1- Spontaneously broken and dynamically enhanced global and local-symmetries
2 - Continuum (scaling) limits of lattice fields theories (triviality of lg q in d 1=y4 dimensions
3 -Results and problems near the interface between statistical mechanics and quantum field theory
SYMETRIE BRISEE
THEORIE DES CHAMPS
METRIQUE
MECANIQUE STATISTIQUE
THEORIE QUANTIQUE DES CHAMPS
FROHLICH
P/81/56
IHES
1981
A4
26 f.
EN
TEXTE
PREPUBLICATION
P_81_56.pdf
1981
A Heuristic theory of phase transitions
RESEAUX
SYSTEMES COMPLEXES
ESPACES DE BANACH
TRANSITIONS DE PHASE
Abstract : Let Z be a suitable Banach space of interactions for a lattice spin system. If n+1 thermodynamic phases coexist for ?0 ?Z, it is shown that a manifold of codimension n of coexistence of (at least) n+1 phases passes through ?0. There are also n+1 manifolds of codimension n?1 of coexistence of (at least) n phases; these have a common boundary along the manifold of coexistence of n+1 phases. And so on for coexistence of fewer phases. This theorem is proved under a technical condition (R) which says that the pressure is a differentiable function of the interaction at ?0 when restricted to some codimensionn affine subspace of Z. The condition (R) has not been checked in any specific instance, and it is possible that our theorem is useless or vacuous. We believe however that the method of proof is physically correct and constitutes at least a heuristic proof of the Gibbs phase rule.
RUELLE
P/76/149
IHES
10/1976
A4
25 f.
EN
TEXTE
PREPUBLICATION
P_76_149.pdf
1976
A Rigorous mathematical foundation of functional integration
INTEGRATION DE FONCTIONS
PHYSIQUE THEORIQUE
FORMES QUADRATIQUES
VOLUME
THEOREME
THEORIE DES TRELLIS
MESURES GAUSSIENNES
CALCUL INTEGRAL
APPLICATIONS
CARTIER
DEWITT-MORETTE
M/97/86
IHES
11/1997
A4
39 f.
EN
TEXTE
PREPUBLICATION
M_97_86.pdf
1997
A Variational formulation of equilibrium statistical mechanics and the Gibbs phase rule
ENTROPIE
RESEAUX
PHYSIQUE STATISTIQUE
SYSTEMES COMPLEXES
Abstract : It is shown that for an infinite lattice system, thermodynamic equilibrium is the solution of a variational problem involving a mean entropy of states introduced earlier [2]. As an application, a version of the Gibbs phase rule is proved.
RUELLE
P/67/X012
IHES
1967
A4
6 f.
EN
TEXTE
PREPUBLICATION
P_67_X012.pdf
1967
Aspects of long time behaviour of solutions of nonlinear Hamiltonian evolution equations
SYSTEMES HAMILTONIENS
EQUATIONS D’ONDES NON LINEAIRES
EQUATION DE SCHRODINGER
BOURGAIN
M/94/18
IHES
03/1994
A4
22 f.
EN
TEXTE
PREPUBLICATION
M_94_18.pdf
1994
Characterizing volume forms
INTEGRATION DE FONCTIONS
VOLUME
FORMES
THEORIE QUANTIQUE DES CHAMPS
GEOMETRIE DIFFERENTIELLE
CARTIER
BERG
DEWITT-MORETTE
WURM
M/01/17
IHES
04/2001
A4
10 f.
EN
TEXTE
PREPUBLICATION
P_01_17.pdf
2001
Do there exist turbulent crystals ?
CRISTAUX
TURBULENCE
Abstract : We discuss the possibility that, besides periodic and quasiperiodic crystals, there exist turbulent crystals as thermodynamic equilibrium states at non-zero temperature. Turbulent crystals would not be invariant under translation, but would differ from other crystals by the fuzziness of some diffraction peaks. Turbulent crystals could appear by breakdown of long range order in quasiperiodic crystals with two independent modulations.
RUELLE
P/82/02
IHES
01/1982
A4
6 f.
EN
TEXTE
PREPUBLICATION
P_82_02.pdf
1982
Dynamical entropy of C* algebras and Von Neumann algebras
ALGEBRES DE VON NEUMANN
C*-ALGEBRES
CONNES
NARNHOFER
THIRRING
M/87/05
IHES
02/1987
A4
25 f.
