The Stability of Matter: From Atoms to Stars: Selecta of Elliot H. LiebThe first edition of "The Stability of Matter: From Atoms to Stars" was sold out after a time unusually short for a selecta collection and we thought it ap propriate not just to make a reprinting but to include eight new contributionso They demonstrate that this field is still lively and keeps revealing unexpected featureso Of course, we restricted ourselves to developments in which Elliott Lieb participated and thus the heroic struggle in Thomas-Fermi theory where 7 3 5 3 the accuracy has been pushed from Z 1 to Z 1 is not includedo A rich landscape opened up after Jakob Yngvason's observation that atoms in magnetic fields also are described in suitable limits by a Thomas-Fermi-type theoryo Together with Elliott Lieb and Jan Philip Solovej it was eventually worked out that one has to distinguish 5 regionso If one takes as a dimensionless measure of the magnetic field strength B the ratio Larmor radius/Bohr radius one can compare it with N "' Z and for each of the domains 4 3 (i) B « N 1 , 4 3 (ii) B "' N 1 , 4 3 3 (iii) N 1« B « N , 3 (iv) B "' N , 3 (v) B » N a different version ofmagnetic Thomas-Fermi theory becomes exact in the limit N --+ ooo In two dimensions and a confining potential ("quantum dots") the situation is somewhat simpler, one has to distinguish only (i) B « N, (ii) B "'N, |
Contents
Introduction | 1 |
with S Oxford | 65 |
M Sigal B Simon and W Thirring | 103 |
Copyright | |
15 other sections not shown
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The Stability of Matter: From Atoms to Stars: Selecta of Elliot H. Lieb Elliott H. Lieb No preview available - 2014 |
Common terms and phrases
assume asymptotic atom ball Benguria bosons constant convergence convex Coulomb potential decreasing defined denote density Dirac operator domain E. H. Lieb eigenvalues electron Elliott H Elliott Lieb equation exists fact fermions finite fixed given ground state energy ground-state Hamiltonian Hartree-Fock Hence Hölder's inequality implies inequality integral interaction jellium kinetic energy Lemma Lett lower bound magnetic field Math mathematical minimizing molecules monotone negative neutral non-negative Note nuclear charge nuclei obtain operator particle number Phys Physics positive Princeton problem proof of Theorem prove quantum dots quantum mechanics R₁ radius relativistic Remark replaced repulsion result right side satisfies Schrödinger Schrödinger equation semiclassical sequence Simon solution stability of matter term TF theory thermodynamic limit Thirring Thomas-Fermi theory unique upper bound wave function z₁ zero