Feynman, Wigner, and Hamiltonian Structures Describing the Dynamics of Open Quantum Systems

Dmitry Mozyrsky

John Edward Gough, Tudor Stefan Ratiu, Oleg Georgievich Smolyanov

This paper discusses several methods for describing the dynamics of open quantum systems, where the environment of the open system is infinite-dimensional. These are purifications, phase space forms, master equation and liouville equation forms. The main contribution is in using Feynman-Kac formalisms to describe the infinite-demsional components.

Antonio Camurati, Felipe Sobrero, Bruno Suassuna +1 more

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.

M. O. Burkatskii

A Feynman formula for the solving semigroup describing the evolution of the Wigner function (defined on the phase space of a finite-dimensional Hamiltonian system) is obtained. For an information concerning Feynman formulas, see V. A. Dubravina, Feynman formulas for solutions of evolution equations on ramified surfaces, Russ. J. Math. Phys. 21 (2), 285–288 (2014).

Thomas Unnerstall

Ángel S. Sanz, Salvador Miret-Artés