Hybrid theory for P-wave scattering

Modeling interactions for resonant p-wave scattering.

In view of recent experiments on ultracold polarized fermions, the zero-range potential approach is generalized to situations where two-body scattering is resonant in the p-wave channel. We introduce a modified scalar product which reveals a deep relation between the geometry of the Hilbert space and the interaction. This formulation is used to obtain a simple interpretation for the transfer ra...

Matrix theory of elastic wave scattering

Upon invoking Huygen's principle, matrix equations are obtained describing the scattering of waves by an obstacle of arbitrary shape immersed in an elastic medium. New relations are found connecting surface tractions with the divergence and curl of the displacement, and conservation laws are discussed. When mode conversion effects are arbitrarily suppressed by resetting appropriate matrix eleme...

General Theory of Elastic Wave Scattering

A long-wave multiple scattering theory

One of the most successful techniques for handling multiple scattering is the so-called T-matrix approach in which the full linear solution can be computed once it has been determined how each individual element of an array scatters an arbitrary incident field. In the context of water waves this theory was originally formulated in [1] for constant finite depth, and extended to the deep water ca...

Scattering Theory for P-forms on Hyperbolic Real Space

Abstract. Due to spectral obstructions, a scattering theory in the LaxPhillips sense for the wave equation for differential p-forms on H cannot be developed. As a consequence, Huygens’ principle for the wave equation in this context does not hold. If we restrict the class of forms and we consider the case of coclosed p-forms on H, when n = 2p, Huygens’ principle does hold and thus in this case ...