Dispersive estimates for massive Dirac operators in dimension two

Abstract

We study the massive two dimensional Dirac operator with an electric potential. In particular, we show that the $t^{-1}$ decay rate holds in the $L^1\to L^{\infty }$ setting if the threshold energies are regular. We also show these bounds hold in the presence of s-wave resonances at the threshold. We further show that, if the threshold energies are regular that a faster decay rate of $t^{-1}(\log t{)}^{-2}$ is attained for large $t$, at the cost of logarithmic spatial weights. The free Dirac equation does not satisfy this bound due to the s-wave resonances at the threshold energies.

40 pages

References in corpus (1)

• The Dirac equation in two dimensions: Dispersive estimates and classification of threshold obstructions

Cited by in corpus (4)

• On the one dimensional Dirac equation with potential
• On Absence of Threshold Resonances for Schrodinger and Dirac Operators
• The Massless Dirac Equation in Two Dimensions: Zero-Energy Obstructions and Dispersive Estimates
• The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions