Related papers: Strong Linear Correlation Between Eigenvalues and …
We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…
The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the…
For states of quantum systems of $N$ particles with harmonic interactions we prove that each reduced density matrix $\rho$ obeys a duality condition. This condition implies duality relations for the eigenvalues $\lambda_k$ of $\rho$ and…
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are…
We consider eigenvalue condition numbers and backward errors for a class of symmetric nonlinear eigenvalue problems with eigenvector nonlinearities. For both of these quantities, we derive explicit and computable expressions that can be…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered environments. Sparse non-Hermitian random matrices arise…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
The numerical solution of eigenvalue problems is essential in various application areas of scientific and engineering domains. In many problem classes, the practical interest is only a small subset of eigenvalues so it is unnecessary to…
We prove a new theorem relating the number of distinct eigenvalues of a matrix after perturbation to the prior number of distinct eigenvalues, the rank of the update, and the degree of nondiagonalizability of the matrix. In particular, a…
We investigate how in complex systems the eigenpairs of the matrices derived from the correlations of multichannel observations reflect the cluster structure of the underlying networks. For this we use daily return data from the NYSE and…
Large multidimensionality of high-throughput datasets pertaining to cell signaling and gene regulation renders it difficult to extract mechanisms underlying the complex kinetics involving various biochemical compounds (e.g., proteins,…
We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…
Based on the Hugenholtz-Van Hove theorem, the symmetry energy $J$ and its density slope parameter $L$ are decomposed in terms of the nucleon self-energies within the covariant density functional (CDF) theory. It is found that two structural…
It is shown that the two-body character of the interaction in a many-body system gives rise to specific correlations between the components of compound states, even if this interaction is completely random. Surprisingly, these correlations…
This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…
Research on strongly correlated electron systems faces a fundamental challenge due to the complex nature of intrinsic many-body correlations. A key strategy to address this challenge lies in advancing experimental methods that can directly…
A supereigenvalue model with purely positive bosonic eigenvalues is presented and solved by considering its superloop equations. This model represents the supersymmetric generalization of the complex one matrix model, in analogy to the…
In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical…
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is…