Related papers: New photonic conservation laws in parametric nonli…
We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
Symmetry plays a fundamentally important role in physics. In this work, we find a conservation law, $S^{\dagger}(H_{c}^{\dagger})S(H_{c})=I$, which is valid for any non-Hermitian scattering center $H_c$. As a result, the reflections and…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
Highly directional radiation from photonic structures is important for many applications, including high power photonic crystal surface emitting lasers, grating couplers, and light detection and ranging devices. However, previous…
Motivated by various theoretical arguments that the Planck energy (Ep - 10^19 GeV) - should herald departures from Lorentz invariance, and the possibility of testing these expectations in the not too distant future, two so-called "Doubly…
Conservation laws of the nonlinear Schr\"{o}dinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the self-steepening. In a context of group theory, we derive a…
The peculiar features of the mixing in the neutral pseudoscalar mesons K0--antiK0 can be introduced by the analogy to the optical polarization. The time-reversed not-invariant processes and the related phenomenon of CP-nonconservation can…
The conservation laws of nonrelativistic and relativistic systems are reviewed and some simple illustrations are provided for the restrictive nature of the relativistic conservation law involving the center of energy compared to the…
We show that the asymmetries in the nuclear resonance fluorescence processes with a circular polarized photon beam may be used as a tool for studying the parity non-conservation (PNC) in nuclei. The PNC asymmetry measurements both in…
For nonlinear Schroedinger equations with a power nonlinearity, a new approach to derive the conservation law of the momentum and the pseudo conformal conservation law is obtained. Since this approach does not contain approximating…
We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created fluctuationally from a background Zero Point Field.…
Some of recent important developments are overviewed, several longstanding open problems are discussed, and a perspective is presented for the mathematical theory of multidimensional conservation laws. Some basic features and phenomena of…
We prove that $p $-harmonic systems with antisymmetric potentials can be written in divergence form as a conservation law. This extends to the $p$-harmonic framework the original work from 2006 of the second author for $p=2$…
We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible…
We explore matrix product state approximations to wavefunctions which have spontaneously broken symmetries or are critical. We are motivated by the fact that symmetries, and their associated conservation laws, lead to block-sparse matrix…
We suggest a new relativity principle, which asserts the impossibility to distinguish the state of rest and the state of motion at the constant velocity of a system, if no work is done to the system in question during its motion. We suggest…
Symmetries and their associated selection rules are extremely useful in all fields of science. In particular, for system that include electromagnetic (EM) fields interacting with matter, it has been shown that both of symmetries of matter…
Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing…
We study the conservation laws associated with the asymptotic Poincare symmetry of spacetime in the general teleparallel theory of gravity. Demanding that the canonical Poincare generators have well defined functional derivatives in a…