, Volume 108, Issue 3, pp 353-361

Dilations of quantum dynamical semigroups with classical Brownian motion

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Abstract

We show that any quantum dynamical semigroup can be written with the help of the solution of a vector-valued classical stochastic differential equation. Moreover this equation leads to a natural construction of a unitary dilation in term of Wiener spaces.

On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk, Poland
Bevoegdverklaard navorser N.F.W.O., Belgium
Communicated by H. Araki