Related papers: Time-dependent methods in inverse scattering probl…
An inverse scattering problem is formulated for reconstructing optical properties of biological tissues. A recursive linearization algorithm is used to solve the inverse scattering problem. We employed the idea of finite element boundary…
Based on our previous study [IS3] on the stationary scattering theory for the Schrodinger operator on a manifold possessing an escape function we complete our investigation by doing the time-dependent counterpart. A particular class of…
We consider the Hartree-Fock equation in 1D, for a small and localised initial data and a finite measure potential. We show that there is no long range scattering due to a nonlinear cancellation between the direct term and the exchange term…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
This paper concerns an inverse elastic scattering problem which is to determine a rigid obstacle from time domain scattered field data for a single incident plane wave. By using Helmholtz decomposition, we reduce the initial-boundary value…
In this paper, we study time-harmonic electromagnetic scattering in two scenarios, where the anomalous scatterer is either a pair of electromagnetic sources or an inhomogeneous medium, both with compact supports. We are mainly concerned…
We consider the time-dependent Hamiltonian $H(t)= {1 \over 2} p^2 -E(t) \cdot x + V(t,x)$ on $L^2(R^n)$, where the external electric field $E(t)$ and the short-range electric potential $V(t,x)$ are time-periodic with the same period. It is…
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…
In this paper, we study an inverse scattering problem associated with the time-harmonic Schr\"odinger equation where both the potential and the source terms are unknown. The source term is assumed to be a generalised Gaussian random…
In this paper, we consider the scattering theory of the radial solution to focusing energy-subcritical Hartree equation with inverse-square potential in the energy space $H^{1}(\mathbb{R}^d)$ using the method from \cite{Dodson2016}. The…
We develop the Riemann-Hilbert problem approach to inverse scattering for the two-dimensional Schrodinger equation at fixed energy. We obtain global or generic versions of the key results of this approach for the case of positive energy and…
We investigate the problem of bulk metric reconstruction in holography by leveraging the inverse scattering framework applied to boundary two-point correlation functions. We generalize our previous work of scalar field and show that…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
Study of far-from-equilibrium thermalization dynamics in quantum materials, including the dynamics of different types of quasiparticles, is becoming increasingly crucial. However, the inherent complexity of either the full quantum…
An inverse problem of finding an obstacle and the boundary condition on its surface from the fixed-energy scattering data is studied. A new method is developed for a proof of the uniqueness results. The method does not use the discreteness…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
Transport and scattering phenomena in open quantum-systems with a continuous energy spectrum are conveniently solved using the time-dependent Schrodinger equation. In the time-dependent picture, the evolution of an initially localized…
Describing time-dependent many-body systems where correlation effects play an important role remains a major theoretical challenge. In this paper we develop a time-dependent many-body theory that is based on the two-particle reduced density…