Coherent Forward Scattering Peak and Multifractality

TL;DR

This paper investigates how quantum multifractality influences the coherent forward scattering (CFS) peak in disordered systems, revealing that the CFS peak's shape and dynamics are governed by multifractal dimensions and spectral properties, with implications for experimental detection.

Contribution

It introduces a theoretical framework linking CFS peak features to multifractal dimensions in Floquet systems, supported by numerical and analytical validation.

Findings

CFS peak shape and height are controlled by multifractal dimensions D_1 and D_2.

Numerical simulations confirm the theoretical predictions.

Results provide a new method to detect and characterize multifractality experimentally.

Abstract

It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions $D_1$ and $D_2$, and by the spectral form factor. We check our results using a 1D Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems.