Gaussian stochastic linearization for open quantum systems using quadratic approximation of Hamiltonians

Abstract

A wide class of models for open quantum systems [3, 8], that is, quantum-mechanical objects interacting with the environment, is provided by dynamical systems whose state variables are canonically commuting self-adjoint operators on a Hilbert space. In the Heisenberg picture, these system observables evolve in time according to quantum stochastic differential equations (QSDEs) [18]. Such QSDEs, which are dual to quantum master equations for density operators in the Schrodinger picture [3], are driven by a quantum ¨ Wiener process to take into account the coupling between the environment (regarded as a memoryless heat bath of quantum harmonic oscillators) and the internal dynamics which the system would have in isolation from the surroundings. These internal dynamics are completely specified by the system Hamiltonian, which is a self-adjoint operator on the underlying Hilbert space, usually representable as a function of the system observables. Show more