Stochastic Processes in Quantum Systems

Abel Klein

Sergio A Albeverio, Giulio Casati, D. Merlini

Gian‐Carlo Rota

Masashi Ban, Sachiko Kitajima, Fumiaki Shibata

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.

German A. Skorobogatov, Sergey Igorevich Svertilov

Both quantum mechanics and stochastic-process theory deal with dynamical systems the behaviors of which can be predicted only probabilistically. It is shown here that the measurable behavior of an elementary quantum system can be modeled as a non-Markovian stochastic process. The conclusion that quantum behavior can generally be modeled as a real stochastic process eliminates some mysterious characteristics of quantum mechanics when viewed in Copenhagen-interpretation terms.

C. Barnett, R. F. Streater, Ivan F. Wilde