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 this type, we show that the maximum number of electrons that can be bound is less than aZ+Zf(Z). The function f(Z) represents a small non-linear growth which reduces to A p Z(logZ)2when the magnetic field B=O(Z p) 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.
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Brummelhuis, R., Ruskai, M.B. One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels. Journal of Statistical Physics 116, 547–570 (2004). https://doi.org/10.1023/B:JOSS.0000037229.51177.6d
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DOI: https://doi.org/10.1023/B:JOSS.0000037229.51177.6d