Related papers: Dielectric scattering resonances for high-refracti…
We study the asymptotic behavior of the Schr\"odinger equation in the presence of a nonlinearity of Hartree type in the semi-classical regime. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading…
We demonstrate that a bianisotropic response associated with a broken mirror symmetry of a dielectric resonator allows opening a band gap in simple square lattice arrays of such resonators. Realizing the proposed system as an array of…
We study wave propagation in strongly nonlinear 1D diatomic granular crystals under an impact load. Depending on the mass ratio of the `light' to `heavy' beads, this system exhibits rich wave dynamics from highly localized traveling waves…
We theoretically and experimentally investigate the formation of dissipative coherent structures in Kerr nonlinear optical microresonators, whose integrated dispersion exceeds the free-spectral range. We demonstrate that the presence of any…
In this paper, we study the instability of highly-oscillating solutions to semi-linear hyperbolic systems. A instability criterion was given in \cite{Lu} under rather strong separation conditions of resonance sets: coupled resonance sets…
We study dielectric breakdown in a semi-classical bond percolation model for nonlinear composite materials introduced by us and the related breakdown exponent near the percolation threshold in two dimensions. The breakdown exponent after…
The study of resonant dielectric nanostructures with high refractive index is a new research direction in nanoscale optics and metamaterial-inspired nanophotonics. Because of the unique optically-induced electric and magnetic Mie…
We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for…
We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive…
We study the dynamics of a pair of nonlinear split-ring resonators (a `metadimer') excited by an alternating magnetic field and coupled magnetically. Linear metadimers of this kind have been recently used as the elementary components for…
We investigate the structure of resonance widths of a Bose-Hubbard Dimer with intersite hopping amplitude $k$, which is coupled to continuum at one of the sites with strength $\gamma$. Using an effective non-Hermitian Hamiltonian formalism,…
We investigate a general system of two coupled harmonic oscillators with cubic nonlinearity. Without damping, the system is Hamiltonian, with the origin as an elliptic equilibrium characterized by two distinct linear frequencies. To…
We have realized a hybrid solid-state quantum device in which a single-electron semiconductor double quantum dot is dipole coupled to a superconducting microwave frequency transmission line resonator. The dipolar interaction between the two…
In our earlier work [13], we introduced a novel quasi-Minnaert resonance for three-dimensional elastic wave scattering in the sub-wavelength regime. Therein, we provided a rigorous analysis of the boundary localization and surface resonance…
The propagation of waves in the nonlinear acoustic metamaterials (NAMs) is fundamentally different from that in the conventional linear ones. In this article we consider two one-dimensional NAM systems featuring respectively a diatomic and…
In this study, we present several improvements of the non-relativistic Friedrichs-Lee model with multiple discrete and continuous states and still retain its solvability. Our findings establish a solid theoretical basis for the exploration…
Quantum annealing provides a promising way to solve combinational optimization problems where the solutions correspond to the ground state of the Ising Hamiltonian. We can implement quantum annealing using the Kerr non-linear resonators,…
We investigate resonances in positron-sodium scattering using the $R$-matrix propagation method formulated in hyperspherical coordinates. The interaction between the sodium core and the valence electron is described by analytical model…
High refractive index dielectric spheres present remarkable light-scattering properties in the spectral range dominated by dipolar modes. However, most of these properties are absent for larger spheres under plane wave illumination. Here,…
We consider dynamical systems depending on one or more real parameters, and assuming that, for some ``critical'' value of the parameters, the eigenvalues of the linear part are resonant, we discuss the existence -- under suitable hypotheses…