The Physics and Mathematics of Elliott Lieb

Rupert L. Frank; Ari Laptev; Mathieu Lewin; Robert Seiringer

doi:10.4171/90-2

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
Frontmatter
pp. v–viii
Contents
pp. 1–9
On the construction and exact solution of the Luttinger model by Mattis and Lieb
Edwin Langmann
pp. 11–17
Statistical mechanics of Coulomb systems: From electrons and nuclei to atoms and molecules
Joel L. Lebowitz
pp. 19–29
Relaxed energies, defect measures, and minimal currents
Fang-Hua Lin
pp. 31–45
Elliott Lieb’s work on stability of matter
Michael Loss
pp. 47–71
Comparison of Ising models under change of a priori measure
José Madrid
pp. 73–77
The Polaron problem
Chiranjib MukherjeeSrinivasa R. S. Varadhan
pp. 79–92
From Lieb–Robinson bounds to automorphic equivalence
Bruno Nachtergaele
pp. 93–120
The ionization problem in quantum mechanics
Phan Thành Nam
pp. 121–163
Elliott Lieb, vertex models, and artificial spin ice
Cristiano Nisoli
pp. 165–178
The Lieb–Oxford lower bounds on the Coulomb energy, their importance to electron density functional theory, and a conjectured tight bound on exchange
John P. PerdewJianwei Sun
pp. 179–217
The classical Jellium and the Laughlin phase
Nicolas Rougerie
pp. 219–251
Compactness methods in Lieb’s work
Julien Sabin
pp. 253–275
The state of the Lieb–Thirring conjecture
Lukas Schimmer
pp. 277–305
Bose gases in the Gross–Pitaevskii limit: A survey of some rigorous results
Benjamin Schlein
pp. 307–327
Upper bound on the ground state energy of the two-component charged Bose gas with arbitrary masses
Andreas SchönJan Philip Solovej
pp. 329–344
Wehrl entropy, coherent states and quantum channels
Peter Schupp
pp. 345–360
The Lieb–Oxford bound and the optimal transport limit of DFT
Michael SeidlTarik BenyahiaDerk P. KooiPaola Gori-Giorgi
pp. 361–387
The energy and electron density of heavy atoms
Heinz Siedentop
pp. 389–404
Recent advances on the Lieb–Liniger $δ$ -Bose gas
Herbert Spohn
pp. 405–446
The Lieb–Schultz–Mattis theorem. A topological point of view
Hal Tasaki
pp. 447–500
Lieb’s spin-reflection-positivity method, Lieb lattice and all that
Guang-Shan Tian
pp. 501–516
Lieb’s permanental dominance conjecture
Ian M. Wanless
pp. 517–563
The $L^{p}$ -boundedness of wave operators for four-dimensional Schrödinger operators
Kenji Yajima
pp. 565–584
A direct road to entropy and the second law of thermodynamics
Jakob Yngvason
pp. 585–628
The Brascamp–Lieb inequality and its influence on Fourier analysis
Ruixiang Zhang
pp. 629–652
The Lieb–Liniger gas with cold atoms
Wilhelm Zwerger
pp. 653–676
Publications of Elliott H. Lieb
pp. 677–682
List of contributors
pp. 683–684
List of themes