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UJF NATO ASI
Les Houches
Session LXXVII
2002
Slow relaxations and nonequilibrium dynamics in condensed matter
Relaxations lentes et dynamiques hors d’équilibreen physique de la matière condensée
Conférenciers
Armand AjdariJean-Philippe Bouchaud
Bernard CabaneMichael Cates
Sergio CilibertoLetitia CugliandoloAlexei Finkelstein
Daniel FisherWalter KobMiguel Ocio
Zvi OvadyahuGiorgio ParisiZoltan RaczDavid Wales
ÉCOLE D’ÉTÉ DE PHYSIQUE DES HOUCHES
SESSION LXXVII, 1-26 JULY 2002
NATO ADVANCED STUDY INSTITUTEEURO SUMMER SCHOOL
ÉCOLE THÉMATIQUE DU CNRS
SLOW RELAXATIONS AND NONEQUILIBRIUMDYNAMICS IN CONDENSED MATTER
RELAXATIONS LENTESET DYNAMIQUES HORS D’ÉQUILIBRE
EN PHYSIQUE DE LA MATIÈRE CONDENSÉE
Edited by
Jean-Louis Barrat, Mikhail Feigelman, Jorge Kurchan and Jean Dalibard
Published in cooperation with the NATO Scientific Affair Division
Les Ulis, Paris, Cambridge
Springer
Berlin, Heidelberg, New York,Hong Kong, London, Milan,
Paris, Tokyo
ISSN 0924-8099 print editionISSN 1610-3459 online edition
ISBN 3-540-40141-5 Springer-Verlag Berlin Heidelberg New YorkISBN 2-86883-685-2 EDP Sciences Les Ulis
This work is subject to copyright. All rights are reserved, whether the whole or part of the material isconcerned, 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 thispublication or parts thereof is only permitted under the provisions of the French and GermanCopyright laws of March 11, 1957 and September 9, 1965, respectively. Violations fall under theprosecution act of the French and German Copyright Laws.
© EDP Sciences; Springer-Verlag 2003
Printed in France
ÉCOLE DE PHYSIQUE DES HOUCHES
Service inter-universitaire communà l’Université Joseph Fourier de Grenoble
et à l’Institut National Polytechnique de Grenoble
Subventionné par le Ministère de la Jeunesse,de l’Éducation Nationale et de la Recherche,
le Centre National de la Recherche Scientifique,le Commissariat à l’Énergie Atomique
Membres du conseil d’administration :Yannick Vallée (président), Paul Jacquet (vice-président), ClaudeBertout, Mauricette Dupois, Cécile DeWitt, Alain Falvard,Bertrand Fourcade, Luc Frappat, Jean-François Joanny, MichèleLeduc, Jean-Yves Marzin, Giorgio Parisi, Eva Pebay-Peyroula,Michel Peyrard, Jean-Paul Poirier, Michel Schlenker, FrançoisWeiss, Michel Wilson, Jean Zinn-Justin
Directeur :Jean Dalibard (Laboratoire Kastler Brossel, Paris, France)
Directeurs scientifiques de la session LXXVII :Jean-Louis Barrat (Université Claude Bernard, Lyon, France)Mikhail Feigelman (Landau Institute, Moscow, Russia)Jorge Kurchan (ESPCI, Paris, France)
Lecturers
Armand Ajdari, Physico-Chimie Théorique, ESPCI, 10 rue Vauquelin,75231 Paris Cedex 05, France
Jean-Philippe Bouchaud, CEA Saclay, L’orme des Merisiers,91191 Gif-sur-Yvette, France
Bernard Cabane, Laboratoire PMMH, ESPCI, 10 rue Vauquelin,75231 Paris Cedex 05, France
Michael Cates, Department of Physics & Astronomy, Universityof Edinburgh, JCMB Kings Buildings, Mayfield road,Edinburgh EH9 3JZ, UK
Sergio Ciliberto, Laboratoire de Physique, ENS, 46 allée d’Italie,69007 Lyon, France
Letitia Cugliandolo, LPTHE, Université Pierre et Marie Curie,4 place Jussieu, 75252 Paris Cedex 05, France
Alexei Finkelstein, Russian Academy of Sciences, Institute of Protein Research,Pushchino 142290, Moscow Region, Russia
Daniel Fisher, Physics Department, Harvard University, 17 Oxford Str.,Cambridge, MA 02138, U.S.A.
Walter Kob, Laboratoire des Verres, Case 69, Université Montpellier II,place E. Bataillon, 34095 Montpellier, France
Miguel Ocio, DSM, Service de Physique de l’État Condensé, CEA Saclay,91191 Gif-sur-Yvette, France
Zvi Ovadyahu, Racah Institute of Physics, The Hebrew University,Jerusalem 91904, Israel
Giorgio Parisi, Dipartimento di Fisica , Università di Roma “La Sapienza”,P.le A. Moro 2, 00185 Roma, Italy
Zoltan Racz, Institute for Theoretical Physics, Eötvös University, PazamanyPeter Setenay 1/a, 1117 Budapest, Hungary
David Wales, University Chemical Laboratories, Lensfield Road,Cambridge CB2 1EW, UK
Participants
Achod Aradian, Physique de la Matière Condensée, Collège de France,11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
Chiara Baggio, Lorenz Instituut, Niels Bohrweg 2, 2333 CA Leiden,P.O. Box 9506, 2300 RA Leiden, The Netherlands
Ludovic Berthier, Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, U.K.
Éric Bertin, DSM/DRECAM/SPEC, Orme des Merisiers, CEA Saclay,91191 Gif-sur-Yvette Cedex, France
Giulio Biroli, SPHT CEA/Saclay, Orme des Merisiers,91191 Gif-sur-Yvette Cedex, France
Viktoria Blavatska, Institute for Condensed Matter Physics, 1 Svientsitskii Str.,Lviv 79011, Ukraine
Simon Bogner, Institut für Theoretische Physik, Universität zu Köln,Zülpicherstr. 77, 50937 Köln, Germany
Heidi Bond, Chandler Group, Chemistry Dept., Univ. of California, Berkeley,CA 94720, U.S.A.
