We investigate the nature of one-electron eigenstates in power-law diluted chains for which the probability of occurrence of a bond between sites separated by a distance r decays as p(r) = 1/r1+sigma. Using an exact diagonalization scheme on finite chains, we compute the spreading of an initially localized wave-packet, the time dependent participation number as well as the return probability. Our results show the existence of a phase of extended states. By considering the scale invariance of the fluctuations of the participation number at the Anderson transition, we obtained that extended states emerges for sigma < 0.68. This limiting value is larger than the one reported in the literature for the emergence of extended states in one-dimensional Anderson models with power-law decaying couplings.

Abstract: The vibrational modes with nonzero frequency are localized in harmonic lattice with disordered masses. In our work, we investigated numerically the propagation of vibrational energy in harmonic lattice with long-range correlated disordered masses, which are randomly distributed with power law spectrum S ( k ) ∝ k − α. For α = 0, a standard uncorrelated disordered mass distribution was observed and for α > 0 its distribution exhibits intrinsic long-range correlations. Our procedure was done by the numerical solution of the classical equations for the mass displacement and velocities. Energy flow was investigated after injection of an initial wave-packet with energy E0 and the dynamics of the vibrational energy wave-packet was analyzed. We also investigated the dynamics of a pulse pumped at one side of the lattice. Our calculations suggest that vibrational modes with nonzero frequency propagate within harmonic lattice with correlated disordered masses distribution.

Abstract: There has been a growing interest in disordered optical media in recent years due to their potential applications in solar collectors, random lasers, light confinement, and other advanced photonic functions. This paper studies the transport of light for different incidence angles in a strongly disordered optical medium composed of core-shell TiO2@Silica nanoparticles suspended in an ethanol solution. A decrease of optical conductance and an increase of absorption near the input border are reported when the incidence angle increases. The specular reflection, measured for the photons that enter the sample, is lower than the effective internal reflection undergone by the coherently backscattered photons in the exact opposite direction, indicating a nonreciprocal propagation of light. This study represents a novel approach in order to understand the complex physics involved at the phase transition to localization

Agradecimentos: This work was supported by the NSF (USA) Grants No. DMR-1005751, No. DMR-1410132, and No. PHYS-1066293, by the National High Magnetic Field Laboratory, by the Simons Foundation (H.J.M. and V.D.), by FAPESP (Brazil) Grants No. 015/23849-7 and No. 2016/10826-1 (J.A.H.) and CNPq (Brazil) Grants No. 307548/2015-5 (J.A.H.) and No. 304311/2010-3 (E.M.). We acknowledge the hospitality of the Aspen Center for Physics

Agradecimentos: E.R.-G. and A.B.-A. thank the Instituto de Fisica, UNICAMP, Brazil, where part of this work was performed. The present work was partially financed by the Brazilian Agencies CNPq and FAPESP as well as the Scientific Colombian Agency CODI-University of Antioquia

Agradecimentos: Scientific Colombian Agencies Estrategia de Sostenibilidad (2014–2016), CODI–University of Antioquia, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), São Paulo Research Foundation (FAPESP) (Proc. 2012/51691-0)

The localization of the hybrid modes of phonons and photons in polar matter is investigated in the presence of random scatterers theoretically. We employ the self-consistent generalized Born-Huang approach to derive effective equations describing the phonon-polariton fields. Based on these equations, the density of states and various localization properties are exploited in two-dimensional systems both analytically and numerically within the framework of the Anderson model with a non-Hermitian effective Hamiltonian. Consequently, it is shown that the disorder effect brings some intriguing features which include the appearance of the localized states in the polariton bottleneck in the energy spectrum and the collapse of the energy gap. In addition, an analysis is given of the polariton level-spacing distribution.