相关论文: Long Range Scattering and Modified Wave Operators …

We offer a consistent dynamical formulation of stationary scattering in two and three dimensions that is based on a suitable multidimensional generalization of the transfer matrix. This is a linear operator acting in an infinite-dimensional…

We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators $(\widetilde\Delta,\Delta)$, where $\Delta$ is the free…

This paper is about the scattering theory for one-dimensional matrix Schr\"odinger operators with a matrix potential having a finite first moment. The transmission coefficients are analytically continued and extended to the band edges. An…

We prove that the wave operators of scattering theory for the fourth order Schr\"odinger operators $\Delta^2 + V(x)$ in ${\mathbb R}^4$ are bounded in $L^p({\mathbb R}^4)$ for the set of $p$'s of $(1,\infty)$ depending on the kind of…

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both…

We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of…

We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our aim is to show that the solution scatters to a modified…

We prove that the scattering operators and wave operators are well-defined in the energy space for the system of defocusing Schr\"odinger equations $$ \begin{cases} i\partial_t u_\mu + \Delta u_\mu - \sum_{\mu,\nu=1 }^N…

We provide new formulae for the wave operators in the context of the Friedrichs-Faddeev model. Continuity with respect to the energy of the scattering matrix and a few results on eigenfunctions corresponding to embedded eigenvalues are also…

We study the two-body problem with a spatially modulated interaction potential using a two-channel model, in which the inter-channel coupling is provided by an optical standing wave and its strength modulates periodically in space. As the…

We study a time-dependent scattering theory for Schr\"{o}dinger operators on a manifold with asymptotically polynomially growing ends. We use the Mourre theory to show the spectral properties of self-adjoint second-order elliptic operators.…

The control of wave scattering in complex non-Hermitian settings is an exciting subject -- often challenging the creativity of researchers and stimulating the imagination of the public. Successful outcomes include invisibility cloaks,…

This work considers two linear operators which yield wave modes that are classified as neutrally stable, yet have responses that grow or decay in time. Previously, King et al. (Phys. Rev. Fluids, 1, 2016, 073604:1-19) and Huber et al. (IMA…

We are concerned with the acoustic scattering problem, at a frequency $\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\Omega$ in…

The inverse scattering theory for many-body systems in quantum mechanics is an important and difficult issue not only in physics---atomic physics, molecular physics and nuclear physics---but also mathematics. The major purpose in this paper…

The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complimentary situations, firstly when the…

We study the scattering properties of Schr\"{o}dinger operators with potentials that have short-range decay along a collection of rays in $\bbR^d$. This generalizes the classical setting of short-range scattering in which the potential is…

Recent work by Hintz--Vasy provides a partial asymptotic analysis of the low-energy limit of scattering for Schr\"odinger operators with a short-range potential. Using a slight refinement of Hintz's algorithm, we complete the asymptotic…

In one dimension one can dissect a scattering potential $ v(x) $ into pieces $ v_i(x) $ and use the notion of the transfer matrix to determine the scattering content of $ v(x) $ from that of $ v_i(x) $. This observation has numerous…

The behaviour of solutions to the partial differential equation $(D + \lambda W)f_\lambda = 0$ is discussed, where $D$ is a normal hyperbolic partial differential operator, or pre-normal hyperbolic operator, on $n$-dimensional Minkowski…