Related papers: Lattices of matrices (revised)
We develop a theory for the eigenvalue density of arbitrary non-Hermitian Euclidean matrices. Closed equations for the resolvent and the eigenvector correlator are derived. The theory is applied to the random Green's matrix relevant to wave…
We perform an extensive investigation of the localization properties of the eigenmodes of the Laplace and adjacency matrix for one-dimensional random geometric graphs. We evaluate the density of states, the probability distribution of the…
By using a recently proposed probabilistic approach, we determine the exact ground state of a class of matrix Hamiltonian models characterized by the fact that in the thermodynamic limit the multiplicities of the potential values assumed by…
We discuss a dynamical matrix model by which probability distribution is associated with Gaussian ensembles from random matrix theory. We interpret the matrix M as a Hamiltonian representing interaction of a bosonic system with a single…
A number of recent papers have provided evidence that practical design questions about neural networks may be tackled theoretically by studying the behavior of random networks. However, until now the tools available for analyzing random…
We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…
The spectral properties of the Laplacian operator on ``small-world'' lattices, that is mixtures of unidimensional chains and random graphs structures are investigated numerically and analytically. A transfer matrix formalism including a…
We consider level crossing in a matrix family $H=H_0+\lambda V$ where $H_0$ is a fixed $N\times N$ matrix and $V$ belongs to one of the standard Gaussian random matrix ensembles. We study the probability distribution of level crossing…
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a…
The aim of this work is to study the dynamics of quantum systems subjected to a localized fermionic source in the presence of bulk dephasing. We consider two classes of one-dimensional lattice systems: (i) a non-interacting lattice with…
We study the entanglement spectrum of a translationally-invariant lattice system under a random partition, implemented by choosing each site to be in one subsystem with probability $p\in[0, 1]$. We apply this random partitioning to a…
Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random…
We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this…
We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows…
We investigate the behavior of entanglement-entropy on a broad scale, that is, a large class of systems, Hamiltonians and states describing the interaction of many degrees of freedom. It is one of our aims to show which general…
A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…
A density functional theory for many-body lattice models is considered in which the single-particle density matrix is the basic variable. Eigenvalue equations are derived for solving Levy's constrained search of the interaction energy…
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…
We calculate the properties of a one-dimensional $Z_2$ lattice gauge theory in different Gauss law sectors, corresponding to different configurations of static charges set by the orientations of the gauge spins. Importantly, in quantum…