Quantum stochastic limits of physical noise

John Gough, Nottingham Trent University

The aim of this talk is to show how the unitary adapted stochastic processes introduced by Robin Hudson and K.R. Parthasarathy in 1984 can arise from the limit of realistic physical models. The main feature will be the Markov approximation which leads naturally to a "Dyson" time-ordered exponential. Surprisingly, this is different from the "Holevo" time-ordered exponential. The former arises from Markov approximations to differential equations (and may be considered as the quantum version of the Wong-Zakai approximation theorem), the latter to the time-continuous limit of difference equations. This fact is of relevance to authors in the wider physical community who do not make this distinction, and who also choose to avoid the rigorous theory of quantum stochastic calculus.