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New Journal of Physics Volume 16 January 2014.
Bojan Žunkovič
Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile.
Abstract
We study the Lindblad master equation in the space of operators and provide simple criteria for closeness of the hierarchy of equations for correlations. We separately consider the time evolution of closed and open systems and show that open systems satisfying the closeness conditions are not necessarily of Gaussian type. In addition, we show that dissipation can induce the closeness of the hierarchy of correlations in interacting quantum systems. As an example we study an interacting optomechanical model, the Fermi–Hubbard model, and the Rabi model, all coupled to a fine-tuned Markovian environment and obtain exact analytic expressions for the time evolution of two-point correlations.
