Neutral atom and a charged wire: From elastic scattering to absorption

Abstract

We solve the problem of a neutral atom interacting with an charged wire, giving rise to an attractive 1/r 2 potential in two dimensions. We show how a suitable average over all possible self-adjoint extensions of the radial Schroedinger Hamiltonian eventually leads to the classical formula for absorption of the atom, a formula shown to be in agreement with a recent experiment.

Analytic structure of the S-matrix for singular quantum mechanics

“…[19], an average expression at the level of Green's functions is used to relate particular cases of unitary and nonunitary solutions. Subsequently, it was pointed out [21] that a similar result can be obtained for the S-matrix of the two-dimensional ISP: an average of unitary solutions coincides with the solution for perfect absorption.…”

“…As a corollary of relations (19)- (21), the functionŜ(Ω) is analytic in the closed unit circle D, i.e., it is a meromorphic function with no poles for |Ω| ≤ 1. This is simply due to the fact that the unique purported pole is located at Ω 2 = 1/R, as shown by the Blaschke factor-but this location of Ω 2 could also be established independently by a similar subset of arguments, via the suppression of the building block u 2 combined with Eq.…”

Regularization of the singular inverse square potential in quantum mechanics with a minimal length

“…Indeed, the problem of atoms interacting with a charged wire, relevant to the fabrication of nanoscale atom optical devices, is known to provide an experimental realization of an attractive 1/R 2 potential [32,33]. It is a fundamental (long range) part of the potential describing dipole-bound anions in polar molecules [34], and has some applications in black holes physics [35].…”

Singular inverse square potential in arbitrary dimensions with a minimal length: Application to the motion of a dipole in a cosmic string background

“…Indeed, this potential appears in the study of electron capture by polar molecules with static dipole moments [21,22]. The problem of atoms interacting with a charged wire is known to provide an experimental realization of an attractive 1/R 2 potential [23,24]. The Efimov effect in three-body systems [25] arises from the existence of a long range effective 1/R 2 interaction, where R is built from the relative distances between the three particles.…”