# Chaotic dynamics in a quantum Fermi-Pasta-Ulam problem

## TL;DR

This paper explores how quantum anharmonic atomic chains transition from localized to chaotic behavior, identifying energy thresholds and boundary condition effects through analytical and numerical methods.

## Contribution

It provides a semi-quantitative analysis of resonant interactions and estimates the energy crossover point in quantum Fermi-Pasta-Ulam systems, including boundary condition effects.

## Key findings

- Crossover energy decreases inversely with the number of atoms.
- Chaotic behavior appears at lower energies with free or fixed ends.
- Saturation of energy dependence occurs in the quantum regime.

## Abstract

We investigate the emergence of chaotic dynamics in a quantum Fermi - Pasta - Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed.