On the non-relativistic two-dimensional purely magnetic supersymmetric Pauli operator. (30th April 2015)

• Record Type: Journal Article
• Authors: Grinevich, P G; Mironov, A E; Novikov, S P
• Is Part Of: Russian mathematical surveys. Volume 70:Number 2(2015)
• Page Start: 299
• Page End: 329
• Publication Date: 2015-04-30
• Subjects: Mathematics -- Soviet Union -- Periodicals; Mathematics -- Russia (Federation) -- Periodicals; Mathematics -- Periodicals; Mathematicians -- Soviet Union -- Periodicals; Mathematicians -- Russia (Federation) -- Periodicals; 510.5
• DOI: 10.1070/RM2015v070n02ABEH004948
• Languages: English
• ISSNs: 0036-0279

Abstract

<abstract xml:lang="en"> <title>Abstract</title> <p>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 <inline-graphic xlink:href="ark:/27927/pgj2c910nmd" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink"><alt-text>$ ({2+1})$</alt-text></inline-graphic>-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.</p> <p>Bibliography: 35 titles. </p> </abstract>