Point scatterers in low number of dimensions
Er'el Granot
Abstract
It is well known that in 1D the cross section of a point scatterer increases along with the scatterer's strength (potential). In this paper we show that this is an exceptional case, and in all the other cases, where a point defect has a physical meaning, i.e., 0<d<1 and 1<d<=2 (d is the dimensions number), the cross section does not increase monotonically with the scatterer's strength. In fact, the cross section exhibits a resonance dependence on the scatterer's strength, and in the singular 2D case it gets its maximum value for an infinitely weak strength. We use this fact to show that two totally different generalized functions can describe exactly the same physical entity (the same scatterer).
Create a lesson
Related papers
Parametric Glassiness in Graphene-based Electronic Lévy Glass
Caue N. da Silva, Diego B. Fonseca, Adauto J. F. de Souza et al.
Giant geometric nonlinear transport in inhomogeneously strained Bi2Se3 single crystalline slabs
Igor Veremchuk, Pavlo Makushko, Anita Guarino et al.
Controlling the Atomic Reconstruction in Twisted MoSe2/WSe2 with a Monolayer hBN Spacer
Johannes Figueiredo, Kaiyuan Chen, Aubrey Penn et al.
Pulse-by-pulse imaging of reversible, collective reshaping in laser-excited gold nanorods
Mees Dieperink, Loriane Monin, Ichiro Ohnishi et al.
Atomic Edge Resonators Flatten Phonon Bands in Biphenylene Nanoribbons
V. L. Katkov, N. M. Chtchelkatchev, V. A. Osipov
Theory of exciton-exciton interactions in crystalline systems
L. Maisel Licerán, H. T. C. Stoof