Related papers: Generalized random matrix model with additional in…
We will derive here the relaxation behavior of a simple quantum random matrix model. The aim is to derive the effective equations which rise when a random matrix interaction is taken in the weak coupling limit. The physical situation this…
Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such…
We consider the dynamics of an arbitrary quantum system coupled to a large arbitrary and fully quantum mechanical environment through a random interaction. We establish analytically and check numerically the typicality of this dynamics, in…
The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze…
Random matrix ensembles are introduced that respect the local tensor structure of Hamiltonians describing a chain of $n$ distinguishable spin-half particles with nearest-neighbour interactions. We prove a central limit theorem for the…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We report on the dynamics of thermalization by extending a generalization of the Caldeira-Leggett model, developed in the context of cold atomic gases confined in a harmonic trap, to higher dimensions. Universal characteristics en route to…
Based on the proposed earlier by the Author approach to macroscopic description of scalar interaction, this paper develops the macroscopic model of relativistic plasma with a fantom scalar interaction of elementary particles. In the given…
This paper introduces a method for studying the correlation structure of a range of responses modelled by a multivariate generalised linear mixed model (MGLMM). The methodology requires the existence of clusters of observations and that…
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolution of the system as a whole is described by the…
The validity of estimation and smoothing parameter selection for the wide class of generalized additive models for location, scale and shape (GAMLSS) relies on the correct specification of a likelihood function. Deviations from such…
We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method,…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
We consider population-imbalanced two-component Fermi gases under external harmonic confinement interacting through short-range two-body potentials with diverging s-wave scattering length. Using the fixed-node diffusion Monte Carlo method,…
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…
Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here…
The hydrogen atom as relativistic bound-state system of a proton and an electron in the complex-mass scheme is investigated. Interaction of a proton and an electron in the atom is described by the Lorentz-scalar Coulomb potential; the…
We consider Coulomb gas models for which the empirical measure typically concentrates, when the number of particles becomes large, on an equilibrium measure minimizing an electrostatic energy. We study the behavior when the gas is…
A system of interacting atoms is represented as an union of two subsystems, one of which is the system of atoms, and the other is an auxiliary scalar covariant field, which is equivalent to a given static interatomic potential of general…
We present a new, simple renormalization group method of investigating groundstate properties of interacting bosonic systems. Our method reduces the number of particles in a system, which makes numerical calculations possible for large…