RESUMO
The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder-Lévy disorder-leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.
RESUMO
We perform a detailed numerical study of the conductance G through one-dimensional (1D) tight-binding wires with on-site disorder. The random configurations of the on-site energies ε of the tight-binding Hamiltonian are characterized by long-tailed distributions: For large ε, P(ε)â¼1/ε^{1+α} with α∈(0,2). Our model serves as a generalization of the 1D Lloyd model, which corresponds to α=1. First, we verify that the ensemble average ã-lnGã is proportional to the length of the wire L for all values of α, providing the localization length ξ from ã-lnGã=2L/ξ. Then, we show that the probability distribution function P(G) is fully determined by the exponent α and ã-lnGã. In contrast to 1D wires with standard white-noise disorder, our wire model exhibits bimodal distributions of the conductance with peaks at G=0 and 1. In addition, we show that P(lnG) is proportional to G^{ß}, for Gâ0, with ß≤α/2, in agreement with previous studies.
RESUMO
Experimental evidence demonstrating that anomalous localization of waves can be induced in a controllable manner is reported. A microwave waveguide with dielectric slabs randomly placed is used to confirm the presence of anomalous localization. If the random spacing between slabs follows a distribution with a power-law tail (Lévy-type distribution), unconventional properties in the microwave-transmission fluctuations take place revealing the presence of anomalous localization. We study both theoretically and experimentally the complete distribution of the transmission through random waveguides characterized by α=1/2 ("Lévy waveguides") and α=3/4, α being the exponent of the power-law tail of the Lévy-type distribution. As we show, the transmission distributions are determined by only two parameters, both of them experimentally accessible. Effects of anomalous localization on the transmission are compared with those from the standard Anderson localization.