相关论文: Inverse problems in N-body scattering

We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated…

In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges…

Direct and inverse scattering problems for a third-order self-adjoint differential operator on the whole axis are studied. This operator is the sum of three summands: operator of third derivative, operator of multiplication by a function,…

Non Efimovian $N$-body resonances are investigated in the regime of a large two-body s wave scattering length. In view of a universal description of low-energy bound and quasi-bound states, a contact model is introduced. The modeling…

Effective Field Theory (EFT) provides a powerful framework that exploits a separation of scales in physical systems to perform systematically improvable, model-independent calculations. Particularly interesting are few-body systems with…

We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…

We explore systematically a rigorous theory of the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at…

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…

A brief description of the novel approach towards solving few-body scattering problems in a finite-dimensional functional space of the $L_2$-type is presented. The method is based on the complete few-body continuum discretization in the…

In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…

We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model…

A generalized inverse scattering method has been applied to the linear problem associated with the coupled higher order nonlinear schr\"odinger equation to obtain it's $N$-soliton solution. An infinite number of conserved quantities have…

Atom-dimer scattering below the three-body break-up threshold is studied for a system of three identical bosons. The atom-dimer scattering length and the energy of the most weakly-bound three-body state are shown to be strongly correlated.…

In order to approach the pion--multinucleon problem, we have found it convenient to reformulate the general N--body theory starting from the fully unclusterized (i.e., N <- N) amplitude. If we rewrite such an amplitude in terms of new…

These are my lecture notes from a minicourse I gave at the Universite de Nantes about many-body scattering. I also discuss the relationship between many-body scattering and higher rank symmetric spaces, whose description is the result of…

We consider the small-angle multiple neutron scattering and a possibility of its model-free analysis by the inverse problem method. We show that the ill-defined problem is essentially regularized by use of a planar detector without a…

We study solutions of the Newtonian $n$-body problem which tend to infinity hyperbolically, that is, all mutual distances tend to infinity with nonzero speed as $t \rightarrow +\infty$ or as $t \rightarrow -\infty$. In suitable coordinates,…

In these lectures I give an introduction to the time-dependent approach to inverse scattering, that has been developed recently. The aim of this approach is to solve various inverse scattering problems with time-dependent methods that…

We discuss an alternative approach to studying the low energy limit of quantum general relativity. We investigate the low energy limit of a scattering cross-section for two massive scalar particles. Unlike calculations involving the…

Many-body quantum-mechanical scattering problem is solved asymptotically when the size of the scatterers (inhomogeneities) tends to zero and their number tends to infinity. A method is given for calculation of the number of small…