Related papers: Emergent percolation length and localization in ra…
We study by exact diagonalization the localization properties of phonons in mass-disordered harmonic crystals of dimension $d=1,2,3$. We focus on the behavior of the typical Inverse Participation Ratio $Y_2(\omega,L)$ as a function of the…
We study the electronic structure of the binary alloy and (quantum) percolation model. Our study is based on a self-consistent scheme for the distribution of local Green functions. We obtain detailed results for the density of states, from…
We deduce the dynamic frequency-domain-lattice Green's function of a linear chain with properties (masses and next-neighbor spring constants) of exponential spatial dependence. We analyze the system as discrete chain as well as the…
Percolation refers to an interesting class of problems related to the properties of disordered systems, usually formulated in terms of objects randomly placed on an underlying lattice or continuum. Despite the simplicity of the setup, most…
Percolation theory and the associated conductance networks have provided deep insights into the flow and transport properties of a vast number of heterogeneous materials and media. In practically all cases, however, the conductance of the…
Quasiperiodic long range order is intermediate between spatial periodicity and disorder, and the excitations in 1D quasiperiodic systems are believed to be transitional between extended and localized. These ideas are tested with a numerical…
We present two complementary simulations that lead to an exploration of Anderson localization, a phenomenon in which wave diffusion is suppressed in disordered media by interference from multiple scattering. To build intuition, the first…
We consider a ring of identical or near identical coupled periodic oscillators in which the connections have randomly heterogeneous strength. We use the master stability function method to determine the possible patterns at the…
Models of many-body localization (MBL) exhibit slow numerical drifts towards delocalization with increasing system size, for which no satisfactory theory exists. Numerics indicates that these drifts are driven by the proliferation of…
All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states…
We consider Anderson localization and the associated metal-insulator transition for non-interacting fermions in D = 1, 2 space dimensions in the presence of spatially correlated on-site random potentials. To assess the nature of the…
Quantum particles in a disordered potential, photons or classical waves in a random medium, or the universe expansion in a fluctuating cosmic field, all share Anderson localization as a communality. In general, localization is enhanced for…
The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed…
Disorder in moire superlattices simultaneously degrades flat-band localization and induces Anderson localization, yet how these two regimes interact has remained unclear. Here, we introduce a combined framework linking localization-length…
We study a one-dimensional model of disordered electrons (also relevant for random spin chains), which exhibits a delocalisation transition at half-filling. Exact probability distribution functions for the Wigner time and transmission…
We study both analytically and numerically how the electronic structure and the transport properties of a two-dimensional disordered system are modified in the presence of resonances. The energy dependence of the density of states and the…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators…
We study Anderson localization in two-dimensional systems with purely off-diagonal disorder. Localization lengths are computed by the transfer-matrix method and their finite-size and scaling properties are investigated. We find various…
Using the density matrix renormalization group algorithm, we investigate the lattice model for spinless fermions in one dimension in the presence of a strong interaction and disorder. The phase sensitivity of the ground state energy is…