Physics

Artificial magnetism at optical frequencies can be realized in metamaterials composed of periodic arrays of subwavelength elements, also called "meta-atoms". Optically-induced magnetic moments can be arranged in both unstaggered structures, naturally associated with ferromagnetic (FM) order, or staggered structures, linked correspondingly to antiferromagnetic (AFM) order. Here we demonstrate that such magnetic dipole orders of the lattices of meta-atoms can appear in low-symmetry Mie-resonant metasurfaces where each asymmetric dielectric (non-magnetic) meta-atom supports a localized trapped mode. We reveal that these all-dielectric resonant metasurfaces possess not only strong optical magnetic response but also they demonstrate a significant polarization rotation of the propagating electromagnetic waves at both FM and AFM resonances. We confirm these findings experimentally by measuring directly the spectral characteristics of different modes excited in all-dielectric metasurfaces, and mapping near-field patterns of the electromagnetic fields at the microwave frequencies.

We prepared a similarity between the Poisson equation in non-homogeneous magnetic material media and Dirac's one-dimensional equation for the zero-energy state, which establishes a connections with the Jackiw-Rebbi model in one dimension for this same state.

The local polarization of electromagnetic (EMW) and gravitational waves (GW) is discussed from an operational point of view, in which all the relevant mathematical framework is constructed in terms of measurements of the power absorbed by a local detector. The intrinsic dependence of the observations upon the nature of the detector is emphasized. In particular, the benefit of using a dual-symmetric detector, equally sensitive to the electric and magnetic fields of the EMW (resp. gravito-electric and gravito-magnetic tensor in the GW case) is pointed out. The Majorana stellar representation of the polarization is introduced, and its physical interpretation is highlighted. Finally, expressions for the energy density, linear momentum density, helicity and spin density of the wave in terms of the Majorana representation are presented.

Superexponential systems are characterized by a potential where dynamical degrees of freedom appear in both the base and the exponent of a power law. We explore the scattering dynamics of many-body systems governed by superexponential potentials. Each potential term exhibits a characteristic crossover via two saddle points from a region with a confining channel to two regions of asymptotically free motion. With increasing scattering energy in the channel we observe a transition from a direct backscattering behaviour to multiple backscattering and recollision events in this channel. We analyze this transition in detail by exploring both the properties of individual many-body trajectories and of large statistical ensembles of trajectories. The recollision trajectories occur for energies below and above the saddle points and typically exhibit an intermittent oscillatory behaviour with strongly varying amplitudes. In case of statistical ensembles the distribution of reflection times into the channel changes with increasing energy from a two-plateau structure to a single broad asymmetric peak structure. This can be understood by analyzing the corresponding momentum-time maps which undergo a transition from a two-valued curve to a broad distribution. We close by providing an outlook onto future perspectives of these uncommon model systems.

Complex systems often have features that can be modeled by advanced mathematical tools [1]. Of special interests are the features of complex systems that have a network structure as such systems are important for modeling technological and social processes [3, 4]. In our previous research we have discussed the flow of a single substance in a channel of network. It may happen however that two substances flow in the same channel of network. In addition the substances may react and then the question arises about the distribution of the amounts of the substances in the segments of the channel. A study of the dynamics of the flow of the substances as well as a study of the distribution of the substances is presented in this paper on the base of a discrete - time model of flow of substances in the nodes of a channel of a network.

In this paper we present a detailed physical analysis of the formation of the propagation transverse modes in planar dielectric waveguides using a mathematical-physics approach. We demonstrate physically that, at the wavelength scale, the pure stationary mode inside planar waveguide is described by the cosine function. Meanwhile, the sine function yields a quasi-stationary periodic mode.

We consider a problem of finding the maximum attainable energy at a cyclotron as an exercise in the introductory relativity course and comment on some subtle points of the solution.

Macroscopic Maxwellian electrodynamics consists of four field quantities along with electric charges and electric currents. The fields occur in pairs, the primary ones being the electric and magnetic fields (E,B), and the other the excitation fields (D,H). The link between the two pairs of field is provided by constitutive relations, which specify (D,H) in terms of (E,B); this last connection enabling Maxwell's (differential) equations to be combined in a way that supports waves. In this paper we examine the role played by the excitation fields (D,H), showing that they can be regarded as not having a physical existence, and are merely playing a mathematically convenient role. This point of view is made particularly relevant when we consider competing constitutive models of permanent magnets, which although having the same measurable magnetic properties, have startlingly different behaviours for the magnetic excitation field H.

A fundamental result of classical electromagnetism is that Maxwell's equations imply that electric charge is locally conserved. Here we show the converse: Local charge conservation implies the local existence of fields satisfying Maxwell's equations. This holds true for any conserved quantity satisfying a continuity equation. It is obtained by means of a strong form of the Poincaré lemma presented here that states: Divergence-free multivector fields locally possess curl-free antiderivatives on flat manifolds. The above converse is an application of this lemma in the case of divergence-free vector fields in spacetime. We also provide conditions under which the result generalizes to curved manifolds.

In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form and the special case of the purely gyroscopic motion on the sphere has been discussed. For the geodetic case when the potential is equal to zero the comparison between the geodetic and geodesic solutions have been done and illustrated in the case of a particular choice of the constants of motion of the problem. The obtained results could be applied, among others, in geophysical problems, e.g., for description of the motion of a drop of fat or a spot of oil on the surface of the ocean (e.g., produced during some "ecological disaster") or the motion of continental plates, or generally in biomechanical problems, e.g., for description of the motion of objects with internal structure on different curved two-dimensional surfaces (e.g., transport of proteins along the curved biological membranes).