Quantum scattering in two dimensions

Abstract

A self-contained discussion of nonrelativistic quantum mechanical potential scattering in two dimensions is presented. The discussion includes, among other topics, partial wave decomposition in coordinate and momentum space, Lippmann–Schwinger integral equations of scattering for the scattering wavefunction and the transition operator, optical theorem, and the unitarity relation for the transition operator. The present definition of the scattering amplitude in terms of the asymptotic wavefunction differs from the usual definition. The present definition has certain advantages, for example, in writing the optical theorem and in studying the analytical properties of the scattering amplitude.

The Virial Expansion of a Dilute Bose Gas in Two Dimensions

“…The Virial expansion developed in this paper is complementary. As the quasi-two dimensional gas of trapped atoms is also experimentally feasible, the result reported in this paper may be brought to a direct comparison with the measurements As is well-known, a perturbative treatment of a dilute Bose gas in two dimensions suffer from two difficulties: 1) The scattering amplitude vanishes in the zero energy limit and the Born expansion breaks down for a large number of potentials [10] [11].…”

Electron scattering on microscopic corrugations in graphene

“…N 2 O 4 ) have resonant, quasilocalized levels near zero energy. It is interesting to note that equation (2.6) is also valid for the case of conventional (non-relativistic) two-dimensional systems (Adhikari 1986). However, in the latter case, resonant scattering is not incidental, like for Dirac fermions, but the essential feature that limits electron mobility because even a weak random potential in conventional two-dimensional systems leads to resonances near the band edge (Landau & Lifshitz 1977).…”

Analytic approach to magneto-strain tuning of electronic transport through a graphene nanobubble: perspectives for a strain sensor

“…We will give below a detailed description that generalizes the method in Ref. [33] to the case of Dirac fermions. Using this method we will be able to compute the differential scattering cross-section that will be used in the next section to compute the electronic transport.…”