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The IMA volumes in mathematics and its applications

Path Integration: Connecting Pure Jump and Wiener Processes

Vassili Nikitich Kolokoltsov

Published Jan 1, 2005• 2 citations
Publisher
DOI
10.1007/978-0-387-29371-4_11

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We establish a direct connection between the Feynman-Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics. By considering a generalized influence functional in the strong decoherence limit, we demonstrate that integrating over the quantum coherence length leads to a derivation of stochastic Langevin dynamics. Specifically, we show that the quantum Feynman measure transforms into the stochastic Wiener measure. Applying this framework to the Wigner function representation, we show that the system follows a stochastic path interpretable via classical probability theory. Finally, we address the inverse problem: constructing an equivalent quantum influence functional from a given classical Langevin equation.