# The Physics and Mathematics of Elliott Lieb

Volume I

## 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–vi Frontmatterpp. vii–viii Prefacepp. ix–xii Contentspp. 1–6 The Affleck–Kennedy–Lieb–Tasaki (AKLT) modelIan Affleck

DOI 10.4171/90-1/1pp. 7–17 On Lieb’s “On the lowest eigenvalue of the Laplacian for the intersection of two domains”Mark S. Ashbaugh

DOI 10.4171/90-1/2pp. 19–65 Hartree–Fock theory, Lieb’s variational principle, and their generalizationsVolker Bach

DOI 10.4171/90-1/3pp. 67–76 Analytic bound on the excess charge for the Hartree modelRafael D. BenguriaTrinidad Tubino

DOI 10.4171/90-1/4pp. 77–108 Reflection positivity and infrared bounds for quantum spin systemsJakob E. BjörnbergDaniel Ueltschi

DOI 10.4171/90-1/5pp. 109–130 Maximal speed of propagation in open quantum systemsSébastien BreteauxJérémy FaupinMarius LemmIsrael Michael Sigal

DOI 10.4171/90-1/6pp. 131–142 Lieb’s most useful contribution to density functional theory?Kieron Burke

DOI 10.4171/90-1/7pp. 143–209 On some convexity and monotonicity inequalities of Elliott LiebEric A. Carlen

DOI 10.4171/90-1/8pp. 211–224 Conserved quantities in general relativity – the view from null infinityPo-Ning ChenMu-Tao WangYe-Kai WangShing-Tung Yau

DOI 10.4171/90-1/9pp. 225–245 Experimental tests of Lieb–Robinson boundsMarc Cheneau

DOI 10.4171/90-1/10pp. 247–268 Hardy–Littlewood–Sobolev and related inequalities: StabilityJean DolbeaultMaria J. Esteban

DOI 10.4171/90-1/11pp. 269–293 Periodic striped states in Ising models with dipolar interactionsDavide FermiAlessandro Giuliani

DOI 10.4171/90-1/12pp. 295–314 Atoms in strong magnetic fieldsSøren Fournais

DOI 10.4171/90-1/13pp. 315–350 Tunneling effect induced by a curved magnetic edgeSøren FournaisBernard HelfferAyman Kachmar

DOI 10.4171/90-1/14pp. 351–375 Rearrangement methods in the work of Elliott LiebRupert L. Frank

DOI 10.4171/90-1/15pp. 377–399 Quantum number towers for the Hubbard and Holstein modelsJames K. Freericks

DOI 10.4171/90-1/16pp. 401–435 Irreversibility and the arrow of timeJürg Fröhlich

DOI 10.4171/90-1/17pp. 437–450 Ground states of atoms and molecules in non-relativistic QEDMarcel Griesemer

DOI 10.4171/90-1/18pp. 451–471 Perturbation theory for a non-equilibrium stationary state of a one-dimensional stochastic wave equationGianluca GuadagniLawrence E. Thomas

DOI 10.4171/90-1/19pp. 473–514 Entropies, majorization flow, and continuity boundsEric Patrick HansonNilanjana Datta

DOI 10.4171/90-1/20pp. 515–525 On Lieb–Robinson bounds for the double bracket flowMatthew B. Hastings

DOI 10.4171/90-1/21pp. 527–559 Lieb variation principle in density-functional theoryTrygve HelgakerAndrew M. Teale

DOI 10.4171/90-1/22pp. 561–582 Phase transitions in Dicke modelsKlaus Hepp

DOI 10.4171/90-1/23pp. 583–608 Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamicsAlexei IlyinAnna KostiankoSergey Zelik

DOI 10.4171/90-1/24pp. 609–635 Review of a Simplified Approach to study the Bose gas at all densitiesIan Jauslin

DOI 10.4171/90-1/25pp. 637–666 Knot theory and statistical mechanicsLouis H. Kauffman

DOI 10.4171/90-1/26pp. 667–668 List of themes