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

Abstract

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 -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.