Related papers: New photonic conservation laws in parametric nonli…
Two approaches (micro- and macro- investigations) are used to determine the dimension dependences of the optical parameters of the nanometer-scale layers of materials. It is shown that both an index of refraction and coefficient of…
The basic laws of geometrical optics can be deduced from energy-momentum conservation for electromagnetic waves, without other wave concepts. However, the concept of quanta is required; it arises naturally, hence such a hypothesis could…
X-ray telescopes are an exceptional tool for searching for new fundamental physics. In particular, X-ray observations have already placed world-leading bounds on the interaction between photons and axion-like particles (ALPs). ALPs are…
We show how a complex Snell's law can be used to describe the refraction of surface plasmon polaritons (SPPs) at an interface between two metals, validating its predictions with 3-D electrodynamics simulations. Refraction gives rise to…
We show that the so-called hidden potential symmetries considered in a recent paper [Gandarias M., Physica A, 2008, V.387, 2234-2242] are ordinary potential symmetries that can be obtained using the method introduced by Bluman and…
The solution of time dependent differential equations with neural networks has attracted a lot of attention recently. The central idea is to learn the laws that govern the evolution of the solution from data, which might be polluted with…
Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion…
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law…
The theory of special relativity can be generalized by means of a new principle called Conservation of Information. This allows a derivation of the constancy of the velocity of light with respect to moving frames, and, consequently, of…
The thermodynamical properties of the photon-plasma system had been studied using statistical physics approach. Photons develop an effective mass in the medium thus -- as a result of the finite chemical potential -- a photon Bose-Einstein…
We demonstrate that hyperuniformity, the suppression of density fluctuations at large length scales, emerges generically from the interplay between conservation laws and non-equilibrium driving. The underlying mechanism for this emergence…
We present a theoretical framework for analyzing the loss of optical angular momentum (AM), including spin (SAM) and orbital (OAM) components, in light-matter interactions. Conventional SAM and OAM conservation laws rely on transverse field…
Conservation laws are of great theoretical and practical interest. We describe a novel approach to machine learning conservation laws of finite-dimensional dynamical systems using trajectory data. It is the first such approach based on…
We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations...etc) in divergence form. This divergence free quantities generalize to target manifolds without…
We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…
There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed…
We study higher-order conservation laws of the non-linearizable elliptic Poisson equation $ \frac{{\partial}^2 u}{\partial z \partial \bar{z}} = -f(u) $ as elements of the characteristic cohomology of the associated exterior differential…
Trapping light in open cavities is a long sought "holy grail" of nanophotonics. Plasmonic materials may offer a unique opportunity in this context, as they may fully suppress the radiation loss and enable the observation of spatially…