相关论文: Fixed energy inverse problem for exponentially dec…
It is found what part of the fixed-energy phase shifts allows one to recover uniquely a compactly supported potential. For example, the knowledge of all phase shifts with even angular momenta is sufficient to recover the above potential.
For the two-dimensional Schr\"odinger equation $$ [- \Delta +v(x)]\psi=E\psi,\ x\in \R^2,\ E=E_{fixed}>0 \ \ \ \ \ (*)$$ at a fixed positive energy with a fast decaying at infinity potential $v(x)$ dispersion relations on the scattering…
A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)].…
The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R^n from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy…
The differential cross-sections for elastic and inelastic neutrino-deuteron scattering are calculated analytically using nucleon-nucleon effective field theory. For elastic scattering, the deuteron axial form factor and the deuteron strange…
A method for solving few-body scattering equations is proposed and examined. The solution of the scattering equations at complex energies is analytically continued to get scattering T-matrix with real positive energy. Numerical examples…
We consider the variational problem of maximizing the weighted equilibrium Green's energy of a distribution of charges free to move in a subset of the upper half-plane, under a particular external field. We show that this problem admits a…
We prove exponential decay of energy for solutions of the damped wave equation on compact hyperbolic surfaces with regular initial data as long as the damping is nontrivial. The proof is based on a similar strategy as in Dyatlov-Jin and in…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
We study an inverse scattering problem at fixed energy for radial magnetic Schr{\"o}dinger operators on R^2 \ B(0, r\_0), where r\_0 is a positive and arbitrarily small radius. We assume that the magnetic potential A satisfies a gauge…
An approximate method is proposed for the recovery of a compactly supported spherically-symmetric potential from the set of fixed-energy phase-shifts known for all angular momenta. The method reduces the inverse scattering problem to a…
We study the inverse scattering problem of determining a magnetic field and electric potential from scattering measurements corresponding to finitely many plane waves. The main result shows that the coefficients are uniquely determined by…
We study one of multidimensional inverse scattering problems for quantum systems in a constant electric field, by utilization of the Enss-Weder time-dependent method. The main purpose of this paper is to propose some methods of sharpening…
Within the class of Derezi{\'n}ski-Enss pair-potentials which includes Coulomb potentials and for which asymptotic completeness is known \cite{De}, we show that all entries of the $N$-body quantum scattering matrix have a well-defined…
We outline a separable matrix ansatz for the potentials in effective field theories of nonrelativistic two-body systems with short-range interactions. We use this ansatz to construct new fixed points of the renormalisation-group equation…
We employ the so-called tangent-point energy as Tikhonov regularizer for ill-conditioned inverse scattering problems in 3D. The tangent-point energy is a self-avoiding functional on the space of embedded surfaces that also penalizes surface…
In this paper, we study the global well-posedness and scattering problem in the energy space for both focusing and defocusing the Klein-Gordon-Hartree equation in the spatial dimension $d \geq 3$. The main difficulties are the absence of an…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field…
A new approach is proposed to the solution of the quantum mechanical inverse scattering problem at fixed energy. The method relates the fixed energy phase shifts to those arising in an auxiliary Sturm-Liouville problem via the interpolation…
Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended…