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1 Journal of Applied Analysis

1 1998

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Flows of quantum noise

Hudson R. L., Lindsay J. M., Parthasarathy K. R.

Journal of Applied Analysis

1998

Vol. 4, nr 2

143-160

The dynamics of classical and quantum systems in the presence of noise is usually described in the language of stochastic differential equations. When the system observables comprise a C*-algebra, stochastic evolutions are obtained by solving such equations driven by creation, preservation and annihilation processes on Fock space, with linear maps on the algebra as coefficients.*-Homomorphic evolutions are obtained precisely when the collection of maps has a certain structure; this structure admits a cohomological description. Here we consider equations governing the joint evolution of the system and noise (from input to output) by supposing that the characteristics of the (input) noise processes are given by a group representation. The structure required for *-homomorphic evolution is determined.