Using the framework of supersymmetric non-linear $σ$-model we develop a general non-perturbative characterisation of universal features of the density $ρ(Γ)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $ρ(Γ)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $ρ(Γ)\sim Γ^{-1}$ for narrow resonances reflecting exponential localization and $ρ(Γ)\sim Γ^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $ρ(Γ)\sim Γ^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts.
Using the properties of random Möbius transformations, we investigate the statistical properties of the reflection coefficient in a random chain of lossy scatterers. We explicitly determine the support of the distribution and the condition for coherent perfect absorption to be possible. We show that at its boundaries the distribution has Lifshits-like tails, which we evaluate. We also obtain the extent of penetration of incoming waves into the medium via the Lyapunov exponent. Our results agree well when compared to numerical simulations in a specific random system.
The universal bimodal distribution of transmission eigenvalues in lossless diffusive systems un- derpins such celebrated phenomena as universal conductance fluctuations, quantum shot noise in condensed matter physics and enhanced transmission in optics and acoustics. Here, we show that in the presence of absorption, density of the transmission eigenvalues depends on the confinement geometry of scattering media. Furthermore, in an asymmetric waveguide, densities of the reflection and absorption eigenvalues also depend of the side from which the waves are incident. With increas- ing absorpotion,…
We study the time delay of reflected and transmitted waves in 1D disordered media with high transmission. Highly transparent and translucent random media are found in nature or can be synthetically produced. We perform numerical simulations of microwaves propagating in disordered waveguides to show that reflection amplitudes are described by complex Gaussian random variables with the remarkable consequence that the time-delay statistics in reflection of 1D disordered media are described as in random media in the diffusive regime. For transmitted waves, we show numerically that the time delay i…
We study the statistical fluctuations of the Casimir potential felt by an atom approaching a dielectric disordered medium. Starting from a microscopic model for the disorder, we calculate the variance of potential fluctuations in the limit of a weak density of heterogeneities. We show that fluctuations are essentially governed by scattering of the radiation on a single heterogeneity, and discuss in which limits they become larger than the average value predicted by effective medium theory. Finally, for denser disorder we show that multiple scattering processes become relevant.
We study Anderson localization of a scalar wave in an ensemble of resonant point scatterers embedded in an anisotropic background medium. For uniaxial anisotropy of moderate strength, the mobility edges and the critical exponent of the localization transition are found to be unaffected by the anisotropy provided that the determinant of the anisotropy tensor is kept equal to one upon introducing the anisotropy. Localized modes have anisotropic spatial shapes although their anisotropy is weaker than the one expected from purely geometric considerations. The modes with the longest lifetimes are f…
The typical medium dynamical cluster approximation (TMDCA) is reformulated in the language of multiple scattering theory to make possible first principles calculations of the electronic structure of substitutionally disordered alloys including the effect of Anderson localization. The TMDCA allows for a systematic inclusion of non-local multi-site correlations and at same time provides an order parameter, the typical density of states, for the Anderson localization transition. The relation between the dynamical cluster approximation and the multiple scattering theory is analyzed, and is illustr…
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 compet…
Great progress has been made in the last several years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean field theory and the coherent potential approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electroni…
Thirty years ago, theorists showed that a properly designed combination of incident waves could be fully transmitted through (or reflected by) a disordered medium, based on the existence of propagation channels which are essentially either closed or open (bimodal law). In this Letter, we study elastic waves in a disordered waveguide and present direct experimental evidence of the bimodal law. Full transmission and reflection are achieved. The wave field is monitored by laser interferometry and highlights the interference effects that take place within the scattering medium.
