The Physics and Mathematics of Elliott Lieb
Volume I
Editors
Rupert L. Frank
Ludwig-Maximilians-Universität München, GermanyAri Laptev
Imperial College London, United KingdomMathieu Lewin
Université Paris Dauphine, FranceRobert 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
pp. 7–17 On Lieb’s “On the lowest eigenvalue of the Laplacian for the intersection of two domains”Mark S. Ashbaugh
pp. 19–65 Hartree–Fock theory, Lieb’s variational principle, and their generalizationsVolker Bach
pp. 67–76 Analytic bound on the excess charge for the Hartree modelRafael D. BenguriaTrinidad Tubino
pp. 77–108 Reflection positivity and infrared bounds for quantum spin systemsJakob E. BjörnbergDaniel Ueltschi
pp. 109–130 Maximal speed of propagation in open quantum systemsSébastien BreteauxJérémy FaupinMarius LemmIsrael Michael Sigal
pp. 131–142 Lieb’s most useful contribution to density functional theory?Kieron Burke
pp. 143–209 On some convexity and monotonicity inequalities of Elliott LiebEric A. Carlen
pp. 211–224 Conserved quantities in general relativity – the view from null infinityPo-Ning ChenMu-Tao WangYe-Kai WangShing-Tung Yau
pp. 225–245 Experimental tests of Lieb–Robinson boundsMarc Cheneau
pp. 247–268 Hardy–Littlewood–Sobolev and related inequalities: StabilityJean DolbeaultMaria J. Esteban
pp. 269–293 Periodic striped states in Ising models with dipolar interactionsDavide FermiAlessandro Giuliani
pp. 295–314 Atoms in strong magnetic fieldsSøren Fournais
pp. 315–350 Tunneling effect induced by a curved magnetic edgeSøren FournaisBernard HelfferAyman Kachmar
pp. 351–375 Rearrangement methods in the work of Elliott LiebRupert L. Frank
pp. 377–399 Quantum number towers for the Hubbard and Holstein modelsJames K. Freericks
pp. 401–435 Irreversibility and the arrow of timeJürg Fröhlich
pp. 437–450 Ground states of atoms and molecules in non-relativistic QEDMarcel Griesemer
pp. 451–471 Perturbation theory for a non-equilibrium stationary state of a one-dimensional stochastic wave equationGianluca GuadagniLawrence E. Thomas
pp. 473–514 Entropies, majorization flow, and continuity boundsEric Patrick HansonNilanjana Datta
pp. 515–525 On Lieb–Robinson bounds for the double bracket flowMatthew B. Hastings
pp. 527–559 Lieb variation principle in density-functional theoryTrygve HelgakerAndrew M. Teale
pp. 561–582 Phase transitions in Dicke modelsKlaus Hepp
pp. 583–608 Applications of the Lieb–Thirring and other bounds for orthonormal systems in mathematical hydrodynamicsAlexei IlyinAnna KostiankoSergey Zelik
pp. 609–635 Review of a Simplified Approach to study the Bose gas at all densitiesIan Jauslin
pp. 637–666 Knot theory and statistical mechanicsLouis H. Kauffman
pp. 667–668 List of themes