# Chaos and Complexity in Quantum Mechanics

## TL;DR

This paper introduces a new diagnostic for quantum chaos based on the evolution of complexity, which correlates with classical chaos measures and identifies a transition time from regular to chaotic behavior.

## Contribution

It presents a novel complexity-based method to diagnose quantum chaos and detect the transition from regular to chaotic regimes in quantum systems.

## Key findings

- Complexity evolution correlates with Lyapunov exponent and scrambling time.
- A new time scale signals the transition from regular to chaotic behavior.
- Complexity-based diagnostics match traditional chaos indicators.

## Abstract

We propose a new diagnostic for quantum chaos. We show that time evolution of complexity for a particular type of target state can provide equivalent information about the classical Lyapunov exponent and scrambling time as out-of-time-order correlators. Moreover, for systems that can be switched from a regular to unstable (chaotic) regime by a tuning of the coupling constant of the interaction Hamiltonian, we find that the complexity defines a new time scale. We interpret this time scale as recording when the system makes the transition from regular to chaotic behaviour.