Related papers: New photonic conservation laws in parametric nonli…
Over the past two decades, open systems that are described by a non-Hermitian Hamiltonian have become a subject of intense research. These systems encompass classical wave systems with balanced gain and loss, semiclassical models with mode…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
Photoluminescence (PL) is a fundamental light-matter interaction in which absorbed photons are re-emitted, playing a key role in science and engineering. It is commonly modeled by introducing a non-zero chemical potential into Planck's law…
We study a recently derived fully relativistic kinetic model for spin-1/2 particles. Firstly, the full set of conservation laws for energy, momentum and angular momentum are given, together with an expression for the (non-symmetric)…
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that anti-symmetric states are subradiant states for distributions…
The Thomson backscattering spectra in combined uniform magnetic and cosine-envelope circularly-polarized laser fields are studied in detail. With an introduction of the envelope modulation, the radiation spectra exhibit high complexity…
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…
General relativity predicts that energy and momentum conservation laws hold and that preferred frames do not exist. The parametrised post-Newtonian formalism (PPN) phenomenologically quantifies possible deviations from general relativity.…
Following Rivi\`ere's study of conservation laws for second order quasilinear systems with critical nonlinearty and Lamm/Rivi\`ere's generalization to fourth order, we consider similar systems of order $2m$. Typical examples are…
Exploiting the dynamics of Plasmonic Parametric Resonance (PPR), we introduce the theory of Plasmonic Parametric Absorbers (PPA). The key insight informing the PPA idea is that in the PPR process a pump field experiences an extinction rate…
Parity-time ($\mathcal{PT}$) symmetry, originally conceived for non-Hermitian open quantum systems, has opened an excitingly new avenue for the coherent control of light. By tailoring optical gain and loss in integrated photonic structures,…
A generalization of the KP equation involving higher-order dispersion is studied. This equation appears in several physical applications. As new results, the Lie point symmetries are obtained and used to derive conservation laws via…
Time-varying materials bring an extra degree of design freedom compared to their conventional time-invariant counterparts. However, few discussions have focused on the underlying physical difference between spatial and temporal boundaries.…
Noether's theorem connects symmetries to invariants in continuous systems, however its extension to discrete systems has remained elusive. Recognizing the lowest-order finite difference as the foundation of local continuity, a viable method…
We derive the Noether identities and the conservation laws for general gravitational models with arbitrarily interacting matter and gravitational fields. These conservation laws are used for the construction of the covariant equations of…
Photonic hyper-crystals combine the most interesting features of hyperbolic metamaterials and photonic crystals. Since the dispersion law of extraordinary photons in hyperbolic metamaterials does not exhibit the usual diffraction limit,…
We extend the generalize conservation law of light propagating in a one-dimensional $\cal PT$-symmetric system, i.e., $|T-1|=\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode…
We study the conservation laws in the teleparallel theory with a positive cosmological constant, an extension of the teleparallel theory possessing solutions with de Sitter asymptotics. Demanding that the canonical generators of the…
A cornerstone equation of optics, Snell's law, relates the angles of incidence and refraction for light passing through an interface between two media. It is built on two fundamental constrains: the conservation of tangential momentum and…
Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large. Underpinning the traditional rules for the refraction of an…