One-dimensional models for atoms in strong magnetic fields, II: Anti-Symmetry in the Landau Levels

TL;DR

This paper analyzes one-dimensional models of electrons in strong magnetic fields, demonstrating bounds on the maximum number of electrons that can be bound, with models including realistic antisymmetric wave functions in the lowest Landau level.

Contribution

It extends previous models by incorporating antisymmetry in the Landau levels and provides bounds on electron binding in these realistic one-dimensional models.

Findings

Maximum number of bound electrons is less than Z + Zf(Z).

Function f(Z) grows quadratically in log Z with increasing magnetic field.

Models include realistic antisymmetric wave functions in the lowest Landau level.

Abstract

Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these type, we show that the maximum number of electrons that can be bound is less than a Z + Z f(Z). The function f(Z) represents a small non-linear growth which is quadratic in log Z when the magnetic field strength grows polynomially with the nuclear charge Z. In contrast to earlier work, the models considered here include those arising from realistic cases in which the full trial wave function for N-electrons is the product of an N-electron trial function in one-dimension and an antisymmetric product of states in the lowest Landau level.