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Anderson localization does not lead to an exponential decay of intensity of an incident wave with the depth inside a strongly disordered three-dimensional medium. Instead, the average intensity is roughly constant in the first half of a disordered slab, sharply drops in a narrow region in the middle of the sample, and then remains low in the second half of the sample. A universal, scale-free spatial distribution of average intensity is found at mobility edges where the intensity exhibits strong sample-to-sample fluctuations. Our numerical simulations allow us to discriminate between two competing local diffusion theories of Anderson localization and to pinpoint a deficiency of the self-consistent theory.
We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian correlation
A microscopic theory for the luminescence of ordered semiconductors is modified to describe photoluminescence of strongly disordered semiconductors. The approach includes both diagonal disorder and the many-body Coulomb interaction. As a case study,
Many-body localization is a fascinating theoretical concept describing the intricate interplay of quantum interference, i.e. localization, with many-body interaction induced dephasing. Numerous computational tests and also several experiments have be
Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the study of
We study the propagation of waves in a medium in which the wave velocity fluctuates randomly in time. We prove that at long times, the statistical distribution of the wave energy is log-normal, with the average energy growing exponentially. For weak