Recently a generalized master equation was derived that extends the Lindblad theory to highly non-Markovian quantum processes (H.-P. Breuer, Phys. Rev. A 75, 022103 (2007)). We perform a stochastic unravelling of this master equation by considering n random state vectors that satisfy the corresponding stochastic differential equation for a piecewise deterministic process. As an application we consider a two-state system randomly coupled to an environment consisting of two energy bands with finite number of levels. Our numerical results are compared to results obtained from the time-convolutionless (TCL) projection operator method using correlated projection superoperators and the exact solution of the Schrödinger equation for this system.

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest inter-dimensional degeneracy in N − 1 and N + 1 spacial dimensions. We derive this property by mapping the Schrödinger eigenvalue problem onto an eigenvalue equation in which D appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.

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We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere.

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