. The purpose of the present contribution is to shed some light on the dynamical properties of entanglement among the environment oscillators. We consider a system consisting of a harmonic oscillator linearly coupled to N others and solve the corresponding dynamical problem analytically. We divide the environment into two arbitrary partitions and the entanglement dynamics between any of these partitions is quantified and it shows that in the case when excitations in each partition are equal, the concurrence reaches the value 1 and the two partitions of the environment are maximally entangled. For long times, the excitations of the main oscillator are completely transferred to environment and the environment oscillators are found entangled.