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Quantum Many Body Systems

Cetraro, Italy 2010, Editors: Alessandro Giuliani, Vieri Mastropietro, Jakob Yngvason

  • Book
  • © 2012

Overview

Authors:
  1. Vincent Rivasseau

    1. Laboratoire de Physique Théorique, Université Paris-Sud, Orsay, France

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  2. Robert Seiringer

    1. Dept. of Mathematics and Statistics, McGill University, Montreal, Canada

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  3. Jan Philip Solovej

    1. University of Copenhagen, Copenhagen, Denmark

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  4. Thomas Spencer

    1. , School of Mathematics, Institute for Advanced Study, Princeton, USA

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  • Tutorial presentation of advanced topics introduces the reader to some of the most exciting topics of modern mathematical physics Examples and physical applications guide the reader towards a deep comprehension of sophisticated mathematical tools Serves as a guide through recent literature on the mathematics of interacting fermionic and bosonic systems
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2051)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (4 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction to the Renormalization Group with Applications to Non-relativistic Quantum Electron Gases

    • Vincent Rivasseau
    Pages 1-54

  3. Cold Quantum Gases and Bose–Einstein Condensation

    • Robert Seiringer
    Pages 55-92

  4. Quantum Coulomb Gases

    • Jan Philip Solovej
    Pages 93-124

  5. SUSY Statistical Mechanics and Random Band Matrices

    • Thomas Spencer
    Pages 125-177

  6. Back Matter

    Pages 179-180
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About this book

The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.

Authors and Affiliations

  • Laboratoire de Physique Théorique, Université Paris-Sud, Orsay, France

    Vincent Rivasseau

  • Dept. of Mathematics and Statistics, McGill University, Montreal, Canada

    Robert Seiringer

  • University of Copenhagen, Copenhagen, Denmark

    Jan Philip Solovej

  • , School of Mathematics, Institute for Advanced Study, Princeton, USA

    Thomas Spencer

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