Probabilistic approach to quantum separation effect for Feynman-Kac semigroup

TL;DR

This paper investigates the conditions under which quantum potentials create impenetrable barriers, leading to the separation of Schrödinger evolution, by analyzing the critical potential magnitude and providing quantitative estimates.

Contribution

It introduces a probabilistic approach to determine the critical potential magnitude for quantum separation and offers quantitative estimates for the separating effect.

Findings

Identifies the critical potential magnitude for quantum separation.

Provides quantitative estimates for the separation effect.

Analyzes the influence of cut-off potentials on tunnelling.

Abstract

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