相关论文: Euclidean random matrices, the glass transition an…

In this paper I will describe some results that have been recently obtained in the study of random Euclidean matrices, i.e. matrices that are functions of random points in Euclidean space. In the case of {\sl translation invariant} matrices…

We show that the phonon-saddle transition in the ensemble of generalized inherent structures (minima and saddles) happens at the same point as the dynamical phase transition in glasses, that has been studied in the framework of the mode…

Despite the presence of topological disorder, phonons seem to exist also in glasses at very high frequencies (THz) and they remarkably persist into the supercooled liquid. A universal feature of such a systems is the Boson peak, an excess…

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystals, elasticity is associated with phonons, quantized sound-wave excitations. Phonon-like excitations exist also in glasses at very high frequencies…

We study numerically and analytically a simple off-lattice model of scalar harmonic vibrations by means of Euclidean random matrix theory. Since the spectrum of this model shares the most puzzling spectral features with the high-frequency…

A simple model of harmonic vibrations in topologically disordered systems, such as glasses and supercooled liquids, is studied analytically by extending Euclidean Random Matrix Theory to include vector vibrations. Rather generally, it is…

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

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…

Vibrational spectra of proteins and topologically disordered solids display a common anomaly at low frequencies, known as Boson peak. We show that such feature in globular proteins can be deciphered in terms of an energy landscape picture,…

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…

The inelastic scattering intensities of glasses and amorphous materials has a maximum at a low frequency, the so called Boson peak. Under applied hydrostatic pressure, $P$, the Boson peak frequency, $\omega_{\rm b}$, is shifted upwards. We…

A close inspection of neutron spectra of glass formers in the frequency region above the boson peak does not show the constant eigenvalue density expected for a random dynamical matrix, but a slow decrease towards higher eigenvalues. In…

The boson peak in metallic glasses is modeled in terms of local structural shear rearrangements. Using Eshelby's solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate…

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency $\omega^*$ . We show that the eigenvector…

We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…

The low-temperature properties of glasses present important differences with respect to crystalline matter. In particular, models such as the Debye model of solids, which assume the existence of an underlying regular lattice, predict that…

Tensor models play an increasingly prominent role in many fields, notably in machine learning. In several applications, such as community detection, topic modeling and Gaussian mixture learning, one must estimate a low-rank signal from a…

The union of the particles of a stationary Poisson process of compact (convex) sets in Euclidean space is called Boolean model and is a classical topic of stochastic geometry. In this paper, Boolean models in hyperbolic space are…

We argue that the intrinsic glassy degrees of freedom in amorphous solids giving rise to the thermal conductivity plateau and the ``boson peak'' in the heat capacity at moderately low temperatures are directly connected to those motions…

We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard…