Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions

Abstract

We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation, annihilation and gauge processes. A weak matrix limit is established for the convergence of the interaction-picture unitary to a unitary, adapted quantum stochastic process and of the Heisenberg dynamics to the corresponding quantum stochastic flow: the convergence strategy is similar to the quantum functional central limits introduced by Accardi, Frigerio and Lu$^{[ 1]}$. The principal terms in the Dyson series expansions are identified and re-summed after the limit to obtain explicit quantum stochastic differential equations with renormalized coefficients. An extension of the Pul\UNICODE{0xe9} inequalities$^{[ 2]}$ allows uniform estimates for the Dyson series expansion for both the unitary operator and the Heisenberg evolution to be obtained.