Weakly coupled bound states of Pauli operators

Creators: Frank, Rupert L.; Morozov, Sergey; Vugalter, Semjon

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Abstract

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov-Casher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.

Additional Information

© 2010 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Received: 27 March 2009. Accepted: 2 May 2010. Published online: 14 July 2010. Communicated by L. Ambrosio. The authors would like to thank T. Weidl for drawing their attention to this problem and for helpful discussions. R.F. has profitted from discussions with T. Ekholm and H. Kovarik. The authors gratefully acknowledge the hospitality at Stuttgart University, KTH Stockholm and ESI Vienna, where parts of this work were done. This work was partially supported through Deutsche Forschungsgemeinschaft's (DFG) grant FR 2664/1-1, US National Science Foundation's grant PHY 06 52854 (R.F.), DFG grant SI 348/12-2, Engineering and Physical Sciences Research Council's grant EP/F029721/1 (S.M.) and DFG grant WE 1964/2 (S.V.).

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