EN
TEXTE
PREPUBLICATION
M_87_05.pdf
1987
Functional labels and syntactic entropy on DNA strings and proteins
ADN
SEQUANCAGE DES ACIDES NUCLEIQUES
GENES
PROTEINES
MACROMOLECULES
HYPERGRAPHES
EVOLUTION
ENTROPIE
GROMOV
CARBONE
M/01/54
IHES
A4
12 f.
EN
TEXTE
M_01_54.pdf
2001
Gibbs measures and quasi-periodic solutions for nonlinear Hamiltonian partial differential equations
SYSTEMES HAMILTONIENS
MESURES DE GIBBS
EQUATIONS DIFFERENTIELLES NON LINEAIRES
EQUATION DE SCHRODINGER
PERTURBATION
BOURGAIN
M/95/13
IHES
02/1995
A4
11 f.
EN
TEXTE
PREPUBLICATION
M_95_13.pdf
1995
Integral representation of measures associated with a foliation
CALCUL INTEGRAL
TOPOLOGIE DIFFERENTIELLE
FEUILLETAGES
THEORIE GEOMETRIQUE DES FONCTIONS
RUELLE
PM/77/181
IHES
05/1977
A4
6 f.
EN
TEXTE
PREPUBLICATION
PM_77_181.pdf
1977
Introduction to spontaneous symmetry breaking : some examples
PHYSIQUE
SYMETRIE BRISEE
MICHEL
P/85/27
IHES
04/1984
A4
14 f.
EN
TEXTE
PREPUBLICATION
P_85_27.pdf
1985
Invariant measures for the 2D-defocusing nonlinear Schrödinger equation
EQUATION DE SCHRODINGER
MESURES INVARIANTES
MECANIQUE STATISTIQUE
PROBLEME DE CAUCHY
BOURGAIN
M/94/28
IHES
04/1994
A4
13 f.
EN
TEXTE
PREPUBLICATION
M_94_28.pdf
1994
Isoperimetry of waists and concentration of maps
INEGALITES ISOPERIMETRIQUES
ENSEMBLES CONVEXES
GROMOV
M/02/04
IHES
A4
22 f.
EN
TEXTE
PREPUBLICATION
M_02_04.pdf
2002
Mathematical slices of molecular biology
BIOMATHEMATIQUES
BIOLOGIE MOLECULAIRE
MATHEMATIQUES
GENETIQUE
CYTOLOGIE
GROMOV
CARBONE
M/01/03
IHES
A4
44 f.
EN
TEXTE
PREPUBLICATION
M_01_03.pdf
2001
On Manifolds of phase coexistence
PHYSIQUE THEORIQUE
PHYSIQUE MATHEMATIQUE
Abstract : Using a theorem on convex functions due to Israel, it is shown that a point of coexistence of n+1n+1 phases cannot be isolated in the space of interactions, but lies on some infinite dimensional manifold.
RUELLE
P/75/128
IHES
12/1975
A4
13 f.
EN
TEXTE
PREPUBLICATION
P_75_128.pdf
1975
On the Absence of spontaneous symmetry breaking and of crytalline ordering in two-dimensional systems
SYMETRIE BRISEE
CRISTALLOGRAPHIE MATHEMATIQUE
MECANIQUE STATISTIQUE
DIMENSIONS
FROHLICH
PFISTER
P/81/31
IHES
1981
A4
22 f.
EN
TEXTE
PREPUBLICATION
P_81_31.pdf
1981
On the Cauchy and invariant measure problem for the periodic Zakharov system
PROBLEME DE CAUCHY
EQUATION DE SCHRODINGER
MECANIQUE STATISTIQUE
BOURGAIN
M/93/63
IHES
11/1993
A4
14 f.
EN
TEXTE
PREPUBLICATION
M_93_63.pdf
1993
On the Ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions
THEORIE ERGODIQUE
GROUPES DISCRETS
MOUVEMENT
HYPERBOLES
SULLIVAN
M/78/229
IHES
06/1978
A4
18 f.
