Probabilistic approach to the quantum separation effect for the Feynman-Kac semigroup

Adam Sikora, Jacek Zienkiewicz

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    Abstract

    The quantum tunnelling phenomenon allows a particle in Schrödinger mechanics to tunnel through a barrier that it classically could not overcome. Even infinite potentials do not always form impenetrable barriers. We discuss the following question: What is a critical magnitude of the potential which creates an impenetrable barrier and for which the corresponding Schrödinger evolution system separates? In addition we describe some quantitative estimates for the separating effect in terms of cut-off potentials.

    Original languageEnglish
    Pages (from-to)1-24
    Number of pages24
    JournalStudia Mathematica
    Volume257
    Issue number1
    DOIs
    Publication statusPublished - 2021

    Keywords

    • Schrödinger operators
    • Brownian motion
    • Feynman–Kac semigroup
    • quantum tunnelling and separation

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