# Classical counterparts of quantum attractors in generic dissipative systems

## TL;DR

This paper demonstrates that for dissipative systems, quantum chaotic attractors have classical counterparts, and provides methods to locate and compare them, revealing deep connections between quantum and classical chaos.

## Contribution

It introduces a general approach to identify classical counterparts of quantum attractors in dissipative systems, linking quantum distributions to classical structures and noise.

## Key findings

- Quantum chaotic attractors have classical analogs.
- Classical structures can be identified via parameter space analysis.
- Quantum chaos can be reproduced by classical dynamics with Gaussian noise.

## Abstract

In the context of dissipative systems, we show that for any quantum chaotic attractor a corre- sponding classical chaotic attractor can always be found. We provide with a general way to locate them, rooted in the structure of the parameter space (which is typically bidimensional, accounting for the forcing strength and dissipation parameters). In the cases where an approximate point like quantum distribution is found, it can be associated to exceptionally large regular structures. Moreover, supposedly anomalous quantum chaotic behaviour can be very well reproduced by the classical dynamics plus Gaussian noise of the size of an effective Planck constant $\hbar_{\rm eff}$. We give support to our conjectures by means of two paradigmatic examples of quantum chaos and transport theory. In particular, a dissipative driven system becomes fundamental in order to extend their validity to generic cases.