Point sources and rays in the phase-space representation of random electromagnetic fields

Random stationary electromagnetic fields can be modeled in terms of point sources disposed onto two distinct layers, named the radiant and the virtual layers. It allows describing the propagation of the power and the states of spatial coherence and polarization of the field by means of separate phase-space ray-maps. Spatial coherence of the field, correlation of the polarization angles and achievement of the Fresnel-Arago laws within the structured spatial coherence supports are the necessary conditions that determine the electromagnetic point sources in the virtual layer. The contributions of these sources produce two types of modulations on the electromagnetic field at the observation plane, one of them of scalar type is the interferometric power modulation, and the other one of vector type is de modulation of the polarization state provided by the radiant point sources, according to the Stokes' parameters. Some examples are presented.     

On the propagation of random electromagnetic fields with position-independent stochastic behavior

A certain kind of vectorial fields with position-independent stochastic behavior is introduced, for which several main features are preserved upon free propagation. For this set of random electromagnetic fields, it is shown that the uniform degree of polarization, the maximum attainable visibility in a Young experiment, and the expansion of the cross-spectral density tensor as the sum of totally-polarized and unpolarized terms are properties that apply for any propagation distance. An elementary example is also shown.     

Optical classification of random image fields using spectral synthetic discriminant functions

It is shown that the problem of classification of images that have the perfectly random nature may be solved with the help of synthetic discriminant functions being synthesized by least-squares technique to separate linearly the power spectra of the corresponding random image fields. The realization of the proposed method by means of an optical technique is discussed, and its efficiency is illustrated by two examples of real-life texture classification.     

A transition in the spectral statistics of quantum optical model by different electromagnetic fields

In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian’s parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit (N _A ~ 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics.     

Proca and electromagnetic fields

In the framework of the proper orthochronous Lorentz group, the old connection is revived between the electromagnetic field characterized by a self-dual tensor and a traceless second-rank spinor obeying the Proca equation. The relationship between this spinor and the Hertz potential also considered as a self-dual tensor is emphasized. The extension of this formalism to meet the covariance under the full Lorentz group is also discussed.     

New spectral representation of random sources and of the partially coherent fields that they generate

It is shown that, contrary to general belief, it is possible to construct a statistical ensemble of monochromatic oscillations, all of the same frequency, that yields rigorously the spectral and cross-spectral densities of a fluctuating, statistically stationary source and of the field that the source generates. New mode representations are also introduced. The modes may be interpreted as natural oscillations of sources and fields of any state of coherence.     

Gaussian random fields

Two results on Gaussian random fields are presented. The first characterizes the unit Gaussian random field by a strong independence property and the second determines Gaussian random fields that are generated by stochastic processes.     

The use of tricubic interpolation with spectral derivatives to integrate particle trajectories in complicated electromagnetic fields

Codes that calculate the trajectories of particles in complicated electromagnetic fields often include spectral methods, which take advantage of the speed of FFTs to rapidly solve for the fields. In this case, Hermite tricubic interpolation can be used to calculate the fields between grid points, with spectral derivates used to determine the interpolation coefficients. This method is extremely accurate, and in the case of electrostatic fields produces an energy conserving force when incorporated into a particle follower code.     

Neutrinos in electromagnetic fields and moving media

The history of the development of the theory of neutrino-flavor and neutrino-spin oscillations in electromagnetic fields and in a medium is briefly surveyed. A new Lorentz-invariant approach to describing neutrino oscillations in a medium is formulated in such a way that it makes it possible to consider the motion of a medium at an arbitrary velocity, including relativistic ones. This approach permits studying neutrinospin oscillations under the effect of an arbitrary external electromagnetic field. In particular, it is predicted that, in the field of an electromagnetic wave, new resonances may exist in neutrino oscillations. In the case of spin oscillations in various electromagnetic fields, the concept of a critical magnetic-field-component strength is introduced above which the oscillations become sizable. In considering neutrino oscillations in moving matter, it is shown within the Lorentz-invariant formalism that the relativistic motion of matter significantly affects the character of neutrino oscillations and can radically change the conditions under which the oscillations are resonantly enhanced. Possible new effects in neutrino oscillations are discussed for the case of neutrino propagation in relativistic fluxes of matter.     