Nikolai Chtchelkatchev, Landau Institute for Theoretical Physics, Kosygina Str.2, 117940, Moscow, Russia
Stefano Ciliberti, Physics Deptartment, University of Roma “La Sapienza”,P.Le A. Moro 5, 00185 Roma, Italy
Miriam Clincy, Deptartment of Physics & Astronomy, Universityof Edinburgh, King’s Buildings, Mayfield Road, Edinburgh EH9 3JZ,U.K.
Alvise De Col, Theoretische Physik, ETH-Hönggerberg, 8093 Zürich,Switzerland
Iryna Demyanchyuk, Kyiv Taras Shevchenko National University, Glushkova 6,312 Room, Kyiv 03022, Ukraine
Daniel Dominguez, Centro Atomico Bariloche, Av. Bustillo 9500,8400 San Carlos de Bariloche, Argentina
Maxym Dudka, Institute for Condensed Matter Physics, 1 Svientsitskii Str.,Lviv UA-79011, Ukraine
x
Cristian Giardina, Dipartimento di Matematica, Piazza di Porta S.Donato 5,40127 Bologna, Italy
Nadejda Gribova, Institute for High Pressure Physics, Russian Academyof Science, 142092 Troitsk, Moscow Region, Russia
Tomas Grigera, Gruppo VIM, Dipartimento di Fisica, Universita di Roma“La Sapienza” P.le Aldo Moro 2, 00185 Roma, Italy
Arsen Grigoryan, Department of Molecular Physics, Faculty of Physics, YerevanState University, 1 Al. Manoogian St., 375025 Yerevan, Armenia
Jonathan Hatchett, King’s College, University of London, The Strand,London WC 2R 2LS, U.K.
Colin Holmes, Room 4306, JCMB, King’s Building, Mayfield Road,Edinburgh EH8 3JZ, U.K.
Adilet Imambekov, L.D. Landau Institute of Theoretical Physics, Kosygina 2,117334 Moscow, Russia
Toby Joseph, Condensed Matter Theory Group, Department of Physics,Indian Institute of Sciences, Bangalore 560012, India
Eytan Katzav, School of Physics & Astronomy, Tel-Aviv University,Ramat-Aviv, Tel Aviv 69978, Israel
Kang Kim, Department of Applied Mathematics and Physics, Graduate Schoolof Imformatics, Kyoto University, Kyoto 606-8501, Japan
Michal Kolar, Fyzikalni Ustav AV CR, Na Slovance 2, 182 21 Praha,Czech Republic
Alejandro Kolton, Centro Atomico Bariloche, Bustillo 9500, 8400 Bariloche,Argentina
Jérôme Koopmann, Theoretische Physik, ETH-Hönggerberg, 8093 Zürich,Switzerland
Florent Krzakala, LPTMS, bâtiment 100, Université Paris-Sud, 91406 Orsay,France
Andrei Lebedev, L.D. Landau Institute of Theoretical Physics, Kosygina 2,Moscow 117334, Russia
Alexandre Lefevre, Laboratoire de Physique Quantique, 118 routede Narbonne, 31062 Toulouse Cedex 4, France
Miki Matsuo, Sasa Laboratory, Graduate School of Arts and Science, Universityof Tokyo, Komaba, 3-8-1, Meguro-ku, Tokyo 153-8902, Japan
xi
Mauro Merolle, Department of Chemistry, University of California, Berkeley,CA 94720-1460, U.S.A.
Swagatam Mukhopadhyay, Loomis Laboratory of Physics, 1110 West GreenStr., Urbana, IL 61801-3080, U.S.A.
Vladimir Orlyanchik, The Racah Institute of Physics, The Hebrew University,Jerusalem 91904, Israel
Guillemette Picard, ESPCI, 10 rue Vauquelin, 75231 Paris Cedex 05, France
Stoyan Pisov, University of Sofia, Department of Atomic Physics, Str. JamesBourchier Bld., Sofia 1126, Bulgaria
Joerg Rottler, Physics & Astronomy, The Johns Hopkins University,3400 N. Charles Str., Baltimore, MD 21218, U.S.A.
Valery Ryazanov, Institute of Solid State Physics, Russian Academyof Sciences, Chernogolovka, Moscow Distr. 142432, Russia
Natalia Savitskaya, Petersburg Nuclear Physics Institute RAS,188300 Gatchina, Russia
Gregory Schehr, LPT, École Normale Supérieure, 24 rue Lhomond,75005 Paris, France
Guilhem Semerjian, LPT, École Normale Supérieure, 24 rue Lhomond,75005 Paris, France
Jacco Snoeijer, Institute Lorentz, LION, University Leiden, P.O. Box 9506,2300 RA Leiden, The Netherlands
Dmitry Syckmanov, Ioffe Physico-Technical Institute, Polytechnicheskaya ul.29, 195251 St Petersburg, Russia
Tatyana Tchesskaya, Information Technology Department, Odessa StateEcological University, Lovovskaya 15, 65016 Odessa, Ukraine
Damien Vandembroucq, Unité Mixte CNRS/Saint-Gobain, 39 Quai LucienLefranc, 93303 Aubervilliers, France
Mikhail Vasin, P.T.I. Ur.B. R.A.S., 426001 Kirova Str., 132 Izhevsk, Russia
Virgile Viasnoff, LPM ESPCI, 10 rue Vauquelin, 75005 Paris, France
Thomas Voigtmann, Theoretische Physik, T37, James-Franck-Str.,85748 Garching, Germany
Olivia White, Harvard University, Department of Physics, JeffersonLaboratories, 17 Oxford Str., Cambridge, MA 02140, U.S.A.
xii
Stephen Whitelam, Department of Theoretical Physics, Oxford University, KebleRoad, Oxford OX1 3NP, U.K.
Emanuela Zaccarelli, G20 – Università “La Sapienza”, Ple A. Moro 2,00185 Roma, Italy
Francesco Zamponi, Dipartimento di Fisica, G20, Università “La Sapienza”,Ple A. Moro 5, 00185 Roma, Italy
Preface
Les ecoles d’ete des Houches ont une longue tradition dans le domainedes systemes desordonnes ou hors equilibre, avec en particulier la celebre31e session de 1978, “La matiere mal condensee”, suivie des sessions de 1986,“Le hasard et la matiere” et 1989, “Liquides, cristallisation et transition vit-reuse”. Ce volume peut donc etre vu comme une continuation logique decette tradition, incorporant les progres considerables de la derniere decennie,construits sur les concepts developpes dans deux communautes differentes,celle des fluides complexes et celle des systemes desordonnes.
