Related papers: Perturbative Scattering Phase Shifts in One-Dimens…
The scattering matrix which describes low-energy, non-relativistic scattering of spin-1/2 fermions interacting via finite-range potentials can be obtained from a geometric action principle in which space and time do not appear explicitly…
We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one dimensional Bose gas and XXZ Heisenberg spin chain.
Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
Linear response time-dependent density functional theory is used to study low-lying electronic continuum states of targets that can bind an extra electron. Exact formulas to extract scattering amplitudes from the susceptibility are derived…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
Rough surface scattering problems are always very challenging both theoretically and numerically. In this paper, we adopt the Bloch transform and the perturbation theory to investigate a special case, i.e., when the rough surface is a…
Quantum scattering by a one-dimensional odd potential proportional to the square of the distance to the origin is considered. The Schr\"odinger equation is solved exactly and explicit algebraic expressions of the wavefunction are given. A…
The mobility problem for suspension of spherical particles immersed in an arbitrary flow of a viscous, incompressible fluid is considered in the regime of low Reynolds numbers. The scattering series which appears in the mobility problem is…
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain…
The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a…
We formulate scattering in one dimension due to the coupled Schr\"{o}dinger equation in terms of the $S$ matrix, the unitarity of which leads to constraints on the scattering amplitudes. Levinson's theorem is seen to have the form $\eta(0)…
It is shown that the simplest multiplicative random complex matrix model generalizes the large-N phase structure found in the unitary case: A perturbative regime is joined to a nonperturbative regime at a point of nonanalyticity.
We present a linear coordinate transform to expand the solution of scattering and emission problems into a basis of forward and backward directional vector harmonics. The transform provides intuitive algebraic and geometric interpretations…
We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
The passage of light or of electrons through a disordered medium is modified in the presence of resonances. We describe a simple model for this problem, and present first results.
The closed form of the first order non-linear differential equation that is satisfied by the effective range within the variable phase formulation of scattering theory is discussed. It is shown that the conventional method of determining…
The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is…
We present a method for calculating scattering phase shifts which utilizes continuum-discretized states obtained in a bound-state type calculation. The wrong asymptotic behavior of the discretized state is remedied by means of the Green's…