EN
TEXTE
PREPUBLICATION
M_78_229.pdf
1978
On the statistical mechanics of classical Coulomb - and dipole gases
MECANIQUE STATISTIQUE
GAZ
PHYSIQUE NUCLEAIRE
FROHLICH
SPENCER
P/80/10
IHES
1980
A4
65 f.
EN
TEXTE
PREPUBLICATION
P_80_10.pdf
1980
Periodic nonlinear Schrödinger equation and invariant measures
EQUATION DE SCHRODINGER
MESURES INVARIANTES
EQUATIONS DE KORTEWEG-DE VRIES
FONCTIONS PERIODIQUES
BOURGAIN
M/93/50
IHES
09/1993
A4
18 f.
EN
TEXTE
PREPUBLICATION
M_93_50.pdf
1993
Phase transitions in anisotropic lattice spin systems
SPIN
PHYSIQUE NUCLEAIRE
ANISOTROPIE
FERROMAGNETISME
FROHLICH
LIEB
P/78/199
IHES
01/1978
A4
35 f.
EN
TEXTE
PREPUBLICATION
P_78_199.pdf
1978
Random walk in random groups
GROUPES INFINIS
ENTROPIE
ESPACES METRIQUES
GROMOV
M/02/03
IHES
A4
35 f.
EN
TEXTE
PREPUBLICATION
M_02_03.pdf
2002
Return to equilibrium
GROUPE DE RENORMALISATION
EQUILIBRE THERMODYNAMIQUE
RAYONNEMENT DU CORPS NOIR
KMS
FROHLICH
BACH
SIGAL
P/00/44
IHES
06/2000
A4
53 f.
EN
TEXTE
PREPUBLICATION
P_00_44.pdf
2000
Sensitive dependence on initial conditions and turbulent behavior of dynamical systems
SYSTEMES DYNAMIQUES
DYNAMIQUE DIFFERENTIABLE
Abstract : The asymptotic behavior of differentiable dynamical systems is analyzed. We discuss its descriptoin by asymptotic measures and the turbulent behavior with senditive dependence on initial condition.
RUELLE
P/77/190
IHES
10/1977
A4
9 f.
EN
TEXTE
PREPUBLICATION
P_77_190.pdf
1977
Some Recent rigorous results in the theory of phase transitions and critical phenomena
TRANSITIONS DE PHASES
PHENOMENES CRITIQUES
THEORIE QUANTIQUE DES CHAMPS
GROUPE DE RENORMALISATION
MODELE D'ISING
FROHLICH
SPENCER
P/82/23
IHES
1982
A4
22 f.
EN
TEXTE
PREPUBLICATION
P_82_23.pdf
1982
Statistical mechanics of a one-dimensional lattice gas
MECANIQUE STATISTIQUE
RESEAUX
GAZ
Abstract : We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result of Van Hove we show that, for a large class of interactions, such a system has no phase transition. The equilibrium state of the system is represented by a measure which is invariant under the effect of lattice translations. The dynamical system defined by this invariant measure is shown to be a K-system.
RUELLE
P/67/X016
IHES
1967
A4
10 f.
EN
TEXTE
PREPUBLICATION
P_67_X016.pdf
1967
Symmetry breakdown in statistical mechanics
SYMETRIE BRISEE
MECANIQUE STATISTIQUE
CONGRES ET CONFERENCES
Lecture given at the Ecole d'Eté de Physique Théorique. Cargèse, Corsica, 1969.
Abstract : We discuss the general problem of symmetry beakdown in the algebraic approach to statistical mechanics. We consider in particular the case of classical quantum lattice systems.
RUELLE
P/69/30
IHES
1969
A4
24 f.
EN
TEXTE
PREPUBLICATION
P_69_30.pdf
1969
Symmetry in condensed matter physics
SYMETRIE
MATIERE CONDENSEE
MICHEL
P/81/58
IHES
11/1981
A4
8 f.
EN
TEXTE
PREPUBLICATION
P_81_58.pdf
1981
Tendances nouvelles en mécanique : Quatre conférences sur la mécanique céleste et les instabilités
MECANIQUE CELESTE
RELATIVITE GENERALE
EXPERIENCES
TROUS NOIRS
STABILITE
CONVECTION THERMIQUE
CARTIER
CARTER
GUYON
MARCHAL
P/79/310
IHