UJF NATO ASI LES HOUCHES Session LXIX 1998 ASPECTS TOPOLOGIQUES DE LA PHYSIQUE EN BASSE DIMENSION TOPOLOGICAL ASPECTS OF LOW DIMENSIONAL SYSTEMS CONFERENCIERS G. DUNNE B. DUPLANTIER M.P.A. FISHER S. GIRVIN J. MYRHEIM S. NECHAEV A.P. POLYCHRONAKOS H. SALEUR M. SHAYEGAN D. THOULESS A. AKKERMANS J.T. CHALKER V. CROQUETTE J. DESBOIS D.C. GLATTLI ÉCOLE DE PHYSIQUE DES HOUCHES - UJF & INPG - GRENOBLE a NATO Advanced Study Institute LES HOUCHES SESSION LXIX 7-31 July 1998 Aspects topologiques de la physique en basse dimension Topological aspects of low dimensional systems Edited by A. COMTET, T. JOLICŒUR, S. OUVRY and F. DAVID SCIENCES 7 avenue du Hoggar, PA de Courtabœuf, B.P. 112, 91944 Les Ulis cedex A, France 875-81 Massachusetts Avenue, Cambridge, MA 02139, U.S.A Springer Berlin, Heidelberg, New York, Barcelona, Hong Kong, London Milan, Paris, Singapore, Tokyo Published in cooperation with the NATO Scientific Affair Division ISBN 3-540-66909-4 Springer-Verlag Berlin Heidelberg New York ISBN 2-86883-424-8 EDP Sciences Les Ulis This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broad- casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the French and German Copyright laws of March 11, 1957 and September 9, 1965, respectively. Violations fall under the prosecution act of the French and German Copyright Laws. © EDP Sciences; Springer-Verlag 1999 Printed in France LES HOUCHES - ECOLE DE PHYSIQUE ÉCOLE D'ÉTÉ DE PHYSIQUE THÉORIQUE SERVICE INTER-UNIVERSITAIRE COMMUN À L'UNIVERSITÉ JOSEPH FOURIER DE GRENOBLE ET À L'INSTITUT NATIONAL POLYTECHNIQUE DE GRENOBLE, SUBVENTIONNÉ PAR LE MINISTÈRE DE L'ÉDUCATION NATIONALE, DE LA RECHERCHE ET DE LA TECHNOLOGIE, LE CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE ET LE COMMISSARIAT À L'ÉNERGIE ATOMIQUE Membres du Conseil d'Administration : Claude Feuerstein (président), Yves Brunet (vice-président), Cécile De Witt, Daniel Decamps, Thierry Dhombre, Hubert Flocard, Jean-François Joanny, Michèle Leduc, James Lequeux, Marcel Lesieur, Giorgio Parisi, Michel Peyrard, Jean-Paul Poirier, Claude Weisbuch, Joseph Zaccai, Jean Zinn-Justin Directeur : François David ECOLE D'ETE DE PHYSIQUE THEORIQUE SESSION LXIX INSTITUT D'ÉTUDES AVANCÉES DE L'OTAN NATO ADVANCED STUDY INSTITUTE 7 juillet — 31 juillet 1998 Directeurs Scientifiques de la session : Alain COMTET, LPTMS, bâtiment 100, 91406 Orsay, France, Thierry JOLICŒUR, SPhT, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France et Stéphane OUVRY, LPTMS, bâtiment 100, 91406 Orsay Cedex, France SESSIONS PRECEDENTES 1951 -1997 Quantum mechanics. Quantum field theory Quantum mechanics. Statistical mechanics. Nuclear physics Quantum mechanics. Solid state physics. Statistical mechanics. Elementary particle physics Quantum mechanics. Collision theory. Nucleon-nucleon interaction. Quantum electrodynamics Quantum mechanics. Non-equilibrium phenomena. Nuclear reactions. Interaction of a nucleus with atomic and molecular fields Quantum perturbation theory. Low temperature physics. Quantum theory of solids; dislocations and plastic properties. Magnesium; ferromagnetism Scattering theory. Recent developments in field theory. Nuclear interaction; strong interactions. High energy electrons. Experiments in high energy nuclear physics The many body problem The theory of neutral and ionized gases* Elementary particles and dispersion relations* Low temperature physics* Geophysics; the earth's environment* Relativity groups and topology* Quantum optics and electronics High energy physics High energy astrophysics* Many body physics* Nuclear physics* I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 