# Multifractality of the kicked rotor at the critical point of the Anderson transition

## TL;DR

This paper demonstrates how the quantum kicked rotor near the Anderson transition exhibits a sharp peak in wavepacket spreading, revealing the wavefunctions' multifractal nature and enabling measurement of the multifractal dimension $d_2$.

## Contribution

It introduces an experimentally feasible method using the quantum kicked rotor to directly access the multifractal properties at the Anderson transition.

## Key findings

- Observation of a sharp peak in wavepacket spreading near the critical point
- Direct measurement of the multifractal dimension $d_2$ from the peak
- Validation of the quantum kicked rotor as a model for studying Anderson transition physics

## Abstract

We show that quantum wavepackets exhibit a sharp macroscopic peak as they spread in the vicinity of the critical point of the Anderson transition. The peak gives a direct access to the mutifractal properties of the wavefunctions and specifically to the multifractal dimension $d\_2$. Our analysis is based on an experimentally realizable setup, the quantum kicked rotor with quasi-periodic temporal driving, an effectively 3-dimensional disordered system recently exploited to explore the physics of the Anderson transition with cold atoms.