Related papers: High-Contrast Transmission Resonances for the Lam\…
We consider the large $L$ limit of one dimensional Schr\"odinger operators $H_L=-d^2/dx^2 + V_1(x) + V_{2,L}(x)$ in two cases: when $V_{2,L}(x)=V_2(x-L)$ and when $V_{2,L}(x)=e^{-cL}\delta(x-L)$. This is motivated by some recent work of…
In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is convolved with the Coulomb potential 1/|x|, and it produces the long-range interaction…
Lattice resonances are collective optical modes supported by periodic arrays of scatterers, arising from their coherent interaction enabled by the underlying periodicity. Owing to their collective nature, these resonances produce optical…
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic…
The propagation of an electromagnetic wave in a one-dimensional fractal object, the Cantor set, is studied. The transfer matrix of the wave amplitude is formulated and its renormalization transformation is analyzed. The focus is on resonant…
When sources of energy gain and loss are introduced to a wave-scattering system, the underlying mathematical formulation will be non-Hermitian. This paves the way for the existence of exceptional points, where eigenmodes are linearly…
We study resonance for the Helmholz equation with a finite frequency in a plasmonic material of negative dielectric constant in two and three dimensions. We show that the quasi-static approximation is valid for diametrically small…
We extend the method of multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of…
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim \epsilon^{-2}$ one component of the system is described in the main…
We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…
A long-standing area of materials science research has been the study of electrostatic, magnetic, and elastic fields in composite with densely packed inclusions whose material properties differ from that of the background. For a general…
Effective mass Klein-Gordon equation for the asymmetric Hulth{\'e}n potential is solved in terms of hypergeometric functions. Results are obtained for the scattering and bound states with the position dependent mass and constant mass, as a…
When waves impinge on a disordered material they are back-scattered and form a highly complex interference pattern. Suppressing any such distortions in the free propagation of a wave is a challenging task with many applications in a number…
Unraveling real eigenfrequencies in non-Hermitian $\mathcal{PT}$-symmetric Hamiltonians has opened new avenues in quantum physics, photonics, and most recently, phononics. However, the existing literature squarely focuses on exploiting such…
A parametric beam lattice model is formulated to analyse the propagation properties of elastic in-plane waves in an auxetic material based on a hexachiral topology of the periodic cell, equipped with inertial local resonators. The…
Recent studies of transport phenomena with complex potentials are explained by generic square root singularities of spectrum and eigenfunctions of non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that such…
We study a molecular lattice Hamiltonian in which polaronic charge carriers interact with non linear potentials provided by local atomic fluctuations between two equilibrium sites. The path integral formalism is applied to select the class…
We consider normal forms in `magnetic bottle' type Hamiltonians of the form $H=\frac{1}{2}(\rho^2_\rho+\omega^2_1\rho^2) +\frac{1}{2}p^2_z+hot$ (second frequency $\omega_2$ equal to zero in the lowest order). Our main results are: i) a…
We analyze some specific features of the beam-plasma instability. In particular, non-perturbative effects in the dispersion relation are studied when the standard perturbative inverse Landau damping treatment breaks down. We also elucidate…
Scattering resonances play a crucial role in understanding wave behavior in various physical systems. While significant progress has been made in analyzing resonances in high-contrast and nonlinear media, a general characterization of…