S. A. Moskalenko / Academy of Sciences of Moldova
D. W. Snoke / University of Pittsburgh

Bose-Einstein Condensation of Excitons and Biexcitons
And Coherent Nonlinear Optics with Excitons Now in Paperback

Paperback (ISBN-10: 0521022355 | ISBN-13: 9780521022354)
November 2005

Bose-Einstein condensation of excitons is a unique effect in which the electronic states of a solid can self-organize to acquire quantum phase coherence. The phenomenon is closely linked to Bose-Einstein condensation in other systems such as liquid helium and laser-cooled atomic gases. This is the first book to provide a comprehensive survey of this field, covering theoretical aspects as well as recent experimental work. After setting out the relevant basic physics of excitons, the authors discuss exciton-phonon interactions as well as the behaviour of biexcitons. They cover exciton phase transitions and give particular attention to nonlinear optical effects including the optical Stark effect and chaos in excitonic systems. The thermodynamics of equilibrium, quasi-equilibrium, and nonequilibrium systems are examined in detail. The authors interweave theoretical and experimental results throughout the book, and it will be of great interest to graduate students and researchers in semiconductor and superconductor physics, quantum optics, and atomic physics.

Contents
1. Introduction; 2. Basic theory; 3. Interaction with phonons; 4. Biexcitons; 5. Phase transitions of excitons; 6. The optical Stark effect; 7. Mixed states of excitons and photons; 8. Nonequilibrium kinetics; 9. Coherent nonlinear optics; 10. New directions; Appendix.

Edited by Yair Minsky / Yale University, Connecticut
Makoto Sakuma / University of Osaka, Japan
Caroline Series / University of Warwick

Spaces of Kleinian Groups

Series: London Mathematical Society Lecture Note Series (No. 329)
Paperback (ISBN-10: 0521617979 | ISBN-13: 9780521617970)
Not yet published - available from February 2006
The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.

* Important and original research from leading names

* Includes results in topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory

* Covers much of the material from the explosion in the area over recent years

Contents

Preface Y. Minsky, M. Sakuma and C. Series; 1. Drilling short geodesics in hyperbolic-3 manifolds K. Bromberg; 2. On topologically tame Kleinian groups with bounded geometry K. Oshika & H. Miyachi; 3. An extension of the Masur domain C. Lecuire; 4. Thurston’s bending measure conjecture for once punctured torus groups C. Series; 5. Complexity of 3-manifolds B. Martelli; 6. Moduli of continuity of Cannon-Thurston maps H. Miyachi; 7. Variations of McShane’s identity for punctured surface groups H. Akiyoshi, H. Miyachi and M. Sakuma; 8. Train tracks and the Gromov boundary of the complex of curves U. Hamenstadt; 9. The pants complex only has one end H. Masur and S. Schleimer; 10. The Weil-Petersson geometry of the five-times punctured sphere J. Aramayona; 11. Convexity of geodesic-length functions: a reprise S. A. Wolpert; 12. A proof of the Ahlfors finiteness theorem A. Marden; 13. On the automorphic functions for Fuchsian groups of genus two Y. Komori; 14. Boundaries for two-parabolic Schottky groups J. Gilman; 15. Searching for the cusp D. J. Wright; 16. Circle packings on surfaces with projective structures: a survey S. Kojima, S. Mizushima and S. P. Tan; 17. Grafting and components of quasi-fuchsian projective structures K. Ito; 18. Computer experiments on the discreteness locus in projective structures Y. Yamashita.

Contributors

Y. Minsky, M. Sakuma, C. Series, K. Bromberg, K. Oshika, H. Miyachi, C. Lecuire, B. Martelli, H. Akiyoshi, U. Hamenstadt, J. Aramayona, S. A. Wolpert, A. Marden, Y. Komori, J. Gilman, D. J. Wright, S. Kojima, S. Mizushima, S. P. Tan, K. Ito, Y. Yamashita

Marian Fecko

Differential Geometry and Lie Groups for Physicists

Hardback (ISBN-10: 0521845076 | ISBN-13: 9780521845076)

September 2006

Differential geometry plays an increasingly important role in modern theoretical physics and applied mathematics. This textbook gives an introduction to geometrical topics useful in theoretical physics and applied mathematics, covering: manifolds, tensor fields, differential forms, connections, symplectic geometry, actions of Lie groups, bundles, spinors, and so on. Written in an informal style, the author places a strong emphasis on developing the understanding of the general theory through more than 1000 simple exercises, with complete solutions or detailed hints. The book will prepare readers for studying modern treatments of Lagrangian and Hamiltonian mechanics, electromagnetism, gauge fields, relativity and gravitation. Differential Geometry and Lie Groups for Physicists is well suited for courses in physics, mathematics and engineering for advanced undergraduate or graduate students, and can also be used for active self-study. The required mathematical background knowledge does not go beyond the level of standard introductory undergraduate mathematics courses.

