Entanglement in a Bipartite Gaussian State.
PhD thesis, National University of Ireland Maynooth.
To examine the loss of entanglement in a two-particle Gaussian system, we
couple it to an environment and use the Non-Rotating Wave master equation
to study the system's dynamics. We also present a derivation of this equation.
We consider two di�fferent types of evolution. Under free evolution we �and that entanglement is lost quickly between the particles. When a harmonic
potential is added between the particles, two very different behaviours can
be observed, namely in the over and under-damped cases respectively, where
the strength of the damping is determined by how large the coupling to the
bath is with respect to the frequency of the potential.
In the over-damped case, we �nd that the entanglement vanishes at even
shorter times than it does in the free evolution. In the (very) under-damped
case, we observe that the entanglement does not vanish. Instead it oscillates
towards a stable value
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