Jensen Inequalities for Tunneling Probabilities in Complex Systems

TL;DR

This paper derives Jensen inequalities for tunneling probabilities in complex systems, providing bounds that help analyze sub-barrier heavy-ion fusion reactions using convexity properties of the tunneling coefficient.

Contribution

It introduces Jensen inequalities based on convexity of the tunneling coefficient to bound tunneling probabilities in multi-degree-of-freedom systems.

Findings

Derived inequalities for tunneling probabilities using Jensen's theorem

Provided insights into sub-barrier heavy-ion fusion reactions

Linked convexity properties to tunneling behavior

Abstract

The Jensen theorem is used to derive inequalities for semi-classical tunneling probabilities for systems involving several degrees of freedom. These Jensen inequalities are used to discuss several aspects of sub-barrier heavy-ion fusion reactions. The inequality hinges on general convexity properties of the tunneling coefficient calculated with the classical action in the classically forbidden region.