Related papers: Fixed energy inverse problem for exponentially dec…
We consider the Schr\"odinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy.…
We study the entanglement entropy between the two outgoing particles in an elastic scattering process. It is formulated within an S-matrix formalism using the partial wave expansion of two-body states, which plays a significant role in our…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
We apply the method of unitary transformations to a model two-nucleon potential and construct from it an effective potential in a subspace of momenta below a given cut-off $\Lambda$. The S-matrices in the full space and in the subspace are…
Bethe-Salpeter equation is applied to nucleon-nucleon elastic scattering at the intermediate energy. The differential cross section and the polarization are calculated in terms of the phase shift analysis method using the two-body potential…
We investigate the scattering phenomena in two dimensions produced by a general finite-range nonseparable potential. This situation can appear either in a Cartesian geometry or in a heterostructure with cylindrical symmetry. Increasing the…
Using the complex energy method, the problem of nucleon-deuteron scattering is solved with a simple three-body force having a separable form. Our results are compared with the results of modern direct two-variable calculations and a good…
We study the entanglement produced in transverse momentum by two-particle scattering at high energy. Employing the S-matrix framework for the derivation of reduced density matrices, we formulate the entanglement entropy for an inelastic…
We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…
In this paper, we study the focusing and defocusing energy--subcritical, nonlinear wave equation in $\mathbb{R}^{1+d}$ with radial initial data for $d = 4,5$. We prove that if a solution remains bounded in the critical space on its interval…
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…
The two-particle finite-volume scattering formalism derived by L\"uscher and generalized in many subsequent works does not hold for energies far enough below the two-particle threshold to reach the nearest left-hand cut. The breakdown of…
We consider low energy inverse problems in three-body scattering and show that if all unknown interactions are small in an appropriate sense then the 2-cluster to 2-cluster S-matrices given at low energies determine the Fourier transform of…
In this paper, we study the low-energy $d-\alpha$ elastic scattering within the two-body cluster effective field theory (EFT) framework. The importance of the $d(\alpha,\alpha) d$ scattering in the $^6 \textrm{Li} $ production reaction…
For a class of long-range potentials, including ultra-strong perturbations of the attractive Coulomb potential in dimension $d\geq3$, we introduce a stationary scattering theory for Schr\"odinger operators which is regular at zero energy.…
Let $A_q(\alpha',\alpha,k)$ be the scattering amplitude, corresponding to a local potential $q(x)$, $x\in\R^3$, $q(x)=0$ for $|x|>a$, where $a>0$ is a fixed number, $\alpha',\alpha\in S^2$ are unit vectors, $S^2$ is the unit sphere in…
We consider the Schr\"odinger equation with a multipoint potential of Bethe-Peierls-Thomas-Fermi type. For this singular potential, we develop scattering and inverse scattering at high energies. In particular, in this framework, our results…
The low-energy scattering of two charged particles is analyzed using a renormalization group approach based on dimensional regularization with power-divergence subtraction. A nontrivial solution with a marginally unstable direction is…
Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…
We consider a certain first-order linear system of ordinary differential equations, and we analyze the direct and inverse scattering problems for that linear system. The linear system involves two potentials in the Schwartz class, and those…