Cette ecole s’est concentree sur le concept unificateur de dynamiquehors equilibre. Aussi curieux que cela puisse paraıtre, la constatation quela comprehension des systemes hors equilibre ne peut pas se limiter a unedescription de leur proprietes statiques “d’equilibre” est relativement recen-te. Cependant, des que l’on s’eloigne du terrain familier de la physiqued’equilibre, il n’y a plus de methode etablie pour decrire les surprenantesentites rencontrees. Les difficultes ne concernent pas seulement les methodesde calcul, mais viennent plus profondement de l’echec de notre intuition clas-sique, fondee sur la notion d’equilibre thermodynamique. Les cours de cetteecole ont presente de nombreux exemples de cette situation : des transitionsde phase inattendues dans les systemes forces, les curieuses lois de comporte-ment des systemes granulaires, pateux ou colloıdaux, les deux temperaturesdans les systemes vieillissants, l’evolution des systemes vivants, de l’echellede la proteine a celle des especes.
Il est amusant de constater que ces situations n’ont rien de parti-culierement exotique, mais constituent la majorite des processus physiquesquotidiens. De la biologie a l’industrie, le non equilibre est la regle, plutotque l’exception. Les outils theoriques developpes pour decrire les situationshors equilibre peuvent donc se reveler utiles dans des contextes tres varies,ce qui explique le tres large spectre des thematiques abordees lors de cetteecole, du repliement des proteines a la mecanique des systemes granulaires.
Etant donne l’etat de developpement du sujet, une ecole dans ce do-maine ne peut etre organisee d’une maniere aussi lineaire et logique que leserait, par exemple, une revue de la theorie des champs ou de la physique
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statistique d’equilibre. Nous nous sommes donc appuyes sur la pedagogie etl’intuition de chaque enseignant pour obtenir une introduction de qualite achacun des domaines abordes, avec l’espoir que les liens entre ces approchesapparaıtraient naturellement aux etudiants. Les sessions de discussion tresactives organisees par les etudiants eux-memes, et dont certaines ont con-duit a des chapitres de ce volume, ont ete une contribution importante al’etablissement de ce cadre de reflexion commun.
Les cours de Z. Racz sur des systemes modeles hors equilibre constituentun point de depart rigoureux pour apprecier les differences macroscopiquesde comportement entre situations d’equilibre et hors equilibre.
Un point de vue different sur les systemes hors d’equilibre, issu de lacommunaute des fluides complexes, est apporte par les contributions deA. Ajdari et M. Cates. Ces deux cours abordent differents aspects du com-portement de systemes “mous” en ecoulement, ce type de systemes etantomnipresent aussi bien dans la matiere vivante que dans les applicationsindustrielles. Ces cours ont ete completes par une serie de seminaires (nonpublies) de B. Cabane, qui a mis en evidence quelques applications pratiquesde la rheologie des fluides complexes.
D’un point de vue theorique, ces approches sont etroitement reliees acelles utilisees pour decrire verres et matiere granulaire. Dans cette optique,la presentation par J.-P. Bouchaud des proprietes statiques de la matieregranulaire a represente un effort important pour montrer les ramificationsmultiples de la physique des systemes desordonnes.
Les verres sont sans aucun doute l’archetype des systemes desordonnes,et de nombreuses methodes et concepts theoriques ont ete elabores pourdecrire leurs proprietes. Trois contributions de grande ampleur parW. Kob, L. Cugliandolo et G. Parisi ont ete consacrees aux aspects theori-ques de ce sujet central. Ces contributions presentent differents aspectsd’une description theorique unifiee qui a emerge dans les dix dernieresannees, et qui est aujourd’hui activement testee dans les experiences etles simulations. D. Fisher, dont le cours (non publie) portait sur l’evolutiondes especes, a bien voulu apporter une contribution ecrite sur le themedes etats d’equilibre et la dynamique des systemes vitreux. Sur le frontexperimental, des comptes rendus tres complets de la situation actuelle ontete donnes par S. Ciliberto et M. Ocio, qui ont en particulier decrit leursexperiences pionnieres sur le vieillissement et la reponse hors equilibre.
Les systemes quantiques sont une source continue de problemes aussiinteressants que difficiles, avec des consequences pour le fonctionnement dedispositifs pratiques. Cette ecole ne pouvait couvrir completement ces as-pects, mais quelques fenetres ont ete ouvertes grace aux efforts deZ. Ovadyahu (vieillissement dans les isolants de Mott), N. Savitskaya et
xv
V. Ryazanov (non publie) sur la dynamique des reseaux de jonctions supra-conductrices.
Les defis poses par les problemes biologiques attirent aujourd’hui denombreux physiciens. Il est raisonnable de penser que les contributions per-tinentes de la physique ne seront pas toujours limitees a des considerationsd’equilibre thermodynamique. Les cours de A. Finkelstein (dynamique desproteines), D. Fisher (evolution des populations, non publie) et D. Wales(paysages d’energie dans des systemes complexes, non publie1) sont desexemples d’application aux systemes biologiques des concepts de la physiquehors equilibre.
Un resultat tres positif de l’ecole, deja mentionne ci-dessus, a ete l’emer-gence de groupes de discussion organises par les etudiants, qui se sont con-clus par une serie de seminaires. Ce systeme “auto-organise” a rassembledes participants venant de domaines et/ou continents differents dans desgroupes de travail informels. Les contributions de Holmes et al., Bond et al.et Berthier et al. constituent un compte rendu synthetique de discussionssouvent animees.
Nous souhaitons remercier l’ensemble des auteurs pour l’effort qu’ils ontfait en preparant ces notes de cours, qui couvrent souvent un domaine pluslarge que celui qu’ils ont pu aborder durant la session. Nous esperons quece volume, suivant la tradition de nombreux autres comptes rendus desecoles des Houches, constituera un ouvrage de reference pendant de nom-breuses annees pour les etudiants et chercheurs travaillant dans ce domaineen evolution rapide.