Transport in random correlated fields

A review is given of recent developments in the diffusion properties of particles in the presence of local random fields as well as the conductivity of the analog random resistor network. The effect of long-range ferro- and antiferro-type correlations between the local fields on the diffusion and conductivity properties is considered. A physical realization for such spatial correlations is diffusion on linear polymers in the presence of external uniform bias field. For this case a universal diffusion law was found independent of the fractal dimension of the polymer chain or the Euclidean dimension in which the polymer is embedded. Recent results for diffusion in two dimensions in the presence of a special case of correlated local fields are also reviewed.     

Acoustic waves in random fields

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength sound waves, reveal frequency and amplitude alteration, the effect of which depends on the type of random field. In particular, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification. In another example, sound waves that are trapped in the vertical direction but are free to propagate horizontally are affected by a space-dependent random mass density field. This effect depends on the direction along which the field is varying. A random field, which varies along the horizontal direction, does not couple vertically standing modes but increases their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate, but the dispersion relation remains the same as in the case of the deterministic medium.     

Reorientations and random fields in plastic crystals

A simple Ising-like model is presented to describe the phase diagram of plastic crystals. In addition to a bilinear coupling between translations and rotations a reorientation-translation coupling is introduced via random fields which couple solely to rotational degrees of freedom. The physical basis of the reorientation-translation coupling is discussed using the rotational state hypothesis. The present approach is found to be consistent with some recent neutron experiments.     

Truesdell invariance in relativistic electromagnetic fields

The Truesdell derivative of a contravariant tensor fieldX ^ab is defined with respect to a null congruencel ^a analogous to the Truesdell stress rate in classical continuum mechanics. The dynamical consequences of the Truesdell invariance with respect to a timelike vectoru ^a of the stress-energy tensor characterizing a charged perfect fluid with null conductivity are the conservation of pressure (p), charged density (e) an expansion-free flow, constancy of the Maxwell scalars, and vanishing spin coefficients+¯ = ¯ – = = 0 (assuming freedom conditionsk = = + ¯ = 0). The electromagnetic energy momentum tensor for the special subcases of Ruse-Synge classification for typesA andB are described in terms of the spin coefficients introduced by Newman-Penrose.     

Four component electromagnetic fields and electrodynamics

Dirac-Maxwell equations with magnetic monopoles are generalized to electromagnetic fields by introducing fourth components to the fields and their solutions are obtained. The formalism is presented into tensor, dyonic as well as quaternionic forms and conservation theorems for the field energy and momenta are obtained involving the new contribution from the mutual interaction of the fields and currents. The generation of the standard modeste, tm andtem ofem waves is also obtained in the formalism.     

Null electromagnetic fields in general relativity

The necessary and sufficient condition that a general Riemannian space-time $$ds^2 = g_{ij} dx^i dx^j$$ , may represent a null electromagnetic field is S = C, where $$S = R_{hijk} F^{hi} F^{jk} ,C = C_{hijk} F^{hi} F^{jk} .$$ .     

Persistent spectral holes in external fields

Experimental results and model calculations of the effects of an external electric field on persistent spectral holes are reviewed. Hole-burning spectroscopy of impurity centers in crystals and amorphous solids yields information on various properties of the centers and their interaction with the electric field. The applications of persistent spectral hole burning presented in this paper include: optical-data storage in the electric-field dimension, modulation and pulse shaping of light beams, determination of the Debye-Waller factor of host-guest systems with strongly inhomogeneously broadened transitions, detection of ultra-sound and high-frequency acoustic phonons. The effects of a magnetic field and external pressure on persistent spectral holes are discussed.     

Quantum processes in short and intensive electromagnetic fields

This work provides an overview of our recent results in studying two most important and widely discussed quantum processes: electron-positron pairs production off a probe photon propagating through a polarized short-pulsed electromagnetic (e.g. laser) wave field or generalized Breit–Wheeler process, and a single a photon emission off an electron interacting with the laser pules, so-called non-linear Compton scattering. We show that the probabilities of particle production in both processes are determined by interplay of two dynamical effects, where the first one is related to the shape and duration of the pulse and the second one is non-linear dynamics of the interaction of charged fermions with a strong electromagnetic field. We elaborate suitable expressions for the production probabilities and cross sections, convenient for studying evolution of the plasma in presence of strong electromagnetic fields.