We generalize the typical medium dynamical cluster approximation to multiband disordered systems. Using our extended formalism, we perform a systematic study of the non-local correlation effects induced by disorder on the density of states and the mobility edge of the three-dimensional two-band Anderson model. We include inter-band and intra-band hopping and an intra-band disorder potential. Our results are consistent with the ones obtained by the transfer matrix and the kernel polynomial methods. We apply the method to K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies. Despite the strong vacancy disord…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT) distribution in a given sample that enables detailed comparison of the two problems. For a system of finite size, the number and spatial arrangement of deep traps yield significant sample-to-sample variations in the FPT statistics. Numerical simulations of a quenched trap model with power-law sojourn times confirm the existence of two characteristic time sca…
We study the effect of uncorrelated random disorder on the temperature dependence of the superfluid stiffness in the two-dimensional classical XY model. By means of a perturbative expansion in the disorder potential, equivalent to the T-matrix approximation, we provide an extension of the effective-medium-theory result able to describe the low-temperature stiffness, and its separate diamagnetic and paramagnetic contributions. These analytical results provide an excellent description of the Monte Carlo simulations for two prototype examples of uncorrelated disorder. Our findings offer an intere…
The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this work, we employ a Green's function based approach, namely the dynamical cluster approximation (DCA), to investigate phonons in mass disordered systems. Detailed benchmarks with previous exact calculations are used to validate the method in a wide parameter space. An extension of the method, namely the typical medium DCA (TMDCA), is used to study Anderson localization of phonons in three dimensions. We show that, for binary isotopic disorder, lighter impurities induce localized modes be…
It has been shown that changes in the energy of a system of nonwetting-liquid clusters confined in a random nanoporous medium in the process of relaxation can be written in the quasiparticle approximation in the form of the sum of the energies of local (metastable) configurations of liquid clusters interacting with clusters in the connected nearest pores. The energy spectrum and density of states of the local configuration have been calculated. It has been shown that the relaxation of the state of the system occurs through the scenario of self-organized criticality (SOC). The process is charac…
A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multi-path interference. Here we show that these intensity variations can be entirely suppressed by adding disorder-specific gain and loss components to the medium. The resulting constant-intensity (CI) waves in such non-Hermitian scattering landscapes are free of any backscattering and feature perfect transmission through the disorder. An experimental demonstration of these unique wave states is envisioned based on spatially modulated pump beams that can flexi…
We study the wave transport through a disordered system inside a waveguide. The expectation value of the complex reflection and transmission coefficients (the coherent fields) as well as the transmittance and reflectance are obtained numerically. The numerical results show that the averages of the coherent fields are only relevant for direct processes, while the transmittance and reflectance are mainly dominated by the diffuse intensities, which come from the statistical fluctuations of the fields.
Light scattering in a magnetic medium with uncorrelated inclusions is theoretically studied in the approximation of ladder diagram. Correlation between polarizations of electromagnetic waves that are produced by infinitely-distant dipole source is considered. Here white noise disorder model with Gaussian distribution is taken into account. In such a medium the magneto-optical interaction leads to correlation between perpendicular light polarizations. Spatial field correlation matrix with nonzero nondiagonal elements is obtained in the first order on gyration.
We use the recently developed typical medium dynamical cluster (TMDCA) approach~[Ekuma \etal,~\textit{Phys. Rev. B \textbf{89}, 081107 (2014)}] to perform a detailed study of the Anderson localization transition in three dimensions for the Box, Gaussian, Lorentzian, and Binary disorder distributions, and benchmark them with exact numerical results. Utilizing the nonlocal hybridization function and the momentum resolved typical spectra to characterize the localization transition in three dimensions, we demonstrate the importance of both spatial correlations and a typical environment for the pro…
Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the computationally expensive density functional theory calculations. Combining many-body techniques with a deep learning approach, we demonstrate that a fully-connected neural network is able to learn the complex collective behavior of electrons in strongly correlated systems. Specifically, we consider the Anderson-Hubbard (AH) model, which is a canonical system fo…
Generalized two-body self-consistent theory of random linear dielectric composites: an effective-medium approach to clustering in highly-disordered media
The mean-field theory for disordered electron systems without interaction is widely and successfully used to describe equilibrium properties of materials over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and information of localization. Vertex corrections due to multiple back-scatterings may drive the electrical conductivity to zero and make expansions around the mean field in strong disorder problematic. Here, we present a method for the calculation of two-particle quantities which enable us to characterize the metal-insulator …
