Coherent forward scattering as a robust probe of multifractality in critical disordered media

TL;DR

This paper demonstrates that coherent forward scattering (CFS) can serve as a universal and robust experimental probe of quantum multifractality in critical disordered systems, with predictions verified across multiple models.

Contribution

It provides a theoretical framework linking CFS dynamics to multifractal dimensions and verifies universality through numerical simulations in three key models.

Findings

CFS peak dynamics are governed by multifractal dimensions D_1 and D_2.

Universal predictions for CFS are confirmed in PRBM, RS, and 3DKR models.

Analytical results match perturbation theory in the strong multifractal regime.

Abstract

We study coherent forward scattering (CFS) in critical disordered systems, whose eigenstates are multifractals. We give general and simple arguments that make it possible to fully characterize the dynamics of the shape and height of the CFS peak. We show that the dynamics is governed by multifractal dimensions $D_1$ and $D_2$, which suggests that CFS could be used as an experimental probe for quantum multifractality. Our predictions are universal and numerically verified in three paradigmatic models of quantum multifractality: Power-law Random Banded Matrices (PRBM), the Ruijsenaars-Schneider ensembles (RS), and the three-dimensional kicked-rotor (3DKR). In the strong multifractal regime, we show analytically that these universal predictions exactly coincide with results from standard perturbation theory applied to the PRBM and RS models.