title: Invariance property of wave scattering through disordered media.
abstract: A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.
authors.affiliation: École Supérieure de Physique et de Chimie Industrielles ParisTech, Paris Sciences et Lettres Research University, CNRS, Institut Langevin, F-75005 Paris, France;
authors.forename: Romain
authors.initials: R
authors.lastname: Pierrat
authors.affiliation: Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria; and.
authors.forename: Philipp
authors.initials: P
authors.lastname: Ambichl
authors.affiliation: Laboratoire Kastler Brossel, Université Pierre et Marie Curie, École Normale Supérieure, CNRS, Collège de France, F-75005 Paris, France.
authors.forename: Sylvain
authors.initials: S
authors.lastname: Gigan
authors.affiliation: Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria; and.
authors.forename: Alexander
authors.initials: A
authors.lastname: Haber
authors.affiliation: École Supérieure de Physique et de Chimie Industrielles ParisTech, Paris Sciences et Lettres Research University, CNRS, Institut Langevin, F-75005 Paris, France;
authors.forename: Rémi
authors.initials: R
authors.lastname: Carminati
authors.affiliation: Institute for Theoretical Physics, Vienna University of Technology, A-1040 Vienna, Austria; and stefan.rotter@tuwien.ac.at.
authors.forename: Stefan
authors.initials: S
authors.lastname: Rotter
keywords: diffusion; disordered media; random walk; time delay; wave scattering