Related papers: Vibrations in glasses and Euclidean Random Matrix …
We review a new theory of viscoelasticity of a glass-forming viscous liquid near and below the glass transition. In our model we assume that each point in the material has a specific viscosity, which varies randomly in space according to a…
We develop an ab initio analytic theory of random lasing in an ensemble of atoms that both scatter and amplify light. The theory applies all the way from low to high density of atoms. The properties of the random laser are controlled by an…
Ultra-stable glasses prepared from the physical vapor deposition of organic molecules present a very low density of two-level states, the kind of glass defects that determine their peculiar low temperature thermal properties. Numerical…
We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the…
Glass-forming liquids have been extensively studied in recent decades, but there is still no theory that fully describes these systems, and the diversity of treatments is in itself a barrier to understanding. Here we introduce a new simple…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between…
Glasses display a wide array of nonlinear acoustic phenomena at temperatures $T\lesssim 1$ K. This behavior has traditionally been explained by an ensemble of weakly-coupled, two-level tunneling states, a theory that is also used to…
To better understand the surprising low-frequency vibrational modes in structural glasses, we study the spectra of a large ensemble of sparse random matrices where disorder is controlled by the distribution of bond weights and network…
The excess low-frequency normal modes for two widely-used models of glasses were studied at zero temperature. The onset frequencies for the anomalous modes for both systems agree well with predictions of a variational argument, which is…
We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminium plate may have an…
We study the Boson Peak phenomenology experimentally observed in globular proteins by means of elastic network models. These models are suitable for an analytic treatment in the framework of Euclidean Random Matrix theory, whose predictions…
The low-frequency vibrations of glasses are markedly different from those of crystals. These vibrations have recently been categorized into two types: spatially extended vibrations, whose vibrational density of states (vDOS) follows a…
The concept of vibrational density of states in glasses has been mirrored in liquids by the instantaneous-normal-mode spectrum. While in glasses instantaneous configurations correspond to minima of the potential-energy hypersurface and all…
Euclidean random matrices appear in a broad class of physical problems involving disorder. The problem of determining their spectra can be mapped, using the replica method, into the study of a scalar field theory with an interaction of the…
We study the role of fluctuations on the thermodynamic glassy properties of plaquette spin models, more specifically on the transition involving an overlap order parameter in the presence of an attractive coupling between different replicas…
We consider polynomial transforms (polyspectra) of Berry's model -- the Euclidean Random Wave model -- and of Random Hyperspherical Harmonics. We determine the asymptotic behavior of variance for polyspectra of any order in the…
The vibrational properties of three sodosilicate glasses have been investigated in the framework of Density Functional Theory. The pure vibrational density of states has been calculated for all systems and the different vibrational modes…
The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between…