Dynamic of entanglement for two-mode continuous variable in open quantum systems

We study the entanglement evolution for two-mode systems consisting of uncoupled harmonic oscillators in the framework of the theory of open systems. It interacts with a thermal bath as the environment. By using the Peres-Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we describe the evolution of entanglement. Such evolution is function of the temperature, dissipation coefficient, magnetic field and asymmetric parameter. The initial states are the coherent states of a spinless charged particle in an anisotropic harmonic potential and a uniform magnetic field. In the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment by increasing the dissipation coefficient and temperature, the entanglement sudden death occurs sooner. Which is in agreement with recent ones.