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This short article presents a table of new equations which can be regarded as the generalized equations of the dispersionless limit of several nonlinear equations. From the definition expressed in an algebraic formula, one can get an…
A nonlinear quantum-optical process is considered: emission of photon pairs by the reflecting end of a fiber excited by a standing laser wave. Radiation occurs due to periodic changes in the optical length of the fiber over time. This…
We study for a dielectric particle the effect of surplus electrons on the anomalous scattering of light arising from the transverse optical phonon resonance in the particle's dielectric constant. Excess electrons affect the polarizability…
General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…
Classically the interaction between light and matter is given by the Maxwell relations. These are briefly reviewed and will be used as a basis to discuss several techniques that are used in optical spectroscopy. We then discuss the quantum…
A Central Limit Theorem is proved for linear random fields when sums are taken over finite disjoint union of rectangles. The approach does not rely upon the use of Beveridge Nelson decomposition and the conditions needed are similar to…
The existence of the weak limit as n --> infinity of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random…
Light propagation is investigated in the context of local anisotropic nonlinear dielectric media at rest with the dielectric coefficients $\epsilon^\mu{}_\nu = \epsilon^\mu{}_\nu (\vec{E},\vec{B})$ and constant $\mu$, in the limit of…
The intuition that the precision of observables is constrained by thermodynamic costs has recently been formalized through thermodynamic and kinetic uncertainty relations. While such trade-offs have been extensively studied in Markovian…
Under certain circumstances, some of which are made explicit here, one can deduce bounds on the full sum of a perturbation series of a physical quantity by using a variational Borel map on the partial series. The method is illustrated by…
We consider dark matter annihilation into Standard Model particles and show that the least detectable final states, namely neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
Nonlinear optical phenomena are generally governed by geometry in matter systems, as they depend on the spatial arrangement of atoms within materials or molecules. Metasurfaces, through precisely designed geometries on a subwavelength…
Mathematical inequalities, combined with atomic-physics sum rules, enable one to derive lower and upper bounds for the Rosseland and/or Planck mean opacities. The resulting constraints must be satisfied, either for pure elements or…
This paper presents the most complete framework to date for understanding the nonlinear optical trapping of highly absorbing nanoparticles within the dipole regime. Highly absorbing and plasmonic particles garner considerable interest due…
We derive upper and lower bounds on the absorption of ultraintense laser light by solids as a function of fundamental laser and plasma parameters. These limits emerge naturally from constrained optimization techniques applied to a…
The optical conductivity is the basic defining property of materials characterizing the current response toward time-dependent electric fields. In this work, following the approach of Kubo's response theory, we study the general properties…
The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems to perform machine learning more efficiently. In…
Nonlinear optical methods are becoming ubiquitous in many areas of modern photonics. They are, however, often limited to a certain range of input parameters, such as pulse energy and average power, since restrictions arise from, for…
We study light absorption in many-electron interacting systems beyond the linear regime by using a {\em single} broadband impulse of an electric field in the instantaneous limit. We determine non-pertubatively the absorption cross section…