* Complex ideas or computations are divided into a sequence of simple and clear statements

* Much of the theory is illustrated through simple exercises (over 1000 altogether), with detailed hints

* End of chapter summaries give important concepts, results and formulas

* Uses both standard mathematical and physical terminology

Contents

Introduction; 1. The concept of a manifold; 2. Vector and tensor fields; 3. Mappings of tensors induced by mappings of manifolds; 4. Lie derivative; 5. Exterior algebra; 6. Differential calculus of forms; 7. Integral calculus of forms; 8. Particular cases and applications of Stoke’s Theorem; 9. Poincare Lemma and cohomologies; 10. Lie Groups - basic facts; 11. Differential geometry of Lie Groups; 12. Representations of Lie Groups and Lie Algebras; 13. Actions of Lie Groups and Lie Algebras on manifolds; 14. Hamiltonian mechanics and symplectic manifolds; 15. Parallel transport and linear connection on M; 16. Field theory and the language of forms; 17. Differential geometry on TM and T*M; 18. Hamiltonian and Lagrangian equations; 19. Linear connection and the frame bundle; 20. Connection on a principal G-bundle; 21. Gauge theories and connections; 22. Spinor fields and Dirac operator; Appendices; Bibliography; Index.

the Societe Mathematique de France.

Seminaire Bourbaki, volume 2003/2004, exposes 924-937

Description

As in the preceding volumes of this seminar, one finds here fourteen survey lectures on topics of current interest: three lectures on algebraic geometry, four on partial differential equations, one on probability, one on number theory, one on dynamical systems, one on operator algebras, one on geometric inequalities, one on the representation theory of groups and one on harmonic analysis. The volume is suitable for graduate students and research mathematicians.

Contents

Novembre 2003
A. Beauville -- La conjecture de Green generique
J. Bertoin -- SLE et Invariance conforme
I. Gallagher -- Resultats recents sur la limite invompressible
R. Krikorian -- Deviations de moyennes ergodiques, flots de Teichmuller et cocycle de Kontsevich-Zorich
B. Maurey -- Inegalite de Brunn-Minkowski-Lusternik, et autres inegalites geometriques et fonctionnelles
Mars 2004
Y. Andre -- Motifs de dimension finie
P. Gerard -- Equations de champ moyen pour la dynamique quantique d'un grand nombre de particules
E. Peyre -- Obstructions au principe de Hasse et a l'approximation faible
J. Serre -- Complete reductibilite
N. Tzvetkov -- On the long time behavior of KdV type equations
Juin 2004
S. Alinhac -- Methodes geometriques dans l'etude des equations d'Einstein
K. Belabas -- Parametrisation de structures algebriques et densite de discriminants
H. Pajot -- Capacite analytique et le probleme de Painlev
S. Vaes -- Etats quasi-libres libres et facteurs de type III

Details:

Series: Asterisque, Number: 299
Publication Year: 2005
ISBN: 2-85629-173-2
Paging: 350 pp.
Binding: Softcover

Claude Sabbah, Ecole Polytechnique, Palaiseau, France

Polarizable twistor mathcal D-modules

Description

In this book, the author proves a decomposition theorem for the direct image of an irreducible local system on a smooth complex projective variety under a morphism with values in another smooth complex projective variety. For this purpose, he constructs a category of polarized twistor mathcal {D}-modules and shows a decomposition theorem in this category.

The book is suitable for graduate students and research mathematicians interested in geometry and topology.

