Related papers: Random Matrix Model and the Calogero-Sutherland Mo…
We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is…
The behavior of the power function of autocorrelation tests such as the Durbin-Watson test in time series regressions or the Cliff-Ord test in spatial regression models has been intensively studied in the literature. When the correlation…
We study the correlations of time delays in a model of chaotic resonance scattering based on the random matrix approach. Analytical formulae which are valid for arbitrary number of open channels and arbitrary coupling strength between…
In this paper, we exhibit a new family of martingale couplings between two one-dimensional probability measures $\mu$ and $\nu$ in the convex order. This family is parametrised by two dimensional probability measures on the unit square with…
We study the eigenvalue problem of the rational Calogero model with the coupling of the inverse-square interaction as a complex number. We show that although this model is manifestly non-invariant under the combined parity and time-reversal…
In this work, we extend the study of the interplay between scaling symmetries and statistics to one-dimensional fluids by studying the Calogero model in a harmonic trap modulated through time. The latter harbors an interpretation in terms…
The conformal covariance of correlation functions is checked in the second-order transition induced by random bonds in the two-dimensional 8-state Potts model. The decay of correlations is obtained {\it via} transfer matrix calculations in…
A Lorentz invariant statistical model is presented for rotational fluctuations in the local inertial frame that arise from new quantum degrees of freedom of space-time. The model assumes invariant classical causal structure, and a Planck…
A random matrix theory approach is applied in order to analyze the localization properties of local spectral density for a generic system of coupled quantum states with strong static imperfection in the unperturbed energy levels. The system…
This paper gives a fresh look at network synchronization. Here we no longer analyze it from the view of mathematics, such as graph theory, while we probe into one from control theory. First, we analyze the synchronization region using the…
By using a model independent Monte Carlo approach, we study the possible structure of charged and neutral lepton mass matrices, under the assumption of an U(2) horizontal symmetry (additional to the usual Standard Model ones) involving the…
We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces $\tr W_1(M) \cdot \tr W_2(M)$ in addition to a single trace $\tr V(M)$. Connected correlation function of density…
We present and compare two families of ensembles of random density matrices. The first, static ensemble, is obtained foliating an unbiased ensemble of density matrices. As criterion we use fixed purity as the simplest example of a useful…
Interacting dark energy-dark matter models have been widely analyzed in the literature in an attempt to find traces of new physics beyond the usual cosmological ($\Lambda$CDM) models. Such a coupling between both dark components is usually…
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…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
We develop Monte Carlo simulations for uniformly charged polymers and machine learning algorithm to interpret the intra-polymer structure factor of the charged polymer system, which can be obtained from small-angle scattering experiments.…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared…
The present article is an extended version of the paper {\it Phys. Rev.} {\bf B 59}, R2490 (1999), where, we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach…