Related papers: Sampling eigenmodes in colloidal solids
Studying the jamming transition of granular and colloidal systems, has lead to a proliferation of theoretical and numerical results formulated in the language of the eigenspectrum of the dynamical matrix for these disordered system. Only…
We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…
We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…
One of the most used approaches in simulating materials is the tight-binding approximation. When using this method in a material simulation, it is necessary to compute the eigenvalues and eigenvectors of the Hamiltonian describing the…
We present an analytic method to determine spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral…
We propose a new method to characterize the spatial distribution of particles' vibrations in solids with much lower computational costs compared to the usual normal mode analysis. We excite the specific vibrational mode in a two dimensional…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of…
Longitudinal contact-based vibrations of colloidal crystals with a controlled layer thickness are studied. These crystals consist of 390 nm diameter polystyrene spheres arranged into close packed, ordered lattices with a thickness of one to…
The detection of vibrational excitations of individual molecules on surfaces by scanning tunneling spectroscopy does not obey strict selection rules but rather propensity rules. The experimental verification of these is challenging because…
Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…
Using random matrix technique we determine an exact relation between the eigenvalue spectrum of the covariance matrix and of its estimator. This relation can be used in practice to compute eigenvalue invariants of the covariance…
We experimentally investigate the recoil dynamics of a colloidal probe particle after shearing it with constant velocity through a viscoelastic fluid. The recoil displays two distinct timescales which are in excellent agreement with a…
Topological properties of solid states have sparked considerable recent interest due to their importance in the physics of lattices with a non-trivial basis and their potential in the design of novel materials. Here we describe an…
We investigate eigenvalues of many-body systems interacting by two-body forces as well as those of random matrices. We find a strong linear correlation between eigenvalues and diagonal matrix elements if both of them are sorted from the…
The salient properties of large empirical covariance and correlation matrices are studied for three datasets of size 54, 55 and 330. The covariance is defined as a simple cross product of the returns, with weights that decay logarithmically…
We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…
We investigate the effective properties (conductivity, diffusivity and elastic moduli) of model random composite media derived from Gaussian random fields and overlapping hollow spheres. The morphologies generated in the models exhibit low…
Starting from a microscopic model, we investigate the optical spectra of molecules in strongly-coupled organic microcavities examining how they might self-consistently adapt their coupling to light. We consider both rotational and…
We present a detailed study of the conduction properties of a molecular wire where hopping processes between electronic sites are coupled to a vibrational mode of the molecule. The latter is sandwiched between two electronic leads at finite…