Analysis of zero modes for Dirac operators with magnetic links

TY - JOUR

T1 - Analysis of zero modes for Dirac operators with magnetic links

AU - Portmann, Fabian

AU - Sok, Jérémy

AU - Solovej, Jan Philip

PY - 2018/8/1

Y1 - 2018/8/1

N2 - In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in S3 (and R3) by Dirac operators with smooth magnetic fields. Then we proceed to prove that under certain assumptions, the spectral flow of paths along these operators is the same in both the smooth and the singular case. We recently characterized the spectral flow of such paths in the singular case. This allows us to show the existence of new smooth, compactly supported magnetic fields in R3 for which the associated Dirac operator has a non-trivial kernel. Using Clifford analysis, we also obtain criteria on the magnetic link for the non-existence of zero modes.

AB - In this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in S3 (and R3) by Dirac operators with smooth magnetic fields. Then we proceed to prove that under certain assumptions, the spectral flow of paths along these operators is the same in both the smooth and the singular case. We recently characterized the spectral flow of such paths in the singular case. This allows us to show the existence of new smooth, compactly supported magnetic fields in R3 for which the associated Dirac operator has a non-trivial kernel. Using Clifford analysis, we also obtain criteria on the magnetic link for the non-existence of zero modes.

U2 - 10.1016/j.jfa.2017.12.006

DO - 10.1016/j.jfa.2017.12.006

M3 - Journal article

SN - 0022-1236

VL - 275

SP - 604

EP - 659

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -