Related papers: Topological Dependence of Universal Correlations i…
This paper establishes the universality of parametric correlations of eigenfunctions in chaotic and weakly disordered systems. We demonstrate this universality in the framework of the gaussian random matrix process and obtain predictions…
A general formulation of translationally invariant, parametrically correlated random matrix ensembles, is used to classify universality in correlation functions. Surprisingly, the range of possible physical systems is bounded, and can be…
We consider the (smoothed) average correlation between the density of energy levels of a disordered system, in which the Hamiltonian is equal to the sum of a deterministic H0 and of a random potential $\varphi$. Remarkably, this correlation…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…
We extend a recent theory of parametric correlations in the spectrum of random matrices to study the response to an external perturbation of eigenvalues near the soft edge of the support. We demonstrate by explicit non-perturbative…
We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show…
When a periodic 1D system described by a tight-binding model is uniformly initialized with equal amplitudes at all sites, yet with completely random phases, it evolves into a thermal distribution with no spatial correlations. However, when…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
We compute the parametric correlation function of the conductance peaks in chaotic and weakly disordered quantum dots in the Coulomb blockade regime and demonstrate its universality upon an appropriate scaling of the parameter. For a…
{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous…
We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp(-|H_{ij}|/V)$, with a parametric…
Numerical study of the parametric motion of energy levels in a model system built on Random Matrix Theory is presented. The correlation function of levels' slopes (the so called velocity correlation function) is determined numerically and…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
Dyson's short-distance universality of the correlation functions implies the universality of P(s), the level-spacing distribution. We first briefly review how this property is understood for unitary invariant ensembles and consider next a…
The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex…
The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by $2\times 2$ Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
Most data is multi-dimensional. Discovering whether any subset of dimensions, or subspaces, of such data is significantly correlated is a core task in data mining. To do so, we require a measure that quantifies how correlated a subspace is.…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
We summarize recent work showing that the $1/r^2$ model of interacting particles in 1-dimension is a universal Hamiltonian for quantum chaotic systems. The problem is analyzed in terms of random matrices and of the evolution of their…