Quantum Theory from Small to Large Scales

Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Edited by Jurg Frohlich, Manfred Salmhofer, Vieri Mastropietro, Wojciech De Roeck, and Leticia F. Cugliandolo

Lecture Notes of the Les Houches Summer School

Addresses fundamental questions of mathematics and physics
Written from a pedagogical perspective
State-of-the-art reviews of a rapidly growing research field
Suggests future lines of research
Combines different areas of the exact sciences

Quantum Theory from Small to Large Scales

Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Edited by Jurg Frohlich, Manfred Salmhofer, Vieri Mastropietro, Wojciech De Roeck, and Leticia F. Cugliandolo

Lecture Notes of the Les Houches Summer School

Description

This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales". Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

Quantum Theory from Small to Large Scales

Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Edited by Jurg Frohlich, Manfred Salmhofer, Vieri Mastropietro, Wojciech De Roeck, and Leticia F. Cugliandolo

Lecture Notes of the Les Houches Summer School

1. A Word from the Organizers
2. Mass Renormalization in Nonrelativstic Quantum Electrodynamics, Volker Bach
3. Quantum Brownian Motion, Laszlo Erdos
4. The Temporal Ultraviolet Limit, Tadeusz Balaban, Joel Feldman, Horst Knorrer and Eugene Trubowitz
5. Locality in Quantum Systems, Matthew B. Hastings
6. Entropic Fluctuations in Quantum Statistical Mechanics - An Introduction, V. Jaksic, Y. Ogata, Y. Pautrat, and C.-A. Pillet
7. Quantum Phase Transitions: Introduction and Some Open Problems, Achim Rosch
8. Cold Quantum Gases and Bose-Einstein Condensation, Robert Seiringer
9. Renormalization Group and Problem of Radiation, Israel Michael Sigal
10. SUSY Statistical Mechanics and Random Band Matrices, Thomas Spencer
11. Long-time diffusion for a quantum particle, Wojciech De Roeck
12. Universality of Generalized Wigner Matrices, Horng-Tzer Yau
13. On Transport in Quantum Devices, Gian Michele Graf
14. The ground state construction of the two-dimennsion Hubbard model on the honeycomb lattice, Alessandro Giuliani

Quantum Theory from Small to Large Scales

Lecture Notes of the Les Houches Summer School: Volume 95, August 2010

Edited by Jurg Frohlich, Manfred Salmhofer, Vieri Mastropietro, Wojciech De Roeck, and Leticia F. Cugliandolo

Lecture Notes of the Les Houches Summer School

Author Information

Jurg Frohlich is Professor at ETH Zurich, Switzerland. In 1984, he was awarded the "Latsis Prize" of the Swiss National Science Foundation. He has also been awarded the Marcel-Benoist Prize 1997, and, in 2001, the Max-
Planck Medal of the German Physical Society. He is a member of the "Academia Europaea" and has been elected an associate member of the "Berlin-Brandenburgische Akademie der Wissenschaften".

Manfred Salmhofer is Professor at Universitat Heidelberg, Germany. His main research interests are theoretical and mathematical physics, in particular quantum field theory and statistical mechanics, the renormalization group, and condensed-matter theory. He presently acts as an associate editor of Journal of Mathematical Physics and as an Editor of Communications in Mathematical Physics.

Vieri Mastropietro is Professor at Universita' di Roma Tor Vergata. His main scientific interests are classical and
quantum Statistical Physics and Quantum Field Theory systems, analyzed through rigorous Renormalization Group methods; he has also worked on dynamical systems and KAM theory. He was awarded the Persico prize (1987 and 1989) of the Accademia dei Lincei and the Annales Poincare' prize (2006). He also acts as an editor of Annales Poincare' and CPAA and is member of the Center for Mathematical and Theoretical Physics (CMTP).

Wojciech De Roeck is a lecturer at Universitat Heidelberg, Germany. He obtained his Physics Degree at the University of Antwerp (UA) in 2002 and his PhD at the University of Antwerp and K.U.Leuven in 2006. From 2007 to 2009, he was a post-doctoral fellow supported by the FWO (Flemish Research Fund).

Leticia F. Cugliandolo is Professor at Universite Pierre et Marie Curie, France. She got her PhD in Physics from Universidad Nacional de La Plata, Argentina, in 1991. Subsequently, she spent a three year post-doc at Universita di Roma I, La Sapienza, and then moved to the Service de Physique de l'Etat Condense at Saclay
(CEA) and Ecole Normale Superieure (ENS) de Paris for a second post-doctoral experience. In 1997 she became assistant professor at ENS Paris and in 2003 full professor at Universite Pierre et Marie Curie - Paris VI where she presently teaches and pursues her research acivities. Since January 2007 she is the Director of Ecole de Physique des Houches.

Contributors:

Volker Bach
László Erdos
Tadeusz Balaban, Joel Feldman, Horst Knörrer and Eugene Trubowitz
Matthew B. Hastings
V. Jaksic, Y. Ogata, Y. Pautrat, and C.-A. Pillet
Achim Rosch
Robert Seiringer
Israel Michael Sigal
Thomas Spencer
Wojciech De Roeck
Horng-Tzer Yau
Gian Michele Graf