Multiple Superadiabatic Transitions and Landau-Zener Formulas

TL;DR

This paper develops a comprehensive theory for nonadiabatic quantum systems with multiple avoided crossings, accurately predicting wavepacket transmission and interference effects, and recovering classical formulas like Landau-Zener.

Contribution

It introduces a general framework that captures multiple transitions and interference effects, extending existing models and algorithms for nonadiabatic dynamics.

Findings

Accurately predicts wavepacket transmission through multiple avoided crossings.

Recovers Landau-Zener formula and surface-hopping algorithms under approximations.

Shows excellent agreement with full quantum dynamics simulations.

Abstract

We consider nonadiabatic systems in which the classical Born-Oppenheimer approximation breaks down. We present a general theory that accurately captures the full transmitted wavepacket after multiple transitions through either a single or distinct avoided crossings, including phase information and associated interference effects. Under suitable approximations, we recover both the celebrated Landau-Zener formula and standard surface-hopping algorithms. Our algorithm shows excellent agreement with the full quantum dynamics for a range of avoided crossing systems, and can also be applied to single full crossings with similar accuracy.