Related papers: On "Universal" Correlations in Disordered and Chao…
Analytical expressions for the width and conductance peak distributions of irregularly shaped quantum dots in the Coulomb blockade regime are presented in the limits of conserved and broken time-reversal symmetry. The results are obtained…
Orthogonal - unitary and symplectic - unitary crossover ensembles of random matrices are relevant in many contexts, especially in the study of time reversal symmetry breaking in quantum chaotic systems. Using skew-orthogonal polynomials we…
We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…
The responses of a $1+\epsilon $ dimensional directed path to temperature and to potential variations are calculated exactly, and are governed by the same scaling form. The short scale decorrelation (strong correlation regime) leads to the…
We use a simple dynamical model in order to investigate the regular or chaotic character of orbits in a barred galaxy with a central, spherically symmetric, dense nucleus and a flat disk. In particular, we explore how the total orbital…
We analytically examine fluctuations of vorticity excited by an external random force in two-dimensional fluid. We develop the perturbation theory enabling one to calculate nonlinear corrections to correlation functions of the flow…
In the core of the vortex of a superconductor, energy levels appear inside the gap. We discuss here through a random matrix approach how these levels are broadened by impurities. It is first shown that the level statistics is governed by an…
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…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
We develop a semiclassical theory of Coulomb blockade peak heights in chaotic quantum dots. Using Berry's conjecture, we calculate the peak height distributions and the correlation functions. We demonstrate that the corrections to the…
We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…
The time-dependence of multi-point observable correlation functions are essential quantities in analysis and simulation of quantum dynamics. Open quantum systems approaches utilize two-point correlations to describe the influence of an…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
We study the two-point correlation function in the model of branched polymers and its relation to the critical behaviour of the model. We show that the correlation function has a universal scaling form in the generic phase with the only…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
The content of this contribution is based on the course on numerical analysis techniques for non-linear dynamics. After introducing basic concepts as the visual analysis of trajectories in phase space and the importance of the nature of…
The tangled nodal lines (wave vortices) in random, three-dimensional wavefields are studied as an exemplar of a fractal loop soup. Their statistics are a three-dimensional counterpart to the characteristic random behaviour of nodal domains…
We investigate properties of the correlation function of clusters of galaxies using geometrical models. On small scales the correlation function depends on the shape and the size of superclusters. On large scales it describes the geometry…