Remerciements
La 77e ecole des Houches et ce volume ont beneficie largement du soutienfinancier des institutions suivantes, que nous remercions chaleureusement:
- le programme “Conferences Scientifiques de Haut Niveau” de laDirection a la Recherche de la Commission Europeenne (contrat HPCF-CT-2001-00075) ;
- le programme “Advanced Scientific Institute” de la Division desAffaires Scientifiques et Environnementales de l’OTAN (contrat ASI-978104) ;
1On trouvera une contribution de D. Wales sur des sujets similaires dans les comptesrendus de la 73e ecole des Houches, edites par C. Guet, P. Hobza, F. Spiegelmann etF. David, EDP Sciences-Springer, 2001.
xvi
- le programme de Formation Permanente du Centre National de laRecherche Scientifique (France) ;
- L’Universite Joseph Fourier, le Centre National de la RechercheScientifique, le Ministere de la Recherche et le Commissariat a l’EnergieAtomique, par leur soutien recurrent a l’Ecole de Physique des Houches.
Le personnel permanent de l’Ecole, en particulier Brigitte Rousset, IsabelleLelievre et Ghyslaine d’Henry, ont apporte une assistance indispensable lorsde toutes les etapes de mise en place et de realisation de l’ecole. Nous lesremercions chaleureusement, au nom de l’ensemble des participants, en-seignants et etudiants. Nos remerciements vont egalement au precedentdirecteur Francois David pour son aide dans la mise en place initiale, etau conseil scientifique de l’ecole pour nous avoir encourage a proposer unesession sur ce theme.
Jean-Louis BarratMikhail Feigelman
Jorge KurchanJean Dalibard
Preface
The les Houches summer schools have a long standing tradition in the fieldof disordered and nonequilibrium systems, starting with the well known31st session “Ill Condensed Matter” in 1978, they continued with sessionssuch as “Chance and Matter” in 1986 and “Liquids, freezing and the glasstransition” in 1989. The present volume can therefore be seen as a logicalcontinuation of this tradition, which incorporates the considerable progressin the field that took place during the last decade, building on conceptsdeveloped in two different communities, that of complex liquids and that ofdisordered systems.
The focus of the summer school reported here was on nonequilibriumdynamics as a unifying concept. In fact, an important realization of the90’s was certainly that – as obvious as this statement may seem – the un-derstanding of nonequilibrium systems cannot be limited to a study of theirstatic, “equilibrium” properties. However, once we abandon the familiar ter-ritory of equilibrium and its surroundings, there are no established ways todeal with all the surprising creatures we encounter. We face difficulties notonly in the calculations, but much more importantly our old, equilibriumintuition fails us. These lectures are full of examples of this: unexpectedphase transitions in driven systems, the bizarre behaviour of granular, pastyand colloidal matter, a two-temperature behaviour in aging systems, andthe evolution of living systems at the protein and the species level.
What is perhaps most astonishing is that these situations do not belongto a far-fetched world, but constitute the basis of our everyday-life physics,from biological to industrial processes, as well as in the very nature ofthe matter that surround us. Nonequilibrium is the rule, rather than theexception. Hence the theoretical tools developed to describe nonequilibriumsituations can be useful in widely different contexts. This explains therather broad range of topics covered in these lectures, from protein foldingto disordered conductors and granular mechanics.
Given its present state of development, a school or a collection of paperson this subject cannot be as articulate and linear as, say, a presentationof field theory or equilibrium statistical mechanics. We have thus relied on
xviii
the good taste and intuition of each lecturer, to introduce the concepts oftheir field in the most pedagogical way, with the hope that the connectionsbetween the different approaches should be naturally apparent to the stu-dents. The lively discussion sessions organized by the students themselves,some of which have led to contributions to this volume, were an importantcontribution to the establishment of such a common framework.
Z. Racz’ lectures about model out of equilibrium systems provide a rig-orous starting point to appreciate the differences between equilibrium andnon-equilibrium macroscopic behaviour.
A rather different point of view on nonequilibrium systems, coming fromthe complex fluid community, is provided by the lectures of A. Ajdari andM. Cates. Both deal with different aspects of soft, flowing matter, a kindof system ubiquitous in living as well as industrial systems. These lectureswere complemented by a series of (unpublished) seminars by B. Cabane,who demonstrated some practical implications of complex fluids rheology.
From the theoretical point of view, these approaches have strong con-nections both with granular matter and with glasses. In this sense, thepresentation by J.-P. Bouchaud of static properties of granular matter wasdone with a special emphasis for showing the multiple ramifications in thephysics of disordered systems.
Glasses are no doubt the historical paradigm of disordered, nonequi-librium systems, and many theoretical methods and concepts have beendesigned for dealing with their properties. On the theory side, three ex-tensive contributions by W. Kob, L. Cugliandolo and G. Parisi have beendevoted to this central topic of the school. These lectures present differentaspects of a unified theoretical picture that has emerged in recent yearsand is now being actively tested. D. Fisher, whose oral lectures (unpub-lished) dealt with species evolution, also contributed in writing a detailedviewpoint on the nature of equilibrium states in glassy systems and glassydynamics. On the experimental side, up to date reviews of the experimentalsituation are presented in the contributions by S. Ciliberto and M. Ocio,who in particular gave a beautiful account of their pioneering experimentson aging.
Quantum systems often pose interesting, though daunting, out of equi-librium problems, especially in relation with devices. The summer schoolcould not do full justice to this field, with the exception of Z. Ovadyahu’slectures on aging of electronic systems, and N. Savitskaya and V. Ryazanov(unpublished) on the dynamics of superconductor systems.
Many physicists are attracted these days by the challenges of biology.There is little doubt that if physics’ contribution to living matter is to berelevant, it has to free itself from the tight limitations of thermal equilibrium.
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The lectures of A. Finkelstein (protein dynamics), D. Fisher (theory ofbiological evolution, unpublished) and D. Wales (chemical reactions andlandscapes; unpublished1) are some examples.
One of the most rewarding experiences of this school, already mentionedabove, has been the discussion groups organized by students, which cul-minated in collective seminars. The system was fully self-organized, andassembled students working in different contexts (and/or continents). Thecontributions of Holmes et al., Bond et al. and Berthier et al. are soberrenderings of what were often animated discussions.
