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This paper is the first in a series devoted to the numerical study of nonlinear interactions of electromagnetic waves with plasma. We start with non-magnetized pair plasmas, where the primary processes are induced (Compton) scattering and…

A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…

Curious spectral properties of an ensemble of random unitary matrices appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in [Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer co-prime m,n and…

For $N$ spin-polarized fermions with harmonic pair interactions in a $1$-dimensional trap an odd-even effect is found. The spectrum of the $1$-particle reduced density matrix of the system's ground state differs qualitatively for $N$ odd…

We numerically investigated the dynamics of a mixture of finite-size active and passive particles in a linear array of convection rolls. The interplay of advection and steric interactions produces a number of interesting effects, like the…

We investigate joint spectral characteristics of a family of matrices $\mathcal F $, associated with products in the semigroup generated by $\mathcal F$. In the literature, extremal measures such as the well-known joint spectral radius and…

Many molecular junctions display stochastic telegraphic switching between two distinct current values, which is therefore an important source of fluctuations in nanoscale quantum transport. We investigate electronic fluctuations arising via…

We study the structure of eigenstates in two-body interaction random matrix ensembles and find significant deviations from random matrix theory expectations. The deviations are most prominent in the tails of the spectral density and…

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…

For a number of non-interacting identical particles entering a multi-channel scatterer in various wave packet states, we construct a generating function for the probabilities of various scattering outcomes. This is used to evaluate the mean…

Some recent publications by authors from the University of Maryland analyse the fluctuations of multi-port model parameters in stochastic environments. These authors use random matrix theory (RMT) for estimates concerning eigenfunction…

We study the ensemble of complex symmetric matrices. The ensemble is useful in the study of effect of dissipation on systems with time reversal invariance. We consider the nearest neighbor spacing distribution and spacing ratio to…

We analyze the spectral properties of correlation matrices between distinct statistical systems. Such matrices are intrinsically non symmetric, and lend themselves to extend the spectral analyses usually performed on standard Pearson…

Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…

A full understanding of transport in dense, interacting suspensions requires analysis frameworks sensitive to self and collective dynamics across all relevant spatial and temporal scales. Here we introduce a trajectory-free approach to…

The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…

We study the fluctuations of the two-time dependent global roughness of finite size elastic lines in a quenched random environment. We propose a scaling form for the roughness distribution function that accounts for the two-time,…

We study the effect of parameter fluctuations on synchronization of a coupled chaotic system. The fluctuations to the parameter can be random or it can be a periodic modulation. For random fluctuations we introduce a new quantity, the…

We use random matrix models to investigate the ground state energy of electrons confined to a nanoparticle. Our expression for the energy includes the charging effect, the single-particle energies, and the residual screened interactions…

We study an infinite system of independent symmetric random walks on a hierarchical group, in particular, the c-random walks. Such walks are used, e.g., in population genetics. The number variance problem consists in investigating if the…