Laboratoire de Physique Théorique
Toulouse - UMR 5152

As recently discovered [PRL 109 190601 (2012)], Anderson localization (AL) in a bulk disordered system triggers the emergence of a coherent forward scattering (CFS) peak in momentum space, which twins the well-known coherent backscattering (CBS) peak observed in weak localization experiments. Going beyond the perturbative regime, we address here the long-time dynamics of the CFS peak in a 1D and 2D random systems [PRA 90, 043605 (2014), arXiv:1410.0774]. Focusing on the 2D case, we show that CFS generally arises due the confinement of the wave in a finite region of space, and explain under which conditions it can be seen as a genuine signature of AL. In the localization regime, our numerical results show that the dynamics of the CFS peak is governed by the level repulsion between localized states, with a time scale related to the Heisenberg time. This is in perfect agreement with recent findings based on the nonlinear sigma model. In the stationary regime, the width of the CFS peak in momentum space is inversely proportional to the localization length, reflecting the exponential decay of the eigenfunctions in real space, while its height is exactly twice the background, reflecting the Poisson statistical properties of the eigenfunctions.