We thank all contributors for the effort they made in preparing theselecture notes, which often cover much more material than the lectures them-selves. We strongly hope that this set of lectures will, in the tradition ofmany earlier volumes of the Les Houches series, provide a useful introduc-tion and serve as a reference for several years for researchers and studentsin this very open and rapidly evolving field.
Acknowledgments
The 57th Les Houches summer school and the present volume have beenmade possible by the financial support of the following institutions, whosecontribution is gratefully acknowledged:
- the “High Level Scientific Conference” program of the ResearchDirectorate of the European Commission under grant HPCF-CT-2001-00075;
- the “Advanced Scientific Institute” program of the Scientific andEnvironmental Affairs division of NATO, under grant ASI-978104;
- the “Lifelong learning” program of the Centre National de la RechercheScientifique (France);
- the Universite Joseph Fourier, the French Ministry of Research and theCommissariat a l’Energie Atomique, through their constant supportto the Physics School.
The permanent staff of the School, especially Brigitte Rousset, IsabelleLelievre and Ghyslaine d’Henry, have been of invaluable assistance at every
1A related contribution by D. Wales can be found in the proceedings of the 73rdLes Houches summer school, edited by C. Guet, P. Hobza, F. Spiegelmann and F. David,EDP Sciences-Springer, 2001.
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stage of the preparation and development of the school, and we would like tothank them warmly on behalf of all students and lecturers. We also thankthe former director Francois David for his help during the early stages ofpreparation, and the school scientific council for encouraging us in preparinga session on this topic.
Jean-Louis BarratMikhail Feigelman
Jorge KurchanJean Dalibard
CONTENTS
Lecturers vii
Participants ix
Preface xiii
Preface xvii
Contents xxi
Course 1. Nonequilibrium Phase Transitions
by Z. Racz 1
1 Introduction 31.1 Nonequilibrium steady states . . . . . . . . . . . . . . . . . . . . . 41.2 Problems with usual thermodynamic concepts . . . . . . . . . . . . 6
2 Phase transitions far from equilibrium 82.1 Differences from equilibrium – constructing models with NESS . . 82.2 Generation of long-range interactions – nonlocal dynamics . . . . . 112.3 Generation of long-range interactions – dynamical anisotropies . . 132.4 Driven lattice gases, surface growth . . . . . . . . . . . . . . . . . . 152.5 Flocking behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 Where do the power-laws come from? 183.1 Self-organized criticality (SOC) . . . . . . . . . . . . . . . . . . . . 193.2 Absorbing state transitions and their connection to SOC . . . . . . 21
4 Distribution functions in nonequilibrium steady states 244.1 Power laws and universality of nonequilibrium distributions . . . . 244.2 Picture gallery of scaling functions . . . . . . . . . . . . . . . . . . 254.3 Upper critical dimension of the KPZ equation . . . . . . . . . . . . 28
5 Quantum phase transitions 305.1 Spin chains with fluxes . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Effective interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 Outlook 37
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Course 2. Mechanical Aging and Non-Linear Rheologyof Concentrated Colloidal Suspensions: ExperimentalFacts and Simple Models
by A. Ajdari 41
1 Introduction 43
1.1 Colloidal glasses? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
1.2 Model and real colloids: Interactions . . . . . . . . . . . . . . . . . 44
1.3 Gels or glasses: Various kinds of soft solids? . . . . . . . . . . . . . 48
1.4 Wrapping up the introduction . . . . . . . . . . . . . . . . . . . . . 49
2 Experimental facts 1: Soft solids that flow and age 50
3 A class of simple models 54
3.1 A Maxwell model with one scalar internal variable . . . . . . . . . 54
3.2 Relation to other models in the literature . . . . . . . . . . . . . . 55
3.3 Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4 Intermediary conclusion . . . . . . . . . . . . . . . . . . . . . . . . 61
4 Experimental facts 2: Soft solids that flow in a strange way 61
4.1 Avalanches and “viscosity bifurcation” . . . . . . . . . . . . . . . . 61
4.2 Parallel with flow induced transitions: Heterogeneous “banded” flows 62
4.3 Description within the simple class of models . . . . . . . . . . . . 63
4.4 Intermediary conclusion . . . . . . . . . . . . . . . . . . . . . . . . 66
5 Criticism of the model and perspectives 67
5.1 A classification of the phenomenologies . . . . . . . . . . . . . . . . 67
5.2 Successes and failures of these models . . . . . . . . . . . . . . . . 68
5.3 Better models: More variables? which collective physics? . . . . . . 69
5.4 Back to facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Course 3. Structural Relaxation and Rheologyof Soft Condensed Matter
by M.E. Cates 75
1 Soft condensed matter 79
2 Rheology 81
2.1 Stress tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
2.2 Statistical mechanics of stress . . . . . . . . . . . . . . . . . . . . . 83
2.3 Strain and strain rate . . . . . . . . . . . . . . . . . . . . . . . . . 85
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3 Linear rheology 87
3.1 Step-strain response . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.2 Oscillatory flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
3.3 Steady shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.4 Typical cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.5 Linear creep measurements . . . . . . . . . . . . . . . . . . . . . . 91
3.6 Simple forms for G(t) . . . . . . . . . . . . . . . . . . . . . . . . . 91
4 Linear viscoelasticity of polymers 92
4.1 Entanglements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2 Entropic elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 Escape from the tube . . . . . . . . . . . . . . . . . . . . . . . . . 94
5 Nonlinear rheology of polymers 95
5.1 Typical experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5.2 Nonlinear relaxation of polymers . . . . . . . . . . . . . . . . . . . 96
5.3 Constitutive equation . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.4 Why are polymers tractable? . . . . . . . . . . . . . . . . . . . . . 99
6 Dumbing down 99
6.1 Dumbell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.2 Scalarisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
7 What rheologists want 101
8 Rheology of soft glasses 102
8.1 The effective temperature problem . . . . . . . . . . . . . . . . . . 102
8.2 Phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
