Related papers: Estimates for the scattering map associated to a t…

We consider the third-order linear differential equation $$\displaystyle\frac{d^3\psi}{dx^3}+Q(x)\,\displaystyle\frac{d\psi}{dx}+P(x)\,\psi=k^3\,\psi,\qquad x\in\mathbb R,$$ where the complex-valued potentials $Q$ and $P$ are assumed to…

We study the linearization of the Dirichlet-to-Neumann map for Poincar\'e-Einstein metrics in even dimensions on an arbitrary compact manifold with boundary. By fixing a suitable gauge, we make the linearized Einstein equation elliptic. In…

In the smooth scattering theory framework, we consider a pair of self-adjoint operators $H_0$, $H$ and discuss the spectral projections of these operators corresponding to the interval $(-\infty,\lambda)$. The purpose of the paper is to…

Let $M$ be a finite volume, non-compact hyperbolic Riemann surface, possibly with elliptic fixed points, and let $\phi(s)$ denote the automorphic scattering determinant. From the known functional equation $\phi(s)\phi(1-s)=1$ one concludes…

We present numerical results for 2-d CP(N-1) models at \theta=0 and \pi obtained in the D-theory formulation. In this formulation we construct an efficient cluster algorithm and we show numerical evidence for a first order transition for…

We consider the scalar wave equation $\square_g \phi$ and the linearized Einstein-scalar field system around generalized Kasner spacetimes with spatial topology $\mathbb{T}^D$. In suitable regimes for the Kasner exponents, it is known that…

We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…

In time-reversal invariant electronic systems the scattering matrix is anti-symmetric. This property enables an effect, designated here as "scattering anomaly", such that the electron transport does not suffer from back reflections,…

Let $f:X\to X$ be a continuous map on a compact metric space with finite topological entropy. Further, we assume that the entropy map $\mu\mapsto h_\mu(f)$ is upper semi-continuous. It is well-known that this implies the continuity of the…

Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…

Scattering thresholds and their associated spectral square root branch points are ubiquitous in photonics. In this Letter, we show that the scattering matrix has a simple universal behavior near scattering thresholds. We use unitarity,…

The acoustic scattering operator on the real line is mapped to a Schr\"odinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse…

We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…

We prove a general Levinson's theorem for Schr\"odinger operators in two dimensions with threshold obstructions at zero energy. Our results confirm and simplify earlier seminal results of Boll\'e, Gesztesy et al., while providing an…

We use the configuration-space Faddeev formalism to study scattering of three particles in the double continuum where all particles are free. All scattering processes, starting from and ending in both single and double continua, are…

We consider 1-equivariant wave maps from \R \times (\R^3 \setminus B) to S^3 where B is a ball centered at 0, and the boundary of B gets mapped to a fixed point on S^3. We show that 1-equivariant maps of degree zero scatter to zero…

Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A…

For a time dependent Schr\"odinger equation, the scattering map is the map sending the asymptotic profile of solution as $t\to-\infty$ to its asymptotic profile as $t\to+\infty$. In this paper we show that, for certain class of metrics, the…

We study the Klein paradox for the semi-classical Dirac operator on $\R$ with potentials having constant limits, not necessarily the same at infinity. Using the complex WKB method, the time-independent scattering theory in terms of incoming…

We consider the operators $H_0=M_0^{-1}(x) P(D)$ and $H =M^{-1} (x) P(D)$ where $M_0 (x)$ and $M (x)$ are positively definite bounded matrix-valued functions and $P(D)$ is an elliptic differential operator. Our main result is that the wave…