# Quantum signatures of chaos in the dynamics of bipartite fluctuations

## TL;DR

This paper investigates how bipartite fluctuations in a quantum kicked Bose-Hubbard model reveal signatures of chaos, distinguishing regular and chaotic dynamics through their quasiperiodic or irregular evolution.

## Contribution

It introduces bipartite fluctuations as a quantum chaos indicator and links their behavior to classical chaos measures like Lyapunov exponents.

## Key findings

- Bipartite fluctuations are quasiperiodic in regular regions.
- Bipartite fluctuations become irregular in chaotic regions.
- Long-term bipartite fluctuations reflect the nature of underlying dynamics.

## Abstract

We study the quantum signatures of chaos by using the concept of bipartite fluctuations in the kicked two-site Bose-Hubbard model, which can be mapped to the well-studied kicked top model. We find that the evolution of bipartite fluctuations is quasiperiodic when the initial state centered in the regular regions, while it becomes irregular as the initial state centered in the chaotic regions. As a result, the quantum signatures of chaos can be identified in both the dynamical bipartite fluctuations and the long time averaged bipartite fluctuations. We further demonstrate that the regular versus irregular behaviors of bipartite fluctuations are induced by the different localization properties of the evolved state in regular and chaotic regimes. Finally, we discuss how to identify the signature of global chaos via bipartite fluctuations; and point out the relationship between bipartite fluctuations and the classical Lyapunov exponent.