Contents

Introduction
Preliminaries
Coherent and holonomic mathcal{R}_{mathcal{X}}-modules
Smooth twistor structures
Specializable mathcal{R}_{mathcal{X}}-modules
Polarizable twister mathcal {D}-modules
Polarizable regular twistor mathcal {D}-modules on curves
The decomposition theorem for polarizable regular twistor mathcal {D}-modules
Integrability
Appendix. Monodromy at infinity and partial Fourier Laplace transform
Bibliography
Notation

Details:

Series: Asterisque, Number: 300
Publication Year: 2005
ISBN: 2-85629-174-0
Paging: 208 pp.
Binding: Softcover

Yves Aubry - Gilles Lachaud (Ed.)

Arithmetic, Geometry and Coding Theory (AGCT 2003)

Seminaires et Congres 11 (2005), xviii+216 pages

Resume :

Arithmetique, geometrie et theorie des codes (AGCT 2003)
En mai 2003 se sont tenus au Centre International de Rencontres Mathematiques a Marseille (France), deux evenements centres sur l'Arithmetique, la Geometrie et leurs applications a la theorie des Codes ainsi qu'a la Cryptographie : une ecole Europeenne ``Geometrie Algebrique et Theorie de l'Information'' ainsi que la 9eme edition du colloque international ``Arithmetique, Geometrie et Theorie des Codes''. Certains des cours et des conferences font l'objet d'un article publie dans ce volume. Les themes abordes furent a la fois theoriques pour certains et tournes vers des applications pour d'autres : varietes abeliennes, corps de fonctions et courbes sur les corps finis, groupes de Galois de pro-p-extensions, fonctions zeta de Dedekind de corps de nombres, semi-groupes numeriques, nombres de Waring, complexite bilineaire de la multiplication dans les corps finis et problemes de nombre de classes.

Mots clefs : Fonctions zeta, varietes abeliennes, corps de fonctions, courbes sur les corps finis, tours de corps de fonctions, corps finis, graphes, semi-groupes numeriques, polynomes sur les corps finis, cryptographie, courbes hyperelliptiques, representations p-adiques, tours de corps de classe, groupe de Galois, points rationels, fractions continues, regulateurs, nombre de classes d'ideaux, complexite bilineaire, jacobienne hyperelliptiques

Abstract:

In may 2003, two events have been held in the ``Centre International de Rencontres Mathematiques'' in Marseille (France), devoted to Arithmetic, Geometry and their applications in Coding theory and Cryptography: an European school ``Algebraic Geometry and Information Theory'' and the 9-th international conference ``Arithmetic, Geometry and Coding Theory''. Some of the courses and the conferences are published in this volume. The topics were theoretical for some ones and turned towards applications for others: abelian varieties, function fields and curves over finite fields, Galois group of pro-p-extensions, Dedekind zeta functions of number fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and class number problems.

Key words:

Zeta functions, abelian varieties, functions fields, curves over finite fields, towers of function fields, finite fields, graphs, numerical semigroups, polynomials over finite fields, cryptography, hyperelliptic curves, p-adic representations, class field towers, Galois groups, rational points, continued fractions, regulators, ideal class number, bilinear complexity, hyperelliptic jacobians

K R Parthasarathy,
Indian Statistical Institute,New Delhi

Mathematical Foundations of Quantum Mechanics

Text and Readings in Mathematics/ 35
October 2005
184 pages
Hardcover
ISBN 81-85931-59-3

This book is based on a course of lectures given to PhD students at the Delhi Centre of the Indian Statistical Institute during the years 1980-1985. The approach is inspired by the lectures of G.W.Mackey and V.S.Varadarajan and brings out the role of group representations as the main thread passing through some major results like Gleason's theorem on the characterization of quantum states, Wigner's unitarity-antiunitarity theorem on the automorphisms of the lattice of orthogonal projections in a Hilbert space, Mackey's imprimitivity theorem for quantum systems with a configuration observable, and the rise of important and physically meaningful observables through the infinitesimal generators of projective unitary representations of the Galilean and the inhomogeneous Lorentz groups.

Contents

Chapter 1. PROBABILITY THEORY ON THE LATTICE OF PROJECTIONS IN A HILBERT SPACE
Chapter 2. SYSTEMS WITH A CONFIGURATION UNDER A GROUP ACTION
Chapter 3. MULTIPLIERS ON LOCALLY COMPACT GROUPS
Chapter 4. THE BASIC OBSERVABLES OF A QUANTUM MECHANICAL SYSTEM
Bibliography