Three-Dimensional Direct Scattering Theory

Bernd Thaller

Jingfeng Liu, Ming Zhou, Zongfu Yu

A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.

S. Brandt, Hans Dieter Dahmen, Tilo Stroh

Sadhan K. Adhikari, W.G. Gibson, T. K. Lim

A parametrization of low-energy two-dimensional quantum scattering is given which is in the tradition of familiar three-dimensional effective-range theory. A scattering length differing from previous treatments is introduced whose behavior reflects the repulsive or attractive nature of the interaction, and whether or not bound states are present. However its definition is subject to an unknown length parameter. An effective-range parameter is also defined and together with the scattering length explains the nonexistence of the Efimov effect in two dimensions. It is also shown that the Ramsauer–Townsend effect exists in 2D. Application to the case of a square-well potential reveals direct relationships between the unknown length parameter and the effective range to the actual range of the potential.

Manuel Valiente, Nikolaj Thomas Zinner

In this chapter, we introduce the main techniques to effectively reduce the dimensions of a three-dimensional system to one spatial dimension via anisotropi trapping. We shall deal with scattering and bound states using two different methods, after introducing one-dimensional scattering theory, which is necessary for the correct interpretation of the results.

Israel Michael Sigal