Sudden death and rebirth of Entanglement for Different Dimensional Systems driven by a Classical Random External Field

The entangled behavior of different dimensional systems driven by classical external random field is investigated. The amount of the survival entanglement between the components of each system is quantified. There are different behaviors of entanglement that come into view decay, sudden death, sudden birth and long-lived entanglement. The maximum entangled states which can be generated from any of theses suggested systems are much fragile than the partially entangled ones. The systems of larger dimensions are more robust than those of smaller dimensions systems, where the entanglement decay smoothly, gradually and may vanish for a very short time. For the class of $2times 3$ dimensional system, the one parameter family is found to be more robust than the two parameters family. Although the entanglement of driven $ 2 times 3$ dimensional system is very sensitive to the classical external random field, one can use them to generate a long-lived entanglement.