As recently discovered PRL $109$ 190601(2012), Anderson localization
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 random system and we relate this novel interference effect to
the statistical properties of the eigenfunctions and eigenspectrum of the
corresponding random Hamiltonian. Our numerical results show that the dynamics
of the CFS peak is governed by the logarithmic level repulsion between
localized states, with a time scale that is, with good accuracy, twice 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. Our results should be easily extended to
higher dimensional systems and other symmetry classes.
Description
Dynamics of localized waves in 1D random potentials: statistical theory
of the coherent forward scattering peak
%0 Generic
%1 lee2014dynamics
%A Lee, Kean Loon
%A Grémaud, Benoît
%A Miniatura, Christian
%D 2014
%K interesting
%T Dynamics of localized waves in 1D random potentials: statistical theory
of the coherent forward scattering peak
%U http://arxiv.org/abs/1405.2979
%X As recently discovered PRL $109$ 190601(2012), Anderson localization
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 random system and we relate this novel interference effect to
the statistical properties of the eigenfunctions and eigenspectrum of the
corresponding random Hamiltonian. Our numerical results show that the dynamics
of the CFS peak is governed by the logarithmic level repulsion between
localized states, with a time scale that is, with good accuracy, twice 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. Our results should be easily extended to
higher dimensional systems and other symmetry classes.
@misc{lee2014dynamics,
abstract = {As recently discovered [PRL ${\bf 109}$ 190601(2012)], Anderson localization
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 random system and we relate this novel interference effect to
the statistical properties of the eigenfunctions and eigenspectrum of the
corresponding random Hamiltonian. Our numerical results show that the dynamics
of the CFS peak is governed by the logarithmic level repulsion between
localized states, with a time scale that is, with good accuracy, twice 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. Our results should be easily extended to
higher dimensional systems and other symmetry classes.},
added-at = {2014-05-14T14:07:38.000+0200},
author = {Lee, Kean Loon and Grémaud, Benoît and Miniatura, Christian},
biburl = {https://www.bibsonomy.org/bibtex/2a077f78a22b3a170c0d52e86439abd48/scavgf},
description = {Dynamics of localized waves in 1D random potentials: statistical theory
of the coherent forward scattering peak},
interhash = {541eb30b41c5cc08cfac477680d1c553},
intrahash = {a077f78a22b3a170c0d52e86439abd48},
keywords = {interesting},
note = {cite arxiv:1405.2979},
timestamp = {2014-05-14T14:07:38.000+0200},
title = {Dynamics of localized waves in 1D random potentials: statistical theory
of the coherent forward scattering peak},
url = {http://arxiv.org/abs/1405.2979},
year = 2014
}