Related papers: Vibrational excitations in systems with correlated…
A theory of vibrational excitations based on power-law spatial correlations in the elastic constants (or equivalently in the internal stress) is derived, in order to determine the vibrational density of states $D(\omega)$ of disordered…
We develop a numerical method for the time evolution of Gaussian wave packets on flat-band lattices in the presence of correlated disorder. To achieve this, we introduce a method to generate random on-site energies with prescribed…
Connectedness and applied stress strongly affect elasticity in solids. In various amorphous solids, mechanical stability can be lost either by reducing connectedness or by increasing pressure. We present an effective medium theory of…
Much of the discussion in the literature of the low frequency part of the density of states of amorphous solids was dominated for years by comparing measured or simulated density of states to the classical Debye model. Since this model is…
The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous…
We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the…
Correlated structures are intimately connected to intriguing phenomena exhibited by a variety of disordered systems such as soft colloidal gels, bio-polymer networks and colloidal suspensions near a shear jamming transition. The universal…
We derive analytically, and validate numerically, the dispersion renormalization and attenuation of acoustic waves propagating through quenched disordered media in the long-wavelength limit. We consider weak spatial fluctuations in elastic…
In scattering experiments, the dynamical structure factor (DSF) characterizes inter-particle correlations and their time evolution. We analytically evaluated the DSF of disordered solids with disorder in the spring constant, by averaging…
We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) \sim…
We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an…
The disordered Bose Hubbard model is studied numerically within the Bogoliubov approximation. First, the spatially varying condensate wavefunction in the presence of disorder is found by solving a nonlinear Schrodinger equation. Using the…
We describe repulsively interacting Bose-Einstein condensates in spatially correlated disorder potentials of arbitrary dimension. The first effect of disorder is to deform the mean-field condensate. Secondly, the quantum excitation spectrum…
We discuss vibrational localization problems in glasses and disordered media in this paper. It is claimed that the essence of the localization problem is already observed in disordered lattice models. These kinds of vibrations belong to a…
All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states…
We investigate the spread of correlations carried by an excitation in a 1-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\propto r^{-\mu}$). The increase…
We study the behavior of stationary non-equilibrium two-body correlation functions for Diffusive Systems with equilibrium reference states (DSe). We describe a DSe at the mesoscopic level by $M$ locally conserved continuum fields that…
An approximate solution of the Dyson equation related to a stochastic Helmholtz equation, which describes the acoustic dynamics of a three-dimensional isotropic random medium with elastic tensor fluctuating in space, is obtained in the…
We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at $T=0$,…
We investigate the stability of stratified fluid layers undergoing homogeneous and periodic tidal deformation. We first introduce a local model which allows to study velocity and buoyancy fluctuations in a Lagrangian domain periodically…