On the Nonrelativistic 2D Purely Magnetic Supersymmetric Pauli Operator

TL;DR

This paper explores the ground state eigenfunctions of the 2D purely magnetic Pauli operator using algebrogeometric methods, revealing new spectral and boundary properties linked to soliton hierarchies and topological ideas.

Contribution

It introduces a novel reduction for the 2D Pauli operator based on algebrogeometric inverse spectral data, connecting it to a 2+1 soliton hierarchy and extending previous topological insights.

Findings

Complete manifold of ground state eigenfunctions characterized.

Identification of additional discrete spectrum points related to boundary states.

New results on self-adjoint boundary problems for the Pauli operator.

Abstract

The Complete Manifold of Ground State Eigenfunctions for the Purely Magnetic 2D Pauli Operator is considered as a by-product of the new reduction found by the present authors few years ago for the Algebrogeometric Inverse Spectral Data (i.e. Riemann Surfaces and Divisors). This reduction is associated with the (2+1) Soliton Hierarhy containing a 2D analog of the famous "Burgers System". This article contains also exposition of the previous works made since 1980 including the first topological ideas in the space of quasimomenta. We present here also new results dedicated to the self-adjoint boundary problems for Pauli Operator. The 2D zero level "nonspectral" Bloch-Floquet functions give discrete points of additional spectrum similar to the "boundary states" of finite-gap 1D potentials in the gaps.