Weighted Energy Decay for 1D Dirac Equation

TL;DR

This paper establishes long-time decay estimates in weighted energy norms for solutions of the 1D Dirac equation with a potential, extending known results from Schrödinger equations to Dirac equations.

Contribution

It introduces a novel decay analysis for the 1D Dirac equation with potential, broadening the understanding of dispersive properties in relativistic quantum mechanics.

Findings

Proves dispersive decay in weighted energy norms for 1D Dirac solutions.

Extends decay results from Schrödinger to Dirac equations.

Demonstrates decay for generic potentials.

Abstract

We obtain a dispersive long-time decay in weighted energy norms for solutions of the 1D Dirac equation with generic potential. The decay extends the results obtained by Jensen, Kato and Murata for the Schr\"odinger equations.