Related papers: Algebraic Model for Quantum Scattering. Reformulat…
The time dependent complex Schr\"odinger equation with cubic nonlinearity is solved by constructing differential quadrature algorithm based on sinc functions. Reduction to a coupled system of real equations enables to approach the space…
I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
Stochastic models for quantum state reduction give rise to statistical laws that are in most respects in agreement with those of quantum measurement theory. Here we examine the correspondence of the two theories in detail, making a…
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
In 'supersingular' scattering the potential $g^2U_A(r)$ involves a variable nonlinear parameter $A$ upon the increase of which the potential also increases beyond all limits everywhere off the origin and develops a uniquely high level of…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…
Quantum computers are ideally set up to solve linear systems which are of a form similar to the Schrodinger/Dirac equation of quantum mechanics. In the framework of linear response theory, the propagation and scattering of electromagnetic…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schr\"odinger equation $iu_t + \Delta u = \pm |u|^2 u$ for large spherically symmetric L^2_x(\R^2) initial data; in the focusing case we require,…
In the quantum mechanics of collision problems we must consider scattering states of the system. For these states, the wave functions do not remain in Hilbert space, but they are expressible in terms of generalized functions of a Gel'fand…
We consider the cubic-quintic nonlinear Schr\"odinger equation: \[ i\partial_t u = -\Delta u - |u|^2u + |u|^4u. \] In the first part of the paper, we analyze the one-parameter family of ground-state solitons associated to this equation with…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
Application of the Hyperspherical Adiabatic expansion to describe three-body scattering states suffers the problem of a very slow convergence. Contrary to what happens for bound states, a huge number of hyperradial equations has to be…
We investigate the scattering theory for the nonlinear Schr\"{o}dinger equation $i \partial_{t}u+ \Delta u+\lambda|u|^\alpha u=0$ in $\Sigma=H^{1}(\mathbb{R}^{d})\cap L^{2}(|x|^{2};dx)$. We show that scattering states $u^{\pm}$ exist in…