Analysis of zero modes for Dirac operators with magnetic links

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Standard

Analysis of zero modes for Dirac operators with magnetic links. / Portmann, Fabian; Sok, Jérémy; Solovej, Jan Philip.

In: Journal of Functional Analysis, Vol. 275, No. 3, 2018, p. 604-659.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Portmann, F, Sok, J & Solovej, JP 2018, 'Analysis of zero modes for Dirac operators with magnetic links', Journal of Functional Analysis, vol. 275, no. 3, pp. 604-659. https://doi.org/10.1016/j.jfa.2017.12.006

APA

Portmann, F., Sok, J., & Solovej, J. P. (2018). Analysis of zero modes for Dirac operators with magnetic links. Journal of Functional Analysis, 275(3), 604-659. https://doi.org/10.1016/j.jfa.2017.12.006

Vancouver

Portmann F, Sok J, Solovej JP. Analysis of zero modes for Dirac operators with magnetic links. Journal of Functional Analysis. 2018;275(3):604-659. https://doi.org/10.1016/j.jfa.2017.12.006

Author

Portmann, Fabian ; Sok, Jérémy ; Solovej, Jan Philip. / Analysis of zero modes for Dirac operators with magnetic links. In: Journal of Functional Analysis. 2018 ; Vol. 275, No. 3. pp. 604-659.

Bibtex

@article{f794697cb8cc46dd879a2c857174b8af,
title = "Analysis of zero modes for Dirac operators with magnetic links",
abstract = "n this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in (and ) 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 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.",
author = "Fabian Portmann and J{\'e}r{\'e}my Sok and Solovej, {Jan Philip}",
year = "2018",
doi = "10.1016/j.jfa.2017.12.006",
language = "English",
volume = "275",
pages = "604--659",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "3",

}

RIS

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

Y1 - 2018

N2 - n this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in (and ) 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 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 - n this paper we provide a means to approximate Dirac operators with magnetic fields supported on links in (and ) 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 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

VL - 275

SP - 604

EP - 659

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 3

ER -

ID: 190444102