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We discuss the recently measured event-by-event multiplicity fluctuations in relativistic heavy-ion collisions. It is shown that the observed non-monotonic behaviour of the scaled variance of multiplicity distribution as a function of…
Using full-wave numerical simulations and analytical multipole expansions we investigated the properties of real-space polarization singularities that emerge in light scattering by subwavelength particles. We considered spherical and torus…
A single paraxial beam reflection at a plane dielectric interface, configured appropriately, can lead to the formation of a polarization singularity in the inhomogeneously polarized output beam-field for any central angle of incidence. In…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
An analysis of the matrix models representing the polarimetric properties of light and material media is carried out by using the concept of the coherency matrix, which leads to the identification and definition of their corresponding…
We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies…
This paper extends the concept of generalized polarization tensors (GPTs), which was previously defined for inclusions with homogeneous conductivities, to inhomogeneous conductivity inclusions. We begin by giving two slightly different but…
We describe isometric embeddings of polar Grassmann graphs formed by non-maximal singular subspaces. In almost all cases, they are induced by collinearity preserving injections of polar spaces. As a simple consequence of this result, we get…
A consistent description of the radiative polarization for relativistic electrons in intense laser fields is derived by generalizing the Sokolov-Ternov effect in general field structure. The new form together with the spin-dependent…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
The polarisation set of a vector-valued distribution generalises the wavefront set and captures fibre-directional information about its singularities in addition to their phase space description. Motivated by problems in quantum field…
We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset…
Polarity is a fundamental reciprocal duality of $n$-dimensional projective geometry which associates to points polar hyperplanes, and more generally $k$-dimensional convex bodies to polar $(n-1-k)$-dimensional convex bodies. It is…
Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…
We derive a generalized unitarity relation for an arbitrary linear scattering system that may violate unitarity, time-reversal invariance, ${\cal PT}$-symmetry, and transmission reciprocity.
An arrangement of hyperplanes is a finite collection of hyperplanes in a real Euclidean space. To such a collection one associates the characteristic polynomial that encodes the combinatorics of intersections of the hyperplanes. Finding the…
The entropic discriminant is a non-negative polynomial associated to a matrix. It arises in contexts ranging from statistics and linear programming to singularity theory and algebraic geometry. It describes the complex branch locus of the…