Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory

TL;DR

This paper proves the integrability of a general linearly time-dependent two-band crossing model, deriving exact relations and a semiclassical approximation for transition probabilities, revealing a dynamic phase transition and topological distinctions.

Contribution

It establishes the integrability of a broad class of Landau-Zener models and develops a semiclassical theory for transition probabilities, advancing understanding of nonadiabatic dynamics.

Findings

Exact relations for transition probabilities derived from integrability

Semiclassical approximation applicable across parameter regimes

Prediction of a dynamic phase transition and topological class differences

Abstract

We demonstrate that the general model of a linearly time-dependent crossing of two energy bands is integrable. Namely, the Hamiltonian of this model has a quadratically time-dependent commuting operator. We apply this property to four-state Landau-Zener (LZ) models that have previously been used to describe the Landau-St\"uckelberg interferometry experiments with an electron shuttling between two semiconductor quantum dots. The integrability then leads to simple but nontrivial exact relations for the transition probabilities. In addition, the integrability leads to a semiclassical theory that provides analytical approximation for the transition probabilities in these models for all parameter values. The results predict a dynamic phase transition, and show that similarly-looking models belong to different topological classes.