The Stability of Matter: From Atoms to Stars

The 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,

I.1 The Stability of Matter: From Atoms to Stars.- II.1 Lower Bound to the Energy of Complex Atoms.- II.2 Improved Lower Bound on the Indirect Coulomb Energy.- II.3 Monotonicity of the Molecular Electronic Energy in the Nuclear Coordinates.- II.4 Proof of the Stability of Highly Negative Ions in the Absence of the Pauli Principle.- II.5 Atomic and Molecular Negative Ions.- II.6 Bound on the Maximum Negative Ionization of Atoms and Molecules.- II.7 Asymptotic Neutrality of Large-Z Ions.- II.8 Approximate Neutrality of Large-Z Ions.- II.9 Universal Nature of van der Waals Forces for Coulomb Systems.- II.10 Electron Density Near the Nucleus of a Large Atom.- II.11 Proof of a Conjecture About Atomic and Molecular Cores Related to Scott's Correction.- II.12 Asymptotics of Natural and Artificial Atoms in Strong Magnetic Fields.- II.13 Ground States of Large Quantum Dots in Magnetic Fields.- III.1 Kinetic Energy Bounds and Their Application to the Stability of Matter.- III.2 Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities.- III.3 On Semi-Classical Bounds for Eigenvalues of Schrödinger Operators.- III.4 The Number of Bound States of One-Body Schrödinger Operators and the Weyl Problem.- III.5 Variational Principle for Many-Fermion Systems.- IV.I Thomas-Fermi and Related Theories of Atoms and Molecules.- IV.2 The Hartree-Fock Theory for Coulomb Systems.- IV.3 There Are No Unfilled Shells in Unrestricted Hartree-Fock Theory.- IV.4 Many-Body Atomic Potentials in Thomas-Fermi Theory.- IV.5 The Positivity of the Pressure in Thomas-Fermi Theory.- IV.6 The Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules.- IV.7 Analysis of the Thomas-Fermi-von Weizsäcker Equation for an InfiniteAtom Without Electron Repulsion.- IV.8 The Most Negative Ion in the Thomas-Fermi-von Weizsäcker Theory of Atoms and Molecules.- V.1 Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter.- V.2 The N5/3 Law for Bosons.- V.3 Stability of Coulomb Systems with Magnetic Fields. I. The One-Electron Atom.- V.4 Stability of Coulomb Systems with Magnetic Fields. II. The Many-Electron Atom and the One-Electron Molecule.- V.5 Stability of Matter in Magnetic Fields.- V.6 A Rigorous Examination of the Chandrasekhar Theory of Stellar Collapse.- V.7 The Chandrasekhar Theory of Stellar Collapse as the Limit of Quantum Mechanics.- V.8 One-Electron Relativistic Molecules with Coulomb Interaction.- V.9 Many-Body Stability Implies a Bound on the Fine-Structure Constant.- V.10 The Stability and Instability of Relativistic Matter.- V.11 Stability of Relativistic Matter Via Thomas-Fermi Theory.- V.1 Stability and Instability of Relativistic Electrons in Classical Electromagnetic Fields.- V.13 The N715 Law for Charged Bosons.- VI.1 The Stability of Matter.- VI.2 Existence of Thermodynamics for Real Matter with Coulomb Forces.- VI.3 Lectures on the Thermodynamic Limit for Coulomb Systems.- VI.4 The Thermodynamic Limit for Jellium.- Publications of Elliott H. Lieb.