# The Physics and Mathematics of Elliott Lieb

Volume II

## Editors

### Rupert L. Frank

Ludwig-Maximilians-Universität München, Germany### Ari Laptev

Imperial College London, United Kingdom### Mathieu Lewin

Université Paris Dauphine, France### Robert Seiringer

Institute of Science and Technology Austria, Klosterneuburg, Austria

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These two volumes are dedicated to Elliott Lieb on the occasion of his 90th birthday. They celebrate his fundamental contributions to the fields of mathematics, physics and chemistry.

Around 50 chapters give an extensive account of Lieb’s impact on a very broad range of topics and the resulting subsequent developments. Many contributions are of an expository character and are accessible to a non-expert audience of researchers in mathematics, physics and chemistry.

A non-exhaustive list of topics covered includes the problem of stability of matter, quantum many-body systems, density functional theory, topics in statistical mechanics, entropy inequalities and matrix analysis, functional inequalities and sharp constants.

pp. i–iv Frontmatterpp. v–viii Contentspp. 1–9 On the construction and exact solution of the Luttinger model by Mattis and LiebEdwin Langmann

DOI 10.4171/90-2/27pp. 11–17 Statistical mechanics of Coulomb systems: From electrons and nuclei to atoms and moleculesJoel L. Lebowitz

DOI 10.4171/90-2/28pp. 19–29 Relaxed energies, defect measures, and minimal currentsFang-Hua Lin

DOI 10.4171/90-2/29pp. 31–45 Elliott Lieb’s work on stability of matterMichael Loss

DOI 10.4171/90-2/30pp. 47–71 Comparison of Ising models under change of a priori measureJosé Madrid

DOI 10.4171/90-2/31pp. 73–77 The Polaron problemChiranjib MukherjeeSrinivasa R. S. Varadhan

DOI 10.4171/90-2/32pp. 79–92 From Lieb–Robinson bounds to automorphic equivalenceBruno Nachtergaele

DOI 10.4171/90-2/33pp. 93–120 The ionization problem in quantum mechanicsPhan Thành Nam

DOI 10.4171/90-2/34pp. 121–163 Elliott Lieb, vertex models, and artificial spin iceCristiano Nisoli

DOI 10.4171/90-2/35pp. 165–178 The Lieb–Oxford lower bounds on the Coulomb energy, their importance to electron density functional theory, and a conjectured tight bound on exchangeJohn P. PerdewJianwei Sun

DOI 10.4171/90-2/36pp. 179–217 The classical Jellium and the Laughlin phaseNicolas Rougerie

DOI 10.4171/90-2/37pp. 219–251 Compactness methods in Lieb’s workJulien Sabin

DOI 10.4171/90-2/38pp. 253–275 The state of the Lieb–Thirring conjectureLukas Schimmer

DOI 10.4171/90-2/39pp. 277–305 Bose gases in the Gross–Pitaevskii limit: A survey of some rigorous resultsBenjamin Schlein

DOI 10.4171/90-2/40pp. 307–327 Upper bound on the ground state energy of the two-component charged Bose gas with arbitrary massesAndreas SchönJan Philip Solovej

DOI 10.4171/90-2/41pp. 329–344 Wehrl entropy, coherent states and quantum channelsPeter Schupp

DOI 10.4171/90-2/42pp. 345–360 The Lieb–Oxford bound and the optimal transport limit of DFTMichael SeidlTarik BenyahiaDerk P. KooiPaola Gori-Giorgi

DOI 10.4171/90-2/43pp. 361–387 The energy and electron density of heavy atomsHeinz Siedentop

DOI 10.4171/90-2/44pp. 389–404 Recent advances on the Lieb–Liniger $δ$-Bose gasHerbert Spohn

DOI 10.4171/90-2/45pp. 405–446 The Lieb–Schultz–Mattis theorem. A topological point of viewHal Tasaki

DOI 10.4171/90-2/46pp. 447–500 Lieb’s spin-reflection-positivity method, Lieb lattice and all thatGuang-Shan Tian

DOI 10.4171/90-2/47pp. 501–516 Lieb’s permanental dominance conjectureIan M. Wanless

DOI 10.4171/90-2/48pp. 517–563 The $L_{p}$-boundedness of wave operators for four-dimensional Schrödinger operatorsKenji Yajima

DOI 10.4171/90-2/49pp. 565–584 A direct road to entropy and the second law of thermodynamicsJakob Yngvason

DOI 10.4171/90-2/50pp. 585–628 The Brascamp–Lieb inequality and its influence on Fourier analysisRuixiang Zhang

DOI 10.4171/90-2/51pp. 629–652 The Lieb–Liniger gas with cold atomsWilhelm Zwerger

DOI 10.4171/90-2/52pp. 653–676 Publications of Elliott H. Liebpp. 677–682 List of contributorspp. 683–684 List of themes