Related papers: Limiting absorption principle for the dissipative …
The resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened, as only a fraction of the ensemble contributes to the absorption at any given optical frequency. Recovering the lost…
In this paper we give new results on domain decomposition preconditioners for GMRES when computing piecewise-linear finite-element approximations of the Helmholtz equation $-\Delta u - (k^2+ {\rm i} \varepsilon)u = f$, with absorption…
We consider the resolvent estimates and properties of virtual states of the higher order derivatives in one dimension, focusing on Schroedinger-type operators of degree $N=3$ (the approach applies to higher orders). The derivation is based…
In this paper I give an explicit construction of an analogue of eigenspace for points of the singular spectrum of a self-adjoint operator. This construction is based on an abstract version of homogeneous Lippmann-Schwinger equation.
We present a new formulation of the multipolar expansion of an exact boundary condition for the wave equation, which is truncated at the quadrupolar order. Using an auxiliary function, that is the solution of a wave equation on the sphere…
A central task of theoretical physics is to analyse spectral properties of quantum mechanical observables. In this endeavour, Mourre's conjugate operator method emerged as an effective tool in the spectral theory of Schr\"odinger operators.…
We present a simple closed expression for determining the condition for Coherent Perfect Absorption derived through electromagnetic wave treatment and interface boundary conditions. Apart from providing physical insight this expression can…
We consider dissipative Schroedinger operators of the form $H=-\Delta+V(x)$ on $L^2(\mathbb R^3)$, with $V(x)$ a complex, bounded and decaying potential with a non-positive imaginary part. We prove a topological version of Levinson's…
We prove exponential decay for the solution of the Schr{\"o}dinger equation on a dissipative waveguide. The absorption is effective everywhere on the boundary but the geometric control condition is not satisfied. The proof relies on…
We consider the asymptotic behavior of solutions to the Monge--Amp\`ere equations with slow convergence rate at infinity and fulfill previous results under faster convergence rate by Bao--Li--Zhang [Calc. Var PDE. 52(2015). pp. 39-63].…
We present calculations of the absorption spectrum of semiconductors and insulators comparing various approaches: (i) the two-particle Bethe-Salpeter equation of Many-Body Perturbation Theory; (ii) time-dependent density-functional theory…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we…
We propose a method for solving constrained fixed point problems involving compositions of Lipschitz pseudo contractive and firmly nonexpansive operators in Hilbert spaces. Each iteration of the method uses separate evaluations of these…
Semi-linear response theory determines the absorption coefficient of a driven system using a resistor network calculation: Each unperturbed energy level of a particle in a vibrating trap, or of an electron in a mesoscopic ring, is regarded…
We consider admissible weak solutions to the compressible Euler system with source terms, which include rotating shallow water system and the Euler system with damping as special examples. In the case of anti-symmetric sources such as…
We prove $L^p$-$L^q$-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. Similar techniques apply to the…
We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…
This paper focuses on infinite-horizon optimal control problems for dissipative systems and the relations to their finite-horizon formulations. We show that, for a large class of problems, dissipativity of the state equation, when a…
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…