This volume contains contributions from the meeting held in honour of G.F. Dell'Antonio for his sixtieth birthday. The topics covered include the theory of classical and quantum dynamical systems and related mathematical disciplines such as functional and stochastic analysis, operator algebras etc. The contributions by leading specialists survey recent developments in Hamiltonian dynamics, non-commutative integration, supersymmetric theories, spin glass theory and other subjects in mathematical physics.
Inequalities play a fundamental role in Functional Analysis and it is widely recognized that finding them, especially sharp estimates, is an art. E. H. Lieb has discovered a host of inequalities that are enormously useful in mathematics as well as in physics. His results are collected in this book which should become a standard source for further research. Together with the mathematical proofs the author also presents numerous applications to the calculus of variations and to many problems of quantum physics, in particular to atomic physics.
This book contains the proceedings of two international conferences: a satellite meeting of the IUPAP Statphys-19 Conference and the Seventh Nankai Workshop, held in Tianjin, China in August 1995. The central theme of the two conferences, which drew participants from 18 countries, was the Yang-Baxter equation and its development and applications. With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in statistical mechanics.
In Statistical Physics one of the ambitious goals is to derive rigorously, from statistical mechanics, the thermodynamic properties of models with realistic forces. Elliott Lieb is a mathematical physicist who meets the challenge of statistical mechanics head on, taking nothing for granted and not being content until the purported consequences have been shown, by rigorous analysis, to follow from the premises. The present volume contains a selection of his contributions to the field, in particular papers dealing with general properties of Coulomb systems, phase transitions in systems with a continuous symmetry, lattice crystals, and entropy inequalities. It also includes work on classical thermodynamics, a discipline that, despite many claims to the contrary, is logically independent of statistical mechanics and deserves a rigorous and unambiguous foundation of its own. The articles in this volume have been carefully annotated by the editors.
Advanced Topics in Theoretical Chemical Physics is a collection of 20 selected papers from the scientific presentations of the Fourth Congress of the International Society for Theoretical Chemical Physics (ISTCP) held at Marly-le-Roi, France, in July 2002. Advanced Topics in Theoretical Chemical Physics encompasses a broad spectrum in which scientists place special emphasis on theoretical methods in chemistry and physics. The chapters in the book are divided into five sections: I: Advances Chemical Thermodynamics II: Electronic Structure of Molecular Systems III: Molecular Interaction and Dynamics IV: Condensed Matter V: Playing with Numbers This book is an invaluable resource for all academics and researchers interested in theoretical, quantum or statistical, chemical physics or physical chemistry. It presents a selection of some of the most advanced methods, results and insights in this exciting area.
This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. This stand-alone special topics volume reports recent advances in electron-transfer research with significant, up-to-date chapters by internationally recognized researchers.
This is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve.
