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.

30 pages, several in-built figures (Includes limit theorems for unitary and Heisenberg flow. Diagrams have been added to elucidate the Dyson series expansions and estimation procedures. There is a new section on resumming the Dyson series. The proof of the convergence of the Heisenberg dynamics has been revised

References in corpus (1)

• Asymptotic Stochastic Transformations for Nonlinear Quantum Dynamical Systems

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