Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem

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    We extend the Ito -to- Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulae from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systemsin much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.
    Original languageEnglish
    Article number113509
    Number of pages19
    JournalJournal of Mathematical Physics
    Issue number11
    Publication statusPublished - 29 Nov 2006


    • calculus
    • stochastic processes
    • Hilbert space
    • noncommutative field theory
    • differential equations


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