8.3 Bouchaud’s trap model . . . . . . . . . . . . . . . . . . . . . . . . . 103
9 The SGR model 105
9.1 Features of the model . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.2 Constitutive equation for SGR . . . . . . . . . . . . . . . . . . . . 108
9.3 Tensorial SGR models . . . . . . . . . . . . . . . . . . . . . . . . . 109
10 Rheological aging 111
10.1 Step stress and step strain . . . . . . . . . . . . . . . . . . . . . . . 111
10.2 Oscillatory flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.3 AOFOT? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
10.4 Weak long term memory . . . . . . . . . . . . . . . . . . . . . . . . 113
10.5 The G′′ problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.6 Aging scenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
10.7 Nonlinear aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
10.8 Ongoing work on aging and rheology . . . . . . . . . . . . . . . . . 118
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11 Shear thickening and jamming 118
11.1 Nonmonotonic flow curves . . . . . . . . . . . . . . . . . . . . . . . 118
11.2 Shear thickening mechanisms . . . . . . . . . . . . . . . . . . . . . 119
11.3 Jamming SGR model . . . . . . . . . . . . . . . . . . . . . . . . . . 121
12 Rheological instability and oscillation 121
12.1 A simpler model for rheo-instability . . . . . . . . . . . . . . . . . 123
13 Rheochaos 124
14 More fundamental approaches 125
15 Conclusion 127
Course 4. Granular Media: Some Ideas from StatisticalPhysics
by J.P. Bouchaud 131
1 Introduction 133
1.1 Basic phenomenology . . . . . . . . . . . . . . . . . . . . . . . . . . 133
1.2 Theoretical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
2 The scalar model I: Discrete version 140
2.1 Definition and motivation . . . . . . . . . . . . . . . . . . . . . . . 140
2.2 Stress distribution and the exponential tail . . . . . . . . . . . . . 141
2.3 The “critical” case . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
3 The scalar model II: Continuous limit and perturbation theory 144
3.1 Continuous limit of the scalar model . . . . . . . . . . . . . . . . . 144
3.2 Calculation of the averaged response and correlation functions . . . 147
3.3 Further results: The un-averaged response function . . . . . . . . . 153
3.4 The scalar model with bias: Edwards’ picture of arches . . . . . . 154
4 Static indeterminacy; elasticity and isostaticity 155
4.1 Elasticity and response functions . . . . . . . . . . . . . . . . . . . 155
4.2 Indeterminacy at the grain level and isostaticity . . . . . . . . . . . 157
4.3 Numerical simulations and Edwards’ assumption . . . . . . . . . . 158
5 A stress-only approach to granular media 160
5.1 A vectorial q-model . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5.2 A constitutive relation between stress components . . . . . . . . . 162
5.3 Some simple situations . . . . . . . . . . . . . . . . . . . . . . . . . 163
5.4 Symmetries and constitutive relations . . . . . . . . . . . . . . . . 164
5.5 Boundary conditions and “fragility” . . . . . . . . . . . . . . . . . 166
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6 Experimental and numerical determination of the stressresponse function 167
7 Force chains scattering I: Weak disorder limit 1687.1 A stochastic wave equation . . . . . . . . . . . . . . . . . . . . . . 1687.2 Calculation of the averaged response function . . . . . . . . . . . . 1717.3 Generalized wave equations . . . . . . . . . . . . . . . . . . . . . . 174
8 Force chains scattering II: Strong disorder limit 1778.1 Introduction and numerical results . . . . . . . . . . . . . . . . . . 1778.2 A Boltzmann description of force chain splitting . . . . . . . . . . 1788.3 The role of chain merging . . . . . . . . . . . . . . . . . . . . . . . 181
9 Statics of granular materials: Concluding remarksand open questions 182
10 Glassy dynamics in granular media: A brief survey 18410.1 Slow compaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18410.2 Self-inhibitory dynamics and dynamical heterogeneities . . . . . . . 18610.3 Granular dynamics and the trap model . . . . . . . . . . . . . . . . 190
Course 5. Supercooled Liquids, the Glass Transition,and Computer Simulations
by W. Kob 199
1 Introduction 201
2 Supercooled liquids and the glass transition: Important factsand concepts 202
3 The mode-coupling theory of the glass transition 2173.1 The Mori-Zwanzig formalism . . . . . . . . . . . . . . . . . . . . . 2173.2 Application of the Mori-Zwanzig formalism to glass-forming
systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
4 Computer simulations of glass-forming systems 230
5 The relaxation dynamics of glass-forming liquidsas investigated by computer simulations 2395.1 Static and dynamic properties of a simple liquid with Newtonian
dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
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5.2 The relaxation dynamics of a simple liquid with stochasticdynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
5.3 Static and dynamic properties of a network forming liquid . . . . . 255
6 Summary and perspectives 261
Course 6. Glasses, Replicas and all that
by G. Parisi 271
1 Introduction 275
1.1 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . 275
1.2 Glassiness, metastability and hysteresis . . . . . . . . . . . . . . . 276
1.3 The organization of these lectures . . . . . . . . . . . . . . . . . . . 280
2 The random energy model 281
2.1 The definition of the model . . . . . . . . . . . . . . . . . . . . . . 281
2.2 Equilibrium properties of the model . . . . . . . . . . . . . . . . . 282
2.3 The properties of the low temperature phase . . . . . . . . . . . . 286
2.4 A careful analysis of the high temperature phase . . . . . . . . . . 290
2.5 The replica method . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
2.6 Dynamical properties of the model . . . . . . . . . . . . . . . . . . 294
3 Models with partially correlated energy 295
3.1 The definition of the models . . . . . . . . . . . . . . . . . . . . . . 295
3.2 The replica solution . . . . . . . . . . . . . . . . . . . . . . . . . . 296
3.3 The physical interpretation . . . . . . . . . . . . . . . . . . . . . . 300
3.4 The two susceptibilities . . . . . . . . . . . . . . . . . . . . . . . . 305
3.5 The cavity method . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
4 Complexity 310
4.1 The basic definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 312
4.2 Computing the complexity . . . . . . . . . . . . . . . . . . . . . . . 314
4.3 Complexity and replicas . . . . . . . . . . . . . . . . . . . . . . . . 319
4.4 A summary of the results . . . . . . . . . . . . . . . . . . . . . . . 324
