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

Volume 257 / 2021

Adam Sikora, Jacek Zienkiewicz Studia Mathematica 257 (2021), 1-24 MSC: Primary 60J35, 35J10. DOI: 10.4064/sm181016-12-3 Published online: 9 December 2020


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.


  • Adam SikoraDepartment of Mathematics
    Macquarie University
    Sydney, NSW 2109, Australia
  • Jacek ZienkiewiczInstytut Matematyczny
    Uniwersytet Wrocławski
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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