Related papers: Sparse random matrices and vibrational spectra of …
The vibrational spectrum of granular packings can be used as a signature of the jamming transition, with the density of states at zero frequency becoming non-zero at the transition. It has been proposed previously that the vibrational…
We study properties of jammed packings of frictionless spheres over a wide range of volume fractions. There exists a crossover volume fraction which separates deeply jammed solids from marginally jammed solids. In deeply jammed solids, all…
We have developed a formulation of density functional perturbation theory for the calculation of vibrational frequencies in molecules and solids, which uses numerical atomic orbitals as a basis set for the electronic states. The (harmonic)…
Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency…
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 $T=0$,…
Numerical studies of amorphous silicon show that the lowest 4% of vibrational modes are plane-wave like ("propagons") and the highest 3% of modes are localized ("locons"). The rest are neither plane-wave like nor localized. We call them…
Several mean-field theories predict that Hessian matrices of amorphous solids can be written by using the random matrix in the limit of the large spatial dimensions $d\to\infty$. Motivated by these results, we here propose a way to map a…
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…
This work analyzes the scattering resonances of general acoustic media in a one-dimensional setting using the propagation matrix approach. Specifically, we characterize the resonant frequencies as the zeros of an explicit trigonometric…
The phonon spectra of solids, described through the measurable vibrational density of states (VDOS), provide a wealth of information about the underlying atomic structure and bonding, and they determine fundamental macroscopic properties…
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…
We investigate the dynamics of a rotating Morse wave packet, appropriate for a ro-vibrating diatomic molecule. The coupling between vibrational and rotational degrees of freedom is explicated in real position space as well as in phase space…
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…
We consider a versatile matrix model of the form ${\bf A}+i {\bf B}$, where ${\bf A}$ and ${\bf B}$ are real random circulant matrices with independent but, in general, nonidentically distributed Gaussian entries. For this model, we derive…
We consider non-Hermitian random matrices $X \in \mathbb{C}^{n \times n}$ with general decaying correlations between their entries. For large $n$, the empirical spectral distribution is well approximated by a deterministic density,…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
The wave propagation in random medium plays a critical role in optics and quantum physics. Multiple scattering of coherent wave in a random medium determines the transport procedure. Brownian motions of the scatterers perturb each…
In recent years, active Brownian particles have emerged as a prominent model system for comprehending the behaviors of active matter, wherein particles demonstrate self-propelled motion by harnessing energy from the surrounding environment.…
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…
We propose a one-dimensional nonintegrable spin model with local interactions that covers Dyson's three symmetry classes (classes A, AI, and AII) depending on the values of parameters. We show that the nearest-neighbor spacing distribution…