Related papers: Spectral Properties of Statistical Mechanics Model…
We present a statistical analysis of spectra of transfer matrices of classical lattice spin models; this continues the work on the eight-vertex model of the preceding paper. We show that the statistical properties of these spectra can serve…
A connection between integrability properties and general statistical properties of the spectra of symmetric transfer matrices of the asymmetric eight-vertex model is studied using random matrix theory (eigenvalue spacing distribution and…
We study the spectral properties of the transfer matrix for a gonihedric random surface model on a three-dimensional lattice. The transfer matrix is indexed by generalized loops in a natural fashion and is invariant under a group of motions…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
The spectral statistics and entanglement within the eigenstates of generic spin chain Hamiltonians are analysed. A class of random matrix ensembles is defined which include the most general nearest-neighbour qubit chain Hamiltonians. For…
We numerically analyze the spectral statistics of the multiparametric Gaussian ensembles of complex matrices with zero mean and variances with different decay routes away from the diagonals. As the latter mimics different degree of…
We describe analytical and numerical results on the statistical properties of complex eigenvalues and the corresponding non-orthogonal eigenvectors for non-Hermitian random matrices modeling one-channel quantum-chaotic scattering in systems…
Supersymmetric quantum mechanics is well known to provide, together with the so-called shape invariance condition, an elegant method to solve the eigenvalue problem of some one-dimensional potentials by simple algebraic manipulations. In…
We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
The thermalization phenomenon and many-body quantum statistical properties are studied on the example of several observables in isolated spin-chain systems, both integrable and generic non-integrable ones. While diagonal matrix elements for…
The spectral properties of interacting strongly chaotic systems are investigated for growing interaction strength. A very sensitive transition from Poisson statistics to that of random matrix theory is found. We introduce a new random…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
We study the spectral properties of a spin-boson Hamiltonian that depends on two continuous parameters $0\leq\Lambda<\infty$ (interaction strength) and $0\leq\alpha\leq\pi/2$ (integrability switch). In the classical limit this system has…
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…
We compute analytically the joint probability density of eigenvalues and the level spacing statistics for an ensemble of random matrices with interesting features. It is invariant under the standard symmetry groups (orthogonal and unitary)…
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…