Related papers: Stationary scattering theory for repulsive Hamilto…
We consider the Hamiltonian system consisting of scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subject to an external potential. The stationary solutions of the system are a Coulomb…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
Scattering on the energy shell is viewed here as the relation between the bound states of the Hamiltonian, restricted to sections on leads that are asymptotically independent, far away from the interaction region. The decomposition is…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
We develop a scattering theory for perturbations of powers of the Laplacian on asymptotically Euclidean manifolds. The (absolute) scattering matrix is shown to be a Fourier integral operator associated to the geodesic flow at time \pi on…
We consider a class of unbounded self-adjoint operators including the Hamiltonian of the Jaynes-Cummings model without the rotating-wave approximation (RWA). The corresponding operators are defined by infinite Jacobi matrices with discrete…
We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates…
We study the stability of the reconstruction of the scattering and absorption coefficients in a stationary linear transport equation from knowledge of the full albedo operator in dimension $n\geq3$. The albedo operator is defined as the…
This paper studies the asymptotic behavior of global solutions to the generalized Hartree equation $$i\dot u+\Delta u+(I_\alpha *|\cdot|^b|u|^p)|x|^b|u|^{p-2}u=0 .$$ Indeed, using a new approach due to \cite{dm}, one proves the scattering…
We characterize the optical response of a three-level atom subjected to an incoherent pump and continuously illuminated with a weak, quasi-resonant probe field. To this end, we apply a wavefunction approach based on QED Hamiltonian…
We study the final state problem for the Hartree equation with repulsive Coulomb potential: \[i\partial_t u+\frac{1}{2}\Delta u-\frac{1}{|x|}u=((-\Delta)^{-1}|u|)^2u\] We show the work in \cite{KaMi} can be extended to the Hartree…
We introduce a novel framework for the analysis of linear wave equations on nonstationary asymptotically flat spacetimes, under the assumptions of mode stability and absence of zero energy resonances for a stationary model operator. Our…
In this article we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with $n$ open ends and where we define the Hamiltonian to be (minus) the Laplace operator with general boundary conditions at the…
In this article we study port-Hamiltonian partial differential equations on certain one-dimensional manifolds. We classify those boundary conditions that give rise to contraction semigroups. As an application we study port-Hamiltonian…
We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H = H_V - i C^* C$, where $H_V = H_0 + V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators…
We establish that solitary stationary waves in three dimensional viscous incompressible fluids are a generic phenomenon and that every such solution is a vanishing wave-speed limit along a one parameter family of traveling waves. The…
This work investigates single-photon scattering in a one-dimensional coupled-resonator waveguide coupled to a giant atom with a complex on-site energy. Within the generalized projection operator formalism, we derive analytical expressions…
Scattering through a straight two-dimensional quantum waveguide Rx(0,d) with Dirichlet boundary conditions on (-\infty,0)x{y=0} \cup (0,\infty)x{y=d} and Neumann boundary condition on (-infty,0)x{y=d} \cup (0,\infty)x{y=0} is considered…
The paper is a presentation of recent investigations on potential scattering in R^3. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. A topological version of Levinson's theorem…
We are concerned with the radially symmetric stationary wave for the exterior problem of two-dimensional Burgers equation. A sufficient and necessary condition to guarantee the existence of such a stationary wave is given and it is also…