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

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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 Pulé inequalities [2] allows uniform estimates for the Dyson series expansion for both the unitary operator and the Heisenberg evolution to be obtained.

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  1. Department of Computing & Mathematics, Nottingham-Trent University, Burton Street, Nottingham, NG1 4BU, United Kingdom

    John Gough

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  1. John Gough
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Correspondence to John Gough.

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Communicated by A. Connes

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Gough, J. Quantum Flows as Markovian Limit of Emission, Absorption and Scattering Interactions. Commun. Math. Phys. 254, 489–512 (2005). https://doi.org/10.1007/s00220-004-1163-y

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  • DOI: https://doi.org/10.1007/s00220-004-1163-y

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