Constraints on scattering amplitudes in multistate Landau-Zener theory

TL;DR

This paper introduces hierarchy constraints on scattering amplitudes in multistate Landau-Zener models, which help derive solutions or reduce complexity by exploiting symmetries.

Contribution

It derives hierarchy constraints for multistate Landau-Zener models and shows how symmetries can lead to relations simplifying the solution process.

Findings

Hierarchy constraints on scattering amplitudes

Symmetries transform constraints into relations

Reduces independent elements in transition probability matrices

Abstract

We derive a set of constraints, which we will call hierarchy constraints (HCs), on scattering amplitudes of an arbitrary multistate Landau-Zener model (MLZM). The presence of additional symmetries can transform such constraints into nontrivial relations between elements of the transition probability matrix. This observation can be used to derive complete solutions of some MLZMs or, for models that cannot be solved completely, to reduce the number of independent elements of the transition probability matrix.