Related papers: Nonlinear Localized Coherent Spectrum of Beam-Beam…
Unsupervised spectral unmixing consists of representing each observed pixel as a combination of several pure materials called endmembers with their corresponding abundance fractions. Beyond the linear assumption, various nonlinear unmixing…
We introduce a one-dimensional (1D) spatially inhomogeneous Bose-Hubbard model (BHM) with the strength of the onsite repulsive interactions growing, with the discrete coordinate $z_{j}$, as $|z_{j}|^{\alpha }$ with $\alpha >0$. Recently,…
Quantum coherent control (1-3) is a powerful tool for steering the outcome of quantum processes towards a desired final state, by accurate manipulation of quantum interference between multiple pathways. Although coherent control techniques…
Building on the Radon transform of the Vlasov-Poisson equations, a macroscopic fluid model for the coherent beam-beam interaction has been developed. It is shown that the Vlasov equation, expressed in action-angle variables, can be reduced…
Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-forming instability in a wide variety of experiments and mathematical models. However, there is currently no mathematical theory to explain this…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the…
We discuss the strong interaction regime of the nonlinear Landau-Zener problem coming up at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation…
We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental…
We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear…
Recent technological advances allowed the coherent optical manipulation of high-energy electron wavepackets with attosecond precision. Here we theoretically investigate the collision of optically-modulated pulsed electron beams with atomic…
We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets,…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
Coupling light to ensembles of strongly interacting particles has emerged as a promising route toward achieving few photon nonlinearities. One specific way to implement this kind of nonlinearity is to interface light with highly excited…
In absence of a lens to form an image, incoherent or partially coherent light scattering off an obstructive or reflective object forms a broad intensity distribution in the far field with only feeble spatial features. We show here that…
Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro-differential equations. The aim of this review is to…
We investigate linear interference of a plane wave with different localised waves using coupled Fokas-Lenells equation(FLE) with four wave mixing (FWM) term. We obtain localised wave solution of the coupled FLE by linear superposition of…
In quantum interferometry, it is vital to control and utilize nonlinear interactions for achieving high-precision measurements. Attribute to their long coherent time and high controllability, ultracold atoms including Bose condensed atoms…
Resonances in the form of quasi-normal modes (QNMs) for open scattering systems can be generally identified in the far field through peaks of scattering spectra (\textit{e.g.} cross sections of scattering, extinction and absorption).…
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is…