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Onedimensional models for atoms in strong magnetic fields
 Antisymmetry in the Landau levels,” quantph/0308040
"... Dedicated to Elliott Lieb on the occasion of his 70th birthday Electrons in strong magnetic fields can be described by onedimensional 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 t ..."
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Dedicated to Elliott Lieb on the occasion of his 70th birthday Electrons in strong magnetic fields can be described by onedimensional 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 aZ+Zf(Z). The function f(Z) represents a small nonlinear growth which reduces to ApZ(log Z) 2 when the magnetic field c○by authors.
and
"... There exist positive constants c0 and c1 = c1(n) such that for every 0 < ɛ < 1/2 the following holds: Let P be a convex polytope in R n having N ≥ cn 0 /ɛ vertices x1,..., xN. Then there exists a subset A ⊂ {1,..., N}, card (A) ≥ (1 − 2ɛ)N, such that for all i ∈ A voln(P) − voln(conv(vert (P) \ { ..."
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There exist positive constants c0 and c1 = c1(n) such that for every 0 < ɛ < 1/2 the following holds: Let P be a convex polytope in R n having N ≥ cn 0 /ɛ vertices x1,..., xN. Then there exists a subset A ⊂ {1,..., N}, card (A) ≥ (1 − 2ɛ)N, such that for all i ∈ A voln(P) − voln(conv(vert (P) \ {xi})) voln(P) n+1 n+1 ≤ c1(n)ɛ n−1 N n−1. Also, if P is a convex polytope in R n having N ≥ cn 0 /ɛ facets. Let H+ i be the half space determined by the facet Fi, which contains P (i = 1,..., N). Then there exists a subset A ⊂ {1,..., N}, card (A) ≥ (1 − 2ɛ)N, such that for all i ∈ A voln 1
One Dimensional Regularizations of the Coulomb Potential with Application to Atoms in Strong Magnetic Fields
"... Abstract. It is wellknown that the functions Vm(x) = Γ(m+1) 0 m e −u √ du x2 +u arise naturally in the study of atoms in strong magnetic fields where they can be regarded as onedimensional regularizations of the Coulomb potential. For manyelectron atoms consideration of the Pauli principle requi ..."
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Abstract. It is wellknown that the functions Vm(x) = Γ(m+1) 0 m e −u √ du x2 +u arise naturally in the study of atoms in strong magnetic fields where they can be regarded as onedimensional regularizations of the Coulomb potential. For manyelectron atoms consideration of the Pauli principle requires convex combinations of such potentials and interactions of the form 1 √ Vm(