Relaxation process of quantum system: Stochastic Liouville equation and initial correlation

Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.