On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator

P. G. Grinevich   ; A. E. Mironov   ; S. P. Novikov

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 70 (2015) no. 2, pp. 299-329

Résumé

The complete manifold of ground-state eigenfunctions for the purely magnetic two-dimensional Pauli operator is considered as a byproduct of a new reduction (found by the authors several years ago) for the algebro-geometric inverse spectral data (that is, Riemann surfaces and divisors). This reduction is associated with a $({2+1})$-soliton hierarchy containing a 2D analogue of the famous ‘Burgers system’. This paper also surveys previous papers since 1980, including the first topological ideas in the space of quasi-momenta, and presents new results on self-adjoint boundary-value problems for the Pauli operator. The ‘non-spectral’ Bloch–Floquet functions of zero 2D level give discrete points of additional spectrum analogous to the ‘boundary states’ of finite-gap 1D potentials in the gaps. Bibliography: 35 titles.

Détail

Keywords: magnetic Pauli operator, algebro-geometric solutions, ground state, Landau levels, boundary-value problems.

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