# Landau-Zener transition in quadratic-nonlinear two-state systems

## TL;DR

This paper develops a comprehensive theory for Landau-Zener transitions in quadratic nonlinear two-state systems, deriving a simple yet accurate formula for transition probabilities across all parameter ranges.

## Contribution

It introduces a new analytic formula for transition probabilities in nonlinear two-state systems, enhancing understanding of Landau-Zener dynamics in such contexts.

## Key findings

- Derived a compact analytic formula for transition probability
- The formula is highly accurate across all parameter ranges
- Provides insights into nonlinear Landau-Zener transitions

## Abstract

A comprehensive theory of the Landau-Zener transition in quadratic nonlinear two-state systems is developed. A compact analytic formula involving elementary functions only is derived for the final transition probability. The formula provides a highly accurate approximation for the whole rage of the variation of the Landau-Zener parameter.

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Source: https://tomesphere.com/paper/0912.4763