Related papers: Random matrix theory for mixed regular-chaotic dyn…
In this paper, we introduce a novel theoretical framework for multi-task regression, applying random matrix theory to provide precise performance estimations, under high-dimensional, non-Gaussian data distributions. We formulate a…
We propose a new application of random tensor theory to studies of non-linear random flows in many variables. Our focus is on non-linear resonant systems which often emerge as weakly non-linear approximations to problems whose linearized…
In the Coulomb blockade regime of a ballistic quantum dot, the distribution of conductance peak spacings is well known to be incorrectly predicted by a single-particle picture; instead, matrix element fluctuations of the residual electronic…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
The nonextensive statistical ensembles are revisited for the complex systems with long-range interactions and long-range correlations. An approximation, the value of nonextensive parameter (1-q) is assumed to be very tiny, is adopted for…
A theory of rank $k\ge 2$ perturbation of symplectic matrices and Hamiltonian systems with periodic coefficients using a base of isotropic subspaces, is presented. After showing that the fundamental matrix ${\displaystyle…
Understanding equilibration times in closed quantum systems is essential for characterising their approach to equilibrium. Chaotic many-body systems are paradigmatic in this context: they are expected to thermalise according to the…
Recently much effort has been made towards the introduction of non-Hermitian random matrix models respecting $PT$-symmetry. Here we show that there is a one-to-one correspondence between complex $PT$-symmetric matrices and split-complex and…
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated to…
The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, the main goal of Random Matrix Theory (RMT) has been to derive the eigenvalue statistics of matrices…
Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
A comparative study of one-dimensional quantum structures which allow analytic expressions for the position and momentum R\'{e}nyi $R(\alpha)$ and Tsallis $T(\alpha)$ entropies, focuses on extracting the most characteristic physical…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
The nonextensive statistics based on Tsallis entropy have been so far used for the systems composed of subsystems having same $q$. The applicability of this statistics to the systems with different $q$'s is still a matter of investigation.…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
Problem of long-range sound propagation in the randomly-inhomogeneous deep ocean is considered. We examine a novel approach for modeling of wave propagation, developed by K.C.Hegewisch and S.Tomsovic. This approach relies on construction of…
The properties of the nonextensive parameter q and the Tsallis distribution for self-gravitating systems are studied. A mathematical expression of q is deduced based on the generalized Boltzmann equation, the q-H theorem and the generalized…
We study the consequences of having translational invariance in space and in time in many-body quantum chaotic systems. We consider an ensemble of random quantum circuits, composed of single-site random unitaries and nearest neighbour…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…