Two-level adiabatic transition probability for small avoided crossings generated by tangential intersections

TL;DR

This paper analyzes the asymptotic behavior of transition probabilities in quantum two-level systems with avoided crossings caused by tangential intersections, focusing on regimes where parameters tend to zero and revealing quantum interference effects.

Contribution

It provides new asymptotic expansions and insights into quantum interference in small avoided crossings generated by tangential intersections, extending previous non-adiabatic regime studies.

Findings

Asymptotic expansion of transition probability derived

Quantum interference effects identified in multiple avoided crossings

Coexistence of different vanishing order regimes analyzed

Abstract

In this paper, the asymptotic behaviors of the transition probability for two-level avoided crossings are studied under the limit where two parameters (adiabatic parameter and energy gap parameter) tend to zero. This is a continuation of our previous works where avoided crossings are generated by tangential intersections and obey a non-adiabatic regime. The main results elucidate not only the asymptotic expansion of transition probability but also a quantum interference caused by several avoided crossings and a coexistence of two-parameter regimes arising from different vanishing orders.