Nonlocal Non-Markovian Effects in Dephasing Environments

We study the nonlocal non-Markovian effects through local interactions between two subsystems and the corresponding two environments. It has been found that the initial correlations between two environments can turn a Markovian to a non-Markovian regime with the extra control on the local interaction time. We further research the nonlocal non-Markovian effects from two situations: without extra control, the nonlocal non-Markovian effects only appear under the condition that two local dynamics are non-Markovian-non-Markovian(both of two local dynamics are non-Markovian), or Markovian-non-Markovian, never appear under the condition of Markovian-Markovian; with extra control, the nonlocal non-Markovian effects can occur under the condition of Markovian-Markovian. It shows that the correlations between two environments has an upper bound: only making a flow of information from the environment back to the global system begin finitely earlier than that back to any one of two local systems, not infinitely. Then, due to observing that the classical correlations between two environments have the same function as the quantum correlations, we advise two special ways to distribute classical correlations between two environments without initial correlations. Finally, from numerical solutions in the spin star configuration we obtain that the self-correlation(internal correlation) of each environment promotes the nonlocal non-Markovian effects.