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Bulletin of the American Physical Society

Some Novel Applications and Interpretations of the Path Integral Formalism

Jareth Baca, Ajit Hira, J. A. de Freitas Pacheco, Tommy Cathey, M. Forcales

Published Mar 4, 2019• 0 citations
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Abstract We establish a formal connection between the Feynman–Vernon path integral formalism for open quantum systems and the Wiener path integral used in classical stochastic dynamics, further exploring its applications. By considering a generalized influence functional in the strong decoherence limit, we demonstrate that integrating over the quantum coherence length leads to stochastic Langevin dynamics. Specifically, under our model, we show that the quantum Feynman differential transforms into an underdamped multiplicative non-Markovian Langevin dynamics. Applying this framework to the Wigner function representation, we show that the system follows a stochastic path interpretable via classical probability theory, allowing for the investigation of decoherence through classical dynamics. Finally, we address the inverse problem: constructing an equivalent quantum influence functional from a given classical Langevin equation.
This article explores the application of the path integral formalism in describing synchronization phenomena in entangled networks, cavities, and reservoirs. We discuss the concept of using Lagrangian mechanics for systems undergoing synchronization and its connection to least-action principles. By replacing the concept of least action with a least signaling term, we investigate how the path integral representation can be applied to study synchronization dynamics in entangled networks, drawing parallels with coupled oscillators in phase space models such as the Kuramoto model, as well as its relation to algorithms, such as the firefly algorithm for potential use in optimization in networks. This article also illustrates how entanglement signals themselves can interact strongly with ordered systems of harmonic oscillators that reach thresholds of classical synchronization with potential therefore for using entangled signals as weak measurement probes where phase dynamics is of interest.