# Chaos induced breakdown of Bose-Hubbard modeling

## TL;DR

This paper demonstrates that chaos can cause the breakdown of the Bose-Hubbard model's validity, even under conditions previously thought to be safe, by linking it to classical chaos theory and numerical observations.

## Contribution

It introduces a simple model that explains the chaos-induced failure of the Bose-Hubbard approximation, connecting many-body effects with classical chaos analysis.

## Key findings

- Bose-Hubbard approximation fails due to chaos even when detuned.
- The model reproduces previous numerical breakdown observations.
- Chaos enhancement explains the breakdown in many-body systems.

## Abstract

We show that the Bose-Hubbard approximation fails due to the emergence of chaos, even when excited modes are far detuned and the standard validity condition is satisfied. This is formally identical to the Melnikov-Arnold analysis of the stochastic pump model. Previous numerical observations of Bose-Hubbard breakdown are precisely reproduced by our simple model and can be attributed to many body enhancement of chaos.