4.5 Some consideration on the free energy landscapeand on the dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 325
4.6 Small fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
5 Structural relations 330
5.1 Stochastic stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
5.2 A simple consequence of stochastic stability . . . . . . . . . . . . . 333
5.3 Fluctuation dissipation relations . . . . . . . . . . . . . . . . . . . 334
6 A short introduction to glasses 335
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7 The replica approach to structural glasses: General formalism 337
7.1 The partition function . . . . . . . . . . . . . . . . . . . . . . . . . 338
7.2 Molecular bound states . . . . . . . . . . . . . . . . . . . . . . . . 339
7.3 The small cage expansion . . . . . . . . . . . . . . . . . . . . . . . 339
8 The replica approach to structural glasses: Some results 346
8.1 Three approximation schemes . . . . . . . . . . . . . . . . . . . . . 346
8.2 Critical temperature and effective temperature . . . . . . . . . . . 347
8.3 Cage size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
8.4 Free energy, specific heat and configurational entropy . . . . . . . . 349
8.5 The missing dynamical transition . . . . . . . . . . . . . . . . . . . 350
8.6 Lenhard-Jones binary mixtures . . . . . . . . . . . . . . . . . . . . 351
9 Discussion and perspectives 354
Course 7. Dynamics of Glassy Systems
by L.F. Cugliandolo 367
1 Introduction 371
2 Some physical systems out of equilibrium 374
2.1 Domain growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374
2.2 Glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377
2.3 Spin-glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
2.4 Quantum fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 382
2.5 Rheology and granular matter . . . . . . . . . . . . . . . . . . . . . 382
2.6 Elastic manifolds in random potentials . . . . . . . . . . . . . . . . 384
2.7 Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
3 Theoretical approach 388
4 Systems in contact with environments 390
4.1 Modeling the coupled system . . . . . . . . . . . . . . . . . . . . . 391
5 Observables and averages 395
5.1 Classical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
5.2 Quantum problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
5.3 Average over disorder . . . . . . . . . . . . . . . . . . . . . . . . . 399
6 Time dependent probability distributions 399
6.1 The Fokker–Planck and Kramers equations . . . . . . . . . . . . . 399
6.2 Approach to equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 400
6.3 Equilibrium dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 401
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7 The fluctuation – dissipation theorem (FDT) 4037.1 Static FDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4037.2 Dynamic FDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4047.3 Quantum FDT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4047.4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405
8 Dynamic generating functionals 4078.1 Classical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4078.2 Supersymmetry (SUSY) . . . . . . . . . . . . . . . . . . . . . . . . 4098.3 Connection with the replica formalism . . . . . . . . . . . . . . . . 4118.4 Quantum models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4118.5 Average over disorder . . . . . . . . . . . . . . . . . . . . . . . . . 415
9 Dynamic equations 4169.1 A useful derivation for fully-connected models . . . . . . . . . . . . 4169.2 Beyond fully-connected models . . . . . . . . . . . . . . . . . . . . 4269.3 Field equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4309.4 The thermodynamic limit and time-scales . . . . . . . . . . . . . . 4319.5 Single spin equation . . . . . . . . . . . . . . . . . . . . . . . . . . 431
10 Diagrammatic techniques 43210.1 Perturbative solution . . . . . . . . . . . . . . . . . . . . . . . . . . 43210.2 The mode coupling approximation (MCA) . . . . . . . . . . . . . . 43410.3 MCA and disordered models . . . . . . . . . . . . . . . . . . . . . . 43510.4 MCA for super-cooled liquids and glasses . . . . . . . . . . . . . . . 438
11 Glassy dynamics: Generic results 43911.1 The weak-ergodicity breaking scenario . . . . . . . . . . . . . . . . 43911.2 The weak long-term memory scenario . . . . . . . . . . . . . . . . 44111.3 Slow time-reparametrization invariant dynamics . . . . . . . . . . . 44211.4 Correlation scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44311.5 Modifications of FDT . . . . . . . . . . . . . . . . . . . . . . . . . . 449
12 Solution to mean-field models 45512.1 Numerical solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 45512.2 Solution at high temperatures . . . . . . . . . . . . . . . . . . . . . 45612.3 Solution at low-T . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
13 Modifications of FDT in physical systems 46913.1 Domain growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46913.2 Structural glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47113.3 Spin-glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47213.4 Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47313.5 Vibrated models and granular matter . . . . . . . . . . . . . . . . 47413.6 Driven vortex systems . . . . . . . . . . . . . . . . . . . . . . . . . 47413.7 Quantum fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 47513.8 Systems of finite size: Preasymptotic behavior . . . . . . . . . . . . 475
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13.9 Critical dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475
13.10 Connection with equilibrium . . . . . . . . . . . . . . . . . . . . . 476
14 Effective temperatures 477
14.1 Thermodynamical tests . . . . . . . . . . . . . . . . . . . . . . . . 479
14.2 Temperature fixing by SUSY breaking . . . . . . . . . . . . . . . . 485
14.3 Fictive temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . 485
14.4 Nonequilibrium thermodynamics . . . . . . . . . . . . . . . . . . . 486
14.5 Statistical mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . 486
15 Metastable states 487
15.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488
15.2 Static TAP approach . . . . . . . . . . . . . . . . . . . . . . . . . . 490
15.3 The TAP equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 492
15.4 Stability of, and barriers between, the TAP solutions . . . . . . . . 493
15.5 Index dependent complexity . . . . . . . . . . . . . . . . . . . . . . 495
15.6 Weighted sums over TAP solutions . . . . . . . . . . . . . . . . . . 495
15.7 Accessing metastable states with replicas . . . . . . . . . . . . . . 497
15.8 Dynamics and quantum systems . . . . . . . . . . . . . . . . . . . 498
16 Conclusions 499
17 Perspectives 505
A Generalized Langevin equations 506
B The Kubo formula 509
C The response in a Langevin process 510
D Grassmann variables and supersymmetry 510
E Integrals in the aging regime 512
Course 8. Equilibrium States and Dynamicsof Equilibration: General Issues and Open Questions
by D.S. Fisher 523
1 Introduction 525
2 Equilibrium states 526
2.1 Infinite system ground states . . . . . . . . . . . . . . . . . . . . . 527
2.2 Positive temperature states . . . . . . . . . . . . . . . . . . . . . . 532
2.3 Number of equilibrium states? . . . . . . . . . . . . . . . . . . . . . 533
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3 Dynamics and barriers 5353.1 Domain coarsening . . . . . . . . . . . . . . . . . . . . . . . . . . . 536
3.2 Dynamics and local equilibrium . . . . . . . . . . . . . . . . . . . . 539
4 Spin glasses 5414.1 Scaling scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5434.2 Observation of many states? . . . . . . . . . . . . . . . . . . . . . . 547
5 Non-random systems: True glasses 549
Course 9. Experimental Analysis of Aging
by S. Ciliberto 555
1 Introduction 557
2 Aging, memory and rejuvenation 5582.1 Aging range: A simple quench experiment . . . . . . . . . . . . . . 558
2.2 Memory and rejuvenation . . . . . . . . . . . . . . . . . . . . . . . 5622.3 Discussion on the memory effect . . . . . . . . . . . . . . . . . . . 573
3 Effective temperature of an aging material 5753.1 The X-ray scattering experiment . . . . . . . . . . . . . . . . . . . 577
3.2 Supercooled liquid experiment . . . . . . . . . . . . . . . . . . . . . 5793.3 Gel electric properties . . . . . . . . . . . . . . . . . . . . . . . . . 5803.4 Polycarbonate dielectric properties . . . . . . . . . . . . . . . . . . 586
3.5 Rheological measurements . . . . . . . . . . . . . . . . . . . . . . . 5953.6 Discussion and conclusions on the effective temperature . . . . . . 600
4 General conclusions 601
Course 10. Fluctuation Dissipation Relationin a Non-Stationary System: Experimental Investigationin a Spin Glass
by M. Ocio and D. Herisson 605
1 Introduction 607
2 Theoretical background 608
3 Experimental 6093.1 Measurement of magnetic fluctuations . . . . . . . . . . . . . . . . 609
3.2 Principle of measurement: An absolute thermometer . . . . . . . . 6113.3 Experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . 614
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4 Discussion 616
5 Conclusion 620
Course 11. Non-Equilibrium Dynamics and Agingin the Electron Glass
by Z. Ovadyahu 623
1 Introduction 625
2 The characteristics of the electron-glass 626
2.1 The field effect technique . . . . . . . . . . . . . . . . . . . . . . . 626
2.2 Preliminary results . . . . . . . . . . . . . . . . . . . . . . . . . . . 627
2.3 Basic features of the electron-glass . . . . . . . . . . . . . . . . . . 631
3 The role of the electron–electron interaction 637
3.1 Experimental evidence for the role of interactions . . . . . . . . . . 637
3.2 The Coulomb gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 643
3.3 Theoretical treatment of relaxation in the presence of interactions 644
4 Concluding remarks 646
Course 12. Proteins: Structural, Thermodynamicand Kinetic Aspects
by A.V. Finkelstein 649
1 Introduction 651
2 Overview of protein architectures and discussion of physicalbackground of their natural selection 651
2.1 Protein structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
2.2 Physical selection of protein structures . . . . . . . . . . . . . . . 656
3 Thermodynamic aspects of protein folding 670
3.1 Reversible denaturation of protein structures . . . . . . . . . . . . 670
3.2 What do denatured proteins look like? . . . . . . . . . . . . . . . . 673
3.3 Why denaturation of a globular protein is the first-order phasetransition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677
3.4 “Gap” in energy spectrum: The main characteristicthat distinguishes protein chains from random polymers . . . . . . 681
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4 Kinetic aspects of protein folding 685
4.1 Protein folding in vivo . . . . . . . . . . . . . . . . . . . . . . . . . 685
4.2 Protein folding in vitro (in the test-tube) . . . . . . . . . . . . . . 685
4.3 Theory of protein folding rates and solution of the Levinthalparadox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692
Course 13. Self-Organized Criticalityin Granular Superconductors
by S.L. Ginzburg and N.E. Savitskaya 705
1 Introduction 707
2 1D multijunction SQUID with random locationof the junctions 708
3 Single-junction SQUID 710
4 1D sandpile model 712
5 The simplified model of 1D multijunction SQUID 713
6 Computer simulation results 715
7 Conclusions 717
Course 14. Hiking through Glassy Phases:Physics beyond Aging
by L. Berthier, V. Viasnoff, O. White, V. Orlyanchikand F. Krzakala 719
1 Introduction 721
2 Experimental facts 723
2.1 Rejuvenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 723
2.2 Overaging and underaging . . . . . . . . . . . . . . . . . . . . . . . 724
2.3 Memory effect of the first kind, or “Kovacs effect” . . . . . . . . . 726
2.4 Memory effect of the second kind . . . . . . . . . . . . . . . . . . . 726
2.5 Need for a generic and robust phenomenology . . . . . . . . . . . . 726
3 Two mean-field theoretical approaches 727
3.1 Trap and multi-trap models . . . . . . . . . . . . . . . . . . . . . . 727
3.2 Infinite-range models . . . . . . . . . . . . . . . . . . . . . . . . . . 728
xxxiii
4 Spatial approaches 7284.1 Domain growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7284.2 A minimal phenomenology . . . . . . . . . . . . . . . . . . . . . . . 7294.3 Back to experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 7314.4 Droplets and chaos in spin glasses . . . . . . . . . . . . . . . . . . 7324.5 Surfing on a critical line . . . . . . . . . . . . . . . . . . . . . . . . 734
5 Two experiments 7365.1 Anderson insulator . . . . . . . . . . . . . . . . . . . . . . . . . . . 7365.2 Colloidal suspension . . . . . . . . . . . . . . . . . . . . . . . . . . 737
6 Conclusion 739
Course 15. Kinetically Constrained Models and DrivenSystems with Slow Dynamics
by H.S. Bond, M. Clincy and S. Whitelam 743
1 Introduction and overview 745
2 The Fredrickson-Andersen model 747
3 The Kob-Andersen model 749
4 The ABC model 751
5 Conclusions and outlook 753
Course 16. Dynamic Transitions in Thermaland Athermal Systems
by C.B. Holmes, J.H. Snoeijer and Th. Voigtmann 755
1 Introduction 757
2 Universal behavior of the force distribution? 758
3 Colloidal glasses and gels 760
4 Jamming transitions 763
5 Conclusion 764
Previous Sessions 767
