Related papers: Potential Scattering on a Spherical Surface
A Green's function formalism to analyze the scattering properties in confined geometries is developed. This includes scattering from a central field inside the guide created e.g. by impurities. For atomic collisions our approach applies to…
We establish upper and lower universal bounds for potentials of weighted designs on the sphere $\mathbb{S}^{n-1}$ that depend only on quadrature nodes and weights derived from the design structure. Our bounds hold for a large class of…
We investigate the many-body properties of a two-dimensional electron gas constrained to the surface of a sphere, a system which is physically realized in multielectron bubbles in liquid helium. A second-quantization formalism, suited for…
In this paper we generalise our previous results [1] concerning scattering on the exterior of collapsing dust clouds to the charged case, including in particular the extremal case. We analyse the energy boundedness of solutions $\phi$ to…
In this article we study the shape of a compact surface of constant mean curvature of Euclidean space whose boundary is contained in a round sphere. We consider the case that the boundary is prescribed or that the surface meets the sphere…
On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particles scattering in a thin crystal when particles fall along one its plane of atoms and in a thin layer of amorphous matter is…
We have performed classical and quantum dynamical simulations to calculate dynamical quantities for physical processes of atom - surface scattering, e.g., trapping probability and average energy loss, final angular distribution of a…
Concept of curvature of liquid surrounding a spherical surface seems obvious in daily life, but based on earthly conditions everywhere. However, our understanding about the concept seems more transparent when we keep the system out of the…
A solution of the scattering problem is obtained for the Schr\"odinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident…
A nonrelativistic scalar particle that is constrained to move on an asymptotically flat curved surface undergoes a geometric scattering that is sensitive to the mean and Gaussian curvatures of the surface. A careful study of possible…
The manifestation of exceptional points in the scattering continuum of atomic nucleus is studied using the real-energy continuum shell model. It is shown that low-energy exceptional points appear for realistic values of coupling to the…
A giant level shift, resulted from the interaction of an electron in a spherical quantum dot with zero--point oscillations of confined modes of the electric field, is divulged. The energy correction depends on the dot radius. This size…
Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous…
The article discusses the correctness of the assumption about the similarity of molecular continuum electron functions with wave functions in electron-atom scattering. The elastic scattering of slow particles by pair of non-overlapping…
We compute the ground state of a Bose-Einstein condensate confined on a curved surface and unravel the effects of curvatures. Starting with a general formulation for any smooth surface, we apply it to a prolate ellipsoid, which is inspired…
We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance $d$ above a plane rigid surface.…
A direct method for the bound states and the low energy scattering from a circular and a spherical delta shell potentials is proposed and the results are compared with the one using the standard partial wave analysis developed for…
When a two-dimensional curved surface is conceived as a limiting case of a curved shell of equal thickness d, where the limit d\rightarrow0 is then taken, the well-known geometric potential is induced by the kinetic energy operator, in fact…
We revisit the scattering of quantum test particles on the conical $(2+1)$-dimensional spacetime and find the scatteting amplitude as a function of the boundary conditions imposed at the appex of the cone. We show that the boundary…
We carry out a model study on two-atom interactions and bound states in quasi-two dimensional traps. The interactions are modeled by two-parameter potentials with parameters being the range $r_0$ and the $s$-wave scattering length $a_s$. We…