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One-Dimensional Models for Atoms in Strong Magnetic Fields, II: Anti-Symmetry in the Landau Levels

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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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Authors and Affiliations

  1. School of Economics, Mathematics and Statistics, Birkbeck College–University of London, Mallet Street, London, United Kingdom

    Raymond Brummelhuis

  2. Department of Mathematics, Tufts University, Medford, Massachusetts, 02155

    Mary Beth Ruskai

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  1. Raymond Brummelhuis
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  2. Mary Beth Ruskai
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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

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