Sessions ayant reçu l'appui du Comité Scientifique de l'OTAN. VIII XIX XX XXI XXII XXIII XXIV XXV XXVI June Inst. XXVII XXVIII XXIX XXX XXXI XXXII XXXIII XXXIV XXXV XXXVI XXXVII XXXVIII XXXIX XL XLI XLII XLIII XLIV XLV XLVI XLVII XLVIII XLIX L LI LII LIII LIV 1969 1970 1971 1972 1972 1973 1973 1974 1975 1975 1975 1976 1977 1978 1979 1979 1980 1980 1981 1981 1982 1982 1983 1983 1984 1984 1985 1985 1986 1986 1988 1988 1988 1989 1989 1990 1990 Physical problems in biological systems Statistical mechanics and quantum field theory Particle physics Plasma physics Black holes Fluids dynamics Molecular fluids* Atomic and molecular physics and the interstellar matter* Structural analysis of collision amplitudes Frontiers in laser spectroscopy* Methods in field theory* Weak and electromagnetic interactions at high energy* Nuclear physics with heavy ions and mesons* Ill-condensed matter Membranes and intercellular communication Physical cosmology Laser plasma interaction Physics of defects Chaotic behaviour of deterministic systems* Gauge theories in high energy physics* New trends in atomic physics* Recent advances in field theory and statistical mechanics* Relativity, groups and topology* Birth and infancy of stars* Cellular and molecular aspects of developmental biology* Critical phenomena, random systems, gauge theories* Architecture of fundamental interactions at short distances* Signal processing* Chance and matter Astrophysical fluid dynamics Liquids at interfaces Fields, strings and critical phenomena Oceanographic and geophysical tomography Liquids, freezing and glass transition Chaos and quantum physics* Fundamental systems in quantum optics* Supernovae* Sessions ayant reçu l'appui du Comité Scientifique de l'OTAN. IX Particles in the nineties* Strongly interacting fermions and high T c superconduc- tivity Gravitation and quantizations Progress in picture processing* Computational fluid dynamics Cosmology and large scale structure Mesoscopic quantum physics Fluctuating geometries in statistical mechanics and quantum field theory Quantum fluctuations* Quantum symmetries* From cell to brain* Trends in nuclear physics, 100 years later Modélisation du climat de la terre et de sa variabilité Particules et interactions : le modèle standard mis à l'épreuve* Sessions ayant reçu l'appui du Comité Scientifique de l'OTAN. Publishers: Session VIII: Dunod, Wiley, Methuen; Sessions IX & X: Herman, Wiley - Session XI: Gordon and Breach, Presses Universitaires - Sessions XII- XXV: Gordon and Breach - Sessions XXVI-LXVIII: North-Holland. LV LVI LVII LVIII LIX LX LXI LXII LXIII LXIV LXV LXVI LXVII LXVIII 1991 1991 1992 1992 1993 1993 1994 1994 1995 1995 1996 1996 1997 1997 [...]... University of Ionnina, 45110 Ionnina, Greece H SALEUR, Department of Physics, University of Southern California, Los-Angeles, CA 90089-0484, U.S.A M SHAYEGAN, Department of Electrical Engineering, Princeton University, Princeton, NJ, U.S.A D.J THOULESS, Department of Physics, Box Washington, Seattle, WA 98195, U.S.A 351560, University of XII SEMINAR SPEAKERS E AKKERMANS, Technion, Israel Institute of Technology,... 707 4.3 Statistics of random walks with topological constraints in the twodimensional lattices of obstacles 709 5 Physical applications Polymer language in statistics of entangled chain-like objects 715 5.1 Polymer chain in 3D-array of obstacles 716 5.2 Collapsed phase of unknotted polymer 719 6 Some tight problems of physics 6.1 Remarks and... tradition There were two sessions devoted to participant's seminars and the list of these is given at the end of the book We were able to admit only a limited number of participants among all the many highly qualified people who applied We hope that the quick publication of this volume will give everyone access to some of the benefits of this school This session LXIX was possible thanks to support from: - Universitộ... Department of Physics, University of Connecticut, Storrs, CT 06269, U.S.A B DUPLANTIER, SPhT, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France M.P.A FISHER, Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, U.S.A S.M GIRVIN, Indiana University, Department of Physics, Bloomington, IN 47405, U.S.A J MYRHEIM, Department of Physics, The Norwegian University of Science... realm of the fractional quantum Hall effect Experimental progress in molecular beam epitaxy techniques leading to high-mobility samples allowed the discovery of this remarkable and novel phenomenon These developments lead also to the attribution of the 1998 Nobel Prize in physics to Laughlin, Stửrmer and Tsui The notions of fractional charge as well as fractional statistics can be interpreted by a topological. .. recent applications to DNA physics XX11 A general overview of the role of topology in physics was given by David Thouless The very notion of topological quantum numbers was illustrated by various examples from quantum Hall physics to superfluids Vortices were also a common theme in a seminar given by Eric Akkermans The all-important role of disorder in the quantum Hall effect was discussed in a review... Department, Rutgers University, Piscataway, NJ 08855-0849, U.S.A., Loomis Laboratory, University of Illinois at UrbanaChampaign, Urbana, IL 61801-3080, U.S.A XV N SANDLER, Univ of Illinois at Urbana-Champaign, Dept of Physics, 1110 West Green St., Urbana, IL 61801, U.S.A F SIANO, Univ of Southern California, Dept of Physics, Los Angeles, CA 90089-0484, U.S.A J SINOVA, Indiana University, Physics Department,... A.2 Three dimensions 637 Course 8 Statistics of Knots and Entangled Random Walks by S Nechaev 643 1 Introduction 645 2 Knot diagrams as disordered Spin Systems 2.1 Brief review of statistical problems in topology 2.2 Abelian problems in statistics of entangled random walks and incompleteness of Gauss invariant 2.3 Nonabelian algebraic knot invariants... PREFACE The use of concepts borrowed from topology has led to major advances in theoretical physics in recent years In quantum field theory, the pioneering work by Skyrme and follow-ups on classical solutions of Yang-Mills-Higgs theories has lead to the discovery of the non-peturbative sectors of gauge theory Topology has also found its way into condensed matter physics Classification of defects in ordered... leads to P-DNA 760 6.1 Phase coexistence of B-DNA and P-DNA in the large torsional stress regime 760 6.2 Chemical evidence of exposed bases 762 7 Conclusions 762 Course 9 Introduction to Topological Quantum Numbers by D.J Thouless 767 Preface 769 1 Winding numbers and topological classication 769 1.1 Precision and topological invariants . VISHVESHWARA, Dept. of Physics, University of California, Santa Barbara, CA 9310 8, U.S .A. A. VISHWANATH, Dept. of Physics, Jadwin Hall, Princeton University, Princeton, NJ 0854 4, U.S .A. X. WAINTAL,. Fisica Teorica, Facultad de Ciencias, Cindad Universitaria s/n, 50009 Zaragoza, Spain L. AMICO, Dpto. Fisica Teorica de la Materia Condensada, Facultad de Ciencias, c-v, Universidad Autonoma de Madrid,. Urbana-Champaign, Dept. of Physics, 1110 West Green St ., Urbana, IL 6180 1, U.S .A. F. SIANO, Univ. of Southern California, Dept. of Physics, Los Angeles, CA 90089-048 4, U.S .A. J. SINOVA, Indiana