Related papers: Green functions and completeness; the $3$-body pro…
We consider the focusing energy-critical inhomogeneous nonlinear Schr\"{o}dinger equation \[ iu_t + \Delta u = -|x|^{-b}|u|^{\alpha}u \] where $n \geq 3$, $0<b<\min(2, n/2)$, and $\alpha=(4-2b)/(n-2)$. We prove the global well-posedness and…
We analyze the collision of three particles with arbitrary mass ratio at zero collision energy, assuming arbitrary short-range potentials, and generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008.…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
In this note, we use an elementary argument to show that the existence and unitarity of radiation fields implies asymptotic partition of energy for the corresponding wave equation. This argument establishes the equipartition of energy for…
We obtain almost-sure scattering for the cubic defocusing Schr{\"o}dinger equation in the Euclidean space {$\mathbb{R}^3$}, with randomized radially-symmetric initial data at some supercritical regularity scales. Since we make no smallness…
Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated…
We study the problem of propagation of linear water waves in a deep water in the presence of a critically submerged body (i.e. the body touching the water surface). Assuming uniqueness of the solution in the energy space, we prove the…
We study the wave function $\phi^{(3)}$ of three identical bosons scattering at zero energy, zero total momentum, and zero orbital angular momentum in two dimensions, interacting via short-range potentials with a finite two-body scattering…
We study the three-body systems of ${}^{3}\mathrm{He}$ and $pd$ scattering and demonstrate, both analytically and numerically, that a new $pd$ three-body force is needed at next-to-leading order in pionless effective field theory. We also…
It is shown that the effective interaction strength of three bosons at small collision energies can be extracted from their wave function at zero energy. An asymptotic expansion of this wave function at large interparticle distances is…
We study scattering solutions $\phi$ of the linear wave equation on extremal Reissner-Nordstr\"{o}m spacetimes, satisfying the following properties: i) $\phi$ attains a prescribed radiation field $\psi_{\mathcal{I}}$ through future null…
This is a continuation of the authors' previous work (A. Kirsch, Math. Meth. Appl. Sci., 45 (2022): 5737-5773.) on well-posedness of time-harmonic scattering by locally perturbed periodic curves of Dirichlet kind. The scattering interface…
Recent work in the literature has studied the restricted three-body problem within the framework of effective-field-theory models of gravity. This paper extends such a program by considering the full three-body problem, when the Newtonian…
We consider the focusing inhomogeneous nonlinear Schr\"odinger equation in $H^1(\mathbb{R}^3)$, \begin{equation} i\partial_t u + \Delta u + |x|^{-b}|u|^{2}u=0,{equation} where $0 < b <\tfrac{1}{2}$. Previous works have established a…
Previous work developed a K-matrix formalism applicable to positive energies for the scattering between two $s$-wave interacting particles with two internal states, isotropic spin-orbit coupling and vanishing center-of-mass momentum [H.…
For a class of negative slowly decaying potentials, including $V(x):=-\gamma|x|^{-\mu}$ with $0<\mu<2$, we study the quantum mechanical scattering theory in the low-energy regime. Using modifiers of the Isozaki-Kitada type we show that…
This book provides a systematic study of spectral and scattering theory for many-body Schr\"odinger operators at two-cluster thresholds. While the two-body problem (reduced after separation of the center of mass motion to a one-body problem…
The new formulation of the theory of multichannel scattering on the example of collinear model is proposed. It is shown, that in the closed three-body scattering system the principle of quantum determinism in general case breaks down and we…
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…
A general treatment of ultracold two-body scattering in the presence of isotropic spin-orbit coupling (SOC) is presented. Owing to the mixing of different partial wave channels, scattering with SOC is in general a coupled multichannel…