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

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.

Submitted to special issue of J. Stat. Phys. in honor of E. Lieb's 70th birthday. (latex, 25 pages)

References in corpus (5)

• Effective Hamiltonians for atoms in very strong magnetic fields
• On the maximal ionization of atoms in strong magnetic fields
• A discrete density matrix theory for atoms in strong magnetic fields
• Study of a Class of Regularizations of 1/|x| using Gaussian Integrals
• A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

Cited by in corpus (3)

• Effective Hamiltonians for atoms in very strong magnetic fields
• The rigged Hilbert space of the algebra of the one-dimensional rectangular barrier potential
• Ground State of the Polaron Hydrogenic Atom in a Strong Magnetic Field