Quantum-mechanical tunnelling and the renormalization group

TL;DR

This paper examines how the exact renormalization group can be applied to quantum tunnelling, showing it predicts qualitative behavior well but needs supplementary methods for quantitative accuracy in large barrier scenarios.

Contribution

It demonstrates the effectiveness and limitations of the exact renormalization group in modeling quantum tunnelling phenomena.

Findings

RG predicts correct qualitative behavior for lowest energy states.

Quantitative accuracy is limited to small barriers.

Alternative methods like saddle-point expansions improve accuracy for large barriers.

Abstract

We explore the applicability of the exact renormalization group to the study of tunnelling phenomena. We investigate quantum-mechanical systems whose energy eigenstates are affected significantly by tunnelling through a barrier in the potential. Within the approximation of the derivative expansion, we find that the exact renormalization group predicts the correct qualitative behaviour for the lowest energy eigenvalues. However, quantitative accuracy is achieved only for potentials with small barriers. For large barriers, the use of alternative methods, such as saddle-point expansions, can provide quantitative accuracy.