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arXiv · 2102.05029

Schwinger-Keldysh path integral for the quantum harmonic oscillator

Yoni BenTov
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Abstract

I review the generating function for quantum-statistical mechanics, known as the Feynman-Vernon influence functional, the decoherence functional, or the Schwinger-Keldysh path integral. I describe a probability-conserving $i\varepsilon$ prescription from a path-integral implementation of Lindblad evolution. I also explain how to generalize the formalism to accommodate out-of-time-ordered correlators (OTOCs), leading to a Larkin-Ovchinnikov path integral. My goal is to provide step-by-step calculations of path integrals associated to the harmonic oscillator.

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Yoni BenTov. 2021-02-09. Schwinger-Keldysh path integral for the quantum harmonic oscillator. https://arxiv.org/abs/2102.05029

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