Feynman–Chernoff iterations and their applications in quantum dynamics

The notion of Chernoff equivalence for operator-valued functions is generalized to the solutions of quantum evolution equations with respect to the density matrix. A semigroup is constructed that is Chernoff equivalent to the operator function arising as the mean value of random semigroups. As applied to the problems of quantum optics, an operator is constructed that is Chernoff equivalent to a translation operator generating coherent states.