A dilation of stable quantum dynamical semigroups

B V Rajarama Bhat, Indian Statistical Institute (Bangalore Centre)

A quantum dynamical semigroup is said to be stable if it decays to zero as the time parameter tends to infinity. Here we exhibit an explicit dilation for uniformly continuous stable quantum dynamical semigroups without using any quantum stochastic differential equation (QSDE). The construction is very similar to a well-known method in the discrete case. Connections with QSDE's and possible generalizations are currently being explored.