Results 1 
7 of
7
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 ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
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.
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 ..."
Abstract
 Add to MetaCart
(Show Context)
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(
ORLICZ NORMS OF SEQUENCES OF RANDOM VARIABLES BY YEHORAM GORDON,1 ALEXANDER LITVAK,2 CARSTEN SCHÜTT3 AND
"... Let fi, i = 1,..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ Rn the expectation E‖(xifi)ni=1‖N is maximal (up to an absolute constant) if fi, i = 1,..., n, are independent. In that case we show that the expectation E‖(xifi)ni=1‖N is equivalent to ..."
Abstract
 Add to MetaCart
(Show Context)
Let fi, i = 1,..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ Rn the expectation E‖(xifi)ni=1‖N is maximal (up to an absolute constant) if fi, i = 1,..., n, are independent. In that case we show that the expectation E‖(xifi)ni=1‖N is equivalent to ‖x‖M, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result. 1. Introduction and main results. Let fi, i = 1,..., n, be identically distributed random variables. We investigate here expectations E ∥∥(xifi(ω))ni=1∥∥N, where ‖ · ‖N is an Orlicz norm. We find out that these expressions are maximal
and
"... There exist positive constants c0 and c1 = c1(n) such that for every 0 < < 1/2 the following holds: Let P be a convex polytope in Rn having N ≥ cn0/ vertices x1,..., xN. Then there exists a subset A ⊂ {1,..., N}, card (A) ≥ (1 − 2)N, such that for all i ∈ A voln(P) − voln(conv(vert (P) \ { ..."
Abstract
 Add to MetaCart
(Show Context)
There exist positive constants c0 and c1 = c1(n) such that for every 0 < < 1/2 the following holds: Let P be a convex polytope in Rn having N ≥ cn0/ vertices x1,..., xN. Then there exists a subset A ⊂ {1,..., N}, card (A) ≥ (1 − 2)N, such that for all i ∈ A voln(P) − voln(conv(vert (P) \ {xi})) voln(P) ≤ c1(n)− n+1 n−1N− n+1 n−1. Also, if P is a convex polytope in Rn having N ≥ cn0/ 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 − 2)N, such that for all i ∈ A voln j 6=iH