Superparabolic Level Glancing Models for Two-State Quantum Systems

TL;DR

This paper introduces superparabolic level glancing models for two-state quantum systems, extending the parabolic model to describe energy levels that touch but do not cross, with implications for understanding quantum degeneracies.

Contribution

It presents a new class of superparabolic models for level glancing, expanding the theoretical framework for two-state quantum systems beyond existing parabolic models.

Findings

Characterization of superparabolic models' properties

Comparison with nonlinear crossing models

Enhanced understanding of level degeneracy behavior

Abstract

Level crossing models for two-state quantum systems are applicable to a wide variety of physical problems. We address the special case of level glancing, i.e., when energy levels reach a degeneracy at a specific point of time, but never actually cross. The simplest model with such behaviour is the parabolic model, and its generalizations, which we call superparabolic models. We discuss their basic characteristics, complementing the previous work on the related nonlinear crossing models [Phys. Rev. A 59, 4580 (1999)].