Some Quantum Dynamical Semi-groups with Quantum Stochastic Dilation

We consider the GNS Hilbert space $\mathcal{H}$ of a uniformly hyper-finite $C^*$- algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic co-cycle, implemented by the Hudson-Parthasarathy flow, is conservative and gives the minimal semi-group associated with the formal Lindbladian. We also associate conservative minimal semi-groups to another class of Lindbladian by solving the corresponding Evan-Hudson equation

Characterization of unitary processes with independent increments

In this paper, we study unitary Gaussian processes with independent increments with which the unitary equivalence to a Hudson-Parthasarathy evolution system is proved. This gives a generalization of results in [11] and [12] in the absence of the stationarity condition

Characterization of unitary processes with independent increments

In this paper, we study unitary Gaussian processes with independent increments with which the unitary equivalence to a Hudson-Parthasarathy evolution system is proved. This gives a generalization of results in [11] and [12] in the absence of the stationarity condition