Properties of Geometric Potential in the Invariant Adiabatic Theory

TL;DR

This paper explores the geometric potential in quantum adiabatic theory, revealing its connection to geodesic curvature and its significant impact on the adiabatic approximation in 2D quantum systems.

Contribution

It establishes a link between geometric potential and geodesic curvature, highlighting its influence on adiabatic processes in quantum mechanics.

Findings

Geometric potential relates to geodesic curvature in 2D quantum systems.

Geometric potential can significantly affect the validity of the adiabatic approximation.

The study deepens understanding of geometric effects in quantum adiabatic theory.

Abstract

We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in 2-dimension quantum systems. We also show that the geometric potential may affect adiabatic approximation remarkably.