# Multistate Landau-Zener models with all levels crossing at one point

## TL;DR

This paper explores the properties and integrability of multistate Landau-Zener models where all levels cross at a single point, providing analytical solutions and applications to quantum systems.

## Contribution

It introduces dual models for previously solved MLZ models, analyzes their integrability, and applies the results to Bose condensate conversion and specific quantum models.

## Key findings

- Analytical scattering matrices for dual MLZ models
- Purely algebraic solutions for bowtie and Tavis-Cummings models
- Application to Bose condensate conversion during Feshbach resonance

## Abstract

We discuss common properties and reasons for integrability in the class of multistate Landau-Zener (MLZ) models with all diabatic levels crossing at one point. Exploring the Stokes phenomenon, we show that each previously solved model has a dual one, whose scattering matrix can be also obtained analytically. For applications, we demonstrate how our results can be used to study conversion of molecular into atomic Bose condensates during passage through the Feshbach resonance, and provide purely algebraic solutions of the bowtie and special cases of the driven Tavis-Cummings model (DTCM).