Related papers: Asymptotic Completeness and S-Matrix for Singular …
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…
In this paper we consider scattering theory on manifolds with special cusp-like metric singularities of warped product type g=dx^2 + x^(-2a)h, where a>0. These metrics form a natural subset in the class of metrics with warped product…
In this work, we investigate time-dependent wave scattering by multiple small particles of arbitrary shape. To approximate the solution of the associated boundary-value problem, we derive an asymptotic model that is valid in the limit as…
We establish necessary and sufficient conditions for convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. We show that this convergence is equivalent to asymptotic independence…
We formulate simple graphical rules which allow explicit calculation of nonperturbative $c=1$ $S$-matrices. This allows us to investigate the constraint of nonperturbative unitarity, which indeed rules out some theories. Nevertheless, we…
Let $A$ and $A_{1}$ are unbounded selfadjoint operators in a Hilbert space $\mathcal{H}$. Following \cite{AK} we call $A_{1}$ a \textit{singular} perturbation of $A$ if $A$ and $A_{1}$ have different domains…
A complete one-dimensional scattering of a spinless particle on a time-independent potential barrier is considered. To describe separately transmitted and reflected particles in the corresponding subsets of identical experiments, we…
Asymptotic representations for large values of the hyperradius are constructed for the scattering wave function of a system of $ N $ particles considered as a generalized function of angular variable coordinates. The coefficients of the…
We study the scattering properties of $N$ identical one-dimensional localized $\mathcal{PT}$-symmetric potentials, connected in series as well as in parallel. We derive a general transfer matrix formalism for parallel coupled quantum…
This paper treats the dynamics and scattering of a model of coupled oscillating systems, a finite dimensional one and a wave field on the half line. The coupling is realized producing the family of selfadjoint extensions of the suitably…
Given two measures $\mu_1$ and $\mu_2$ on a measurable space $X$ such that $d\mu_2=\rho_{1,2} \, d\mu_1$ for some bounded measurable function $\rho_{1,2}:X\to (0,\infty)$, there exist two natural identification operators…
The pre-asymptotic analysis of the multichannel scattering problem for particles with an arbitrary spin and short-range interactions has been presented. The complete operator-valued dependence of the scattered differential flux on the…
We analyze the resolvent and define the scattering matrix for asymptotically hyperbolic manifolds with metrics which have a polyhomogeneous expansion near the boundary, and also prove that there is always an essential singularity of the…
We say that a (∨,0)-semilattice S is conditionally co-Brouwerian, if (1) for all nonempty subsets X and Y of S such that X $\leq$ Y (i.e., x $\leq$ y for all (x, y) $\in$ X x Y), there exists z $\in$ S such that X $\leq$ z $\leq$ Y,…
The asymptotic structure of AdS spacetimes in the context of General Relativity coupled to the Maxwell field in three spacetime dimensions is analyzed. Although the fall-off of the fields is relaxed with respect to that of Brown and…
We analyse the asymptotic symmetries of Maxwell theory at spatial infinity through the Hamiltonian formalism. Precise, consistent boundary conditions are explicitly given and shown to be invariant under asymptotic angle-dependent…
We propose a dual formulation for the S Matrix of N = 4 SYM. The dual provides a basis for the "leading singularities" of scattering amplitudes to all orders in perturbation theory, which are sharply defined, IR safe data that uniquely…
We consider metric perturbations of the Landau Hamiltonian. We investigate the asymptotic behaviour of the discrete spectrum of the perturbed operator near the Landau levels, for perturbations with power-like decay, exponential decay or…
In this paper, a discrete form of the Kato inequality for discrete magnetic Laplacians on graphs is used to study asymptotic properties of the spectrum of discrete magnetic Schrodinger operators. We use the existence of a ground state with…
For an asymptotically hyperbolic metric on the interior of a compact manifold with boundary, we prove that the resolvent and scattering operators are continuous functions of the metric in the appropriate topologies.