Quantum Stochastic Process as Continuous Flow of Fock Space Operators

Franco Fagnola

V. P. Belavkin

R. L. Hudson

David Applebaum

A quantum stochastic calculus for fermions is developed where the basic integrators are based on Dirac fields and the charge operator. The associated Ito formula has seven non-trivial correction terms. Conditions are found for the solutions of stochastic differential equations to be unitary and it is shown that the corresponding quantum stochastic flow manifests a broken symmetry whereby the particle and antiparticle noises no longer balance each other. An abstract theory of such flows is then developed. By employing the unification between boson and fermion stochastic calculi, we are able to develop the entire theory using boson Fock spaces.

Luigi Accardi, A. Frigerio

On the stochastic limit of quantum chromodynamics, L. Accardi et al flows and imprimitivity systems, L. Accardi and A. Mohari fermion stochastic flows on quantum algebras, D. Applebaum examples of unbounded generators leading to nonconservative minimal semigroups, R.B.V. Bhat and K.B. Sinha on the structure of quantum Markov processes, C. Cecchini diffusion processes in fock space, F. Fagnola on the isomorphism of Poisson space and symmetric fock space, V. Liebscher non-linear master equation and non-crossing cumulants, P. Neu and R. Speicher a general central limit theorem and invariance principle, R. Speicher and W. von Waldenfels.

Anatolij Dvurečenskij, Sylvia Pulmannová