# Slow heating in a quantum coupled kicked rotors system

## TL;DR

This paper investigates the dynamics of a finite quantum system of coupled kicked rotors, revealing subdiffusive energy growth near the transition between localized and chaotic regimes, and introduces an anomalous random matrix model for its properties.

## Contribution

It provides numerical and spectral analysis of the subdiffusive regime in coupled kicked rotors, highlighting anomalous scaling and proposing a new random matrix model.

## Key findings

- Kinetic energy grows subdiffusively near the transition boundary.
- Eigenstate properties indicate breaking of eigenstate thermalization.
- Off-diagonal matrix elements follow a non-Gaussian distribution.

## Abstract

We consider a finite-size periodically driven quantum system of coupled kicked rotors which exhibits two distinct regimes in parameter space: a dynamically-localized one with kinetic-energy saturation in time and a chaotic one with unbounded energy absorption (dynamical delocalization). We provide numerical evidence that the kinetic energy grows subdiffusively in time in a parameter region close to the boundary of the chaotic dynamically-delocalized regime. We map the different regimes of the model via a spectral analysis of the Floquet operator and investigate the properties of the Floquet states in the subdiffusive regime. We observe an anomalous scaling of the average inverse participation ratio (IPR) analogous to the one observed at the critical point of the Anderson transition in a disordered system. We interpret the behavior of the IPR and the behavior of the asymptotic-time energy as a mark of the breaking of the eigenstate thermalization in the subdiffusive regime. Then we study the distribution of the kinetic-energy-operator off-diagonal matrix elements. We find that in presence of energy subdiffusion they are not Gaussian and we propose an anomalous random matrix model to describe them.