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 syst
ems 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.
When a resonant laser sent on an optically thick cold atomic cloud is abruptly switched off, a coherent flash of light is emitted in the forward direction. This transient phenomenon is observed due to the highly resonant character of the atomic scatt
erers. We analyze quantitatively its spatio-temporal properties and show very good agreement with theoretical predictions. Based on complementary experiments, the phase of the coherent field is reconstructed without interferometric tools.
