Related papers: Limiting absorption principle for long-range pertu…
Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive…
We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase.…
We study an analogue of the large deviation principle for mixed measures associated with a class of $\log$-concave probability measures whose densities depend on the gauge function of a convex body. For convex bodies in $\mathbb{R}^n$, we…
This work addresses the imposition of outflow boundary conditions for one-dimensional conservation laws. While a highly accurate numerical solution can be obtained in the interior of the domain, boundary discretization can lead to…
Manipulating and controlling the optical energy flow inside random media is a research frontier of photonics and the basis of novel laser designs. In particular, light amplification in randomly dispersed active inclusions under external…
We define a numerical scheme that allows to approximate a given Hamiltonian by an effective one, by requiring several constraints determined by exact properties of generic ''short range'' Hamiltonians. In this way the standard lattice fixed…
We develop eigenvalue estimates for the Laplacians on discrete and metric graphs using different types of boundary conditions at the vertices of the metric graph. Via an explicit correspondence of the equilateral metric and discrete graph…
We present a discretization of the linear advection of differential forms on bounded domains. The framework previously established is extended to incorporate the Lie derivative, $\mathcal L$, by means of Cartan's homotopy formula. The…
A method for realizing asymmetric (one-way) transmission of discretized light in modulated, linear and purely passive optical lattices is suggested, which exploits the idea of unidirectional coherent perfect absorption. The system consists…
We consider an open manifold which is the interior of a compact manifold with boundary. Assuming gauge invariance, we classify magnetic fields with compact support into being trapping or non-trapping. We study spectral properties of the…
We theoretically and experimentally investigate the optical absorption properties of heterostructures composed of graphene films and truncated photonic crystals (PCs) in the visible range. The experimental results show that the absorption…
Translationnally invariant bidimensional magnetic Laplacians are considered. Using an improved version of the harmonic approximation, we establish the absence of point spectrum under various assumptions on the behavior of the magnetic…
We study the discrete version of the $p$-Laplacian. Based on its variational properties we discuss some features of the associated parabolic problem. Our approach allows us in turn to obtain interesting information about positivity and…
Under a rescaling of longitudinal coordinates $x^{0,3}$ by a factor $\lambda$ which is taken to zero, the classical QCD action simplifies dramatically. This is the high-energy limit, as $\lambda$ is of order $s^{-1/2}$, where $s$ is the…
An electro-absorption optical modulator concept based upon a dual-graphene layer is presented. The device consists of a silicon-on-insulator waveguide upon which two graphene layers reside, separated by a thin insulating region. The lower…
We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel…
Within linear-response theory we derive a response function that thoroughly takes into account the influence of elastic scattering and is valid beyond the long-wavelength limit. We apply the theo-ry to plasmons in graphene and the…
Electromagnetic waves propagating in a layered superconductor with arbitrary momentum with respect to the main crystallographic directions display an unavoidable mixing between longitudinal and transverse degrees of freedom. Here we show…
We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity $B$ perpendicularly aligned to the membrane. By expanding…
We derive a new implementation of linear covariant gauges on the lattice, based on a minimizing functional that can be interpreted as the Hamiltonian of a spin-glass model in a random external magnetic field. We show that our method solves…