Abstract
We consider two-dimensional Pauli and Dirac operators with a polynomially vanishing magnetic field. The main results of the paper provide resolvent expansions of these operators in the vicinity of their thresholds. It is proved that the nature of these expansions is fully determined by the flux of the magnetic field. The most important novelty of the proof is a comparison between the spatial asymptotics of the zero modes obtained in two different manners. The result of this matching allows us to compute explicitly all the singular terms in the associated resolvent expansions.As an application we show how the magnetic field influences the time decay of the associated wave-functions quantifying thereby the paramagnetic and diamagnetic effects of the spin.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
