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

Adam Sikora; Jacek Zienkiewicz

doi:10.4064/SM181016-12-3

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 language	English
Pages (from-to)	1-24
Number of pages	24
Journal	Studia Mathematica
Volume	257
Issue number	1
DOIs	https://doi.org/10.4064/SM181016-12-3
Publication status	Published - 2021

Keywords

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

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10.4064/SM181016-12-3

Accepted author manuscriptAccepted author manuscript, 374 KB

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abstract = "The quantum tunnelling phenomenon allows a particle in Schr{\"o}dinger 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 Schr{\"o}dinger evolution system separates? In addition we describe some quantitative estimates for the separating effect in terms of cut-off potentials. ",

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AB - 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.

KW - Schrödinger operators

KW - Brownian motion

KW - Feynman–Kac semigroup

KW - quantum tunnelling and separation

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

Abstract

Keywords

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Harmonic analysis of rough oscillations

Heat kernel and Riesz transform on non-compact metric measure spaces

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

Abstract

Keywords

Access to Document

Other files and links

Projects

Harmonic analysis of rough oscillations

Heat kernel and Riesz transform on non-compact metric measure spaces

Cite this