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Stochastic dilation of minimal quantum dynamical semigroup. (English) Zbl 0766.60119
Summary: A necessary and sufficient condition is formulated for minimal quantum dynamical semigroups to be conservative. The paper also provides a Markovian dilation of the minimal semigroups, as a contractive solution of an associated quantum stochastic differential equation in Boson-Fock space, which is isometric if and only if the minimal semigroup is conservative. By using the reflection principle of Brownian motion a necessary and sufficient condition for the contractive solution to be co- isometric is also obtained.

MSC:
60K40 Other physical applications of random processes
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
81S99 General quantum mechanics and problems of quantization
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