Related papers: High-Velocity Estimates for the Scattering Operato…
The conductance of systems containing two tunnel point-contacts and a single subsurface scatterer is investigated theoretically. The problem is solved in the approximation of s-wave scattering giving analytical expressions for the wave…
By considering a cylindrically symmetric generalization of a plane wave, the first Born approximation of screened Coulomb scattering unfolds two new dimensions in the scattering problem: transverse momentum and orbital angular momentum of…
Many applications require recovering the geometry information of multiple elastic particles based on the scattering information. In this paper, we consider the inverse time-harmonic elastic scattering of multiple rigid particles in three…
Motivated by the research on upper bounds on the rate of quantum transport for one-dimensional operators, particularly, the recent works of Jitomirskaya--Liu and Jitomirskaya--Powell and the earlier ones of Damanik--Tcheremchantsev, we…
The Hamiltonian describing a conductor surrounding an external magnetic field contains a nonvanishing vector potential in the volume accessible to the electrons and nuclei of which the conductor is made. That vector potential cannot be…
An effective Hamiltonian which could model the interaction between a tunneling proton and the conduction electrons of a metal is investigated. A remarkably simple correlation between the motion of the $TLS$-atom and an angular-momentum…
A method is described for dealing with effective theories of hadron scattering. It allows one to reduce the number of independent renormalization prescriptions in those theories and gives a possibility to make numerical predictions. As an…
We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, $a$, which is large compared to the range of the…
We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…
A new method for the determination of the real part of the elastic scattering amplitude is examined for high energy proton-proton elastic scattering at small momentum transfer. This method allows us to decrease the number of model…
We consider the multidimensional (nonrelativistic) Newton equation in a static electromagnetic field $$\ddot x = F(x,\dot x), F(x,\dot x)=-\nabla V(x)+B(x)\dot x, \dot x={dx\over dt}, x\in C^2(\R,\R^n),\eqno{(*)}$$ where $V \in…
In quantum field theory, the photon-fermion vertex can be described in terms of four form factors which encode the static electromagnetic properties of the particle, namely its charge, magnetic dipole moment, electric dipole moment, and…
We consider the elastic wave scattering problem involving rigid obstacles. This work addresses the inverse problem of reconstructing the position and shape of such obstacles using far-field measurements. A novel monotonicity-based approach…
In their seminal paper Aharonov and Bohm (1959) claimed that electromagnetic fields can act at a distance on charged particles even if they are identically zero in the region of space where the particles propagate. They proposed two…
We add a confining potential to the Aharonov-Bohm model resulting in no contact of the particle with the solenoid (border); this is characterized by a unique self-adjoint extension of the initial Hamiltonian operator. It is shown that the…
We present a general method for calculating coherent electronic transport in quantum wires and tunnel junctions. It is based upon a real space high order finite difference representation of the single particle Hamiltonian and wave…
We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of…
We use the Tridiagonal Representation Approach (TRA) to obtain exact scattering and bound states solutions of the Schr\"odinger equation for short-range inverse-square singular hyperbolic potentials. The solutions are series of square…
To recover the three dimensional (3D) volumetric distribution of matter in an object, images of the object are captured from multiple directions and locations. Using these images tomographic computations extract the distribution. In highly…
We consider the scattering theory for the Schrodinger equation with $-\Delta -|x|^{\alpha}$ as a reference Hamiltonian, for $0< \alpha \leq 2$, in any space dimension. We prove that when this Hamiltonian is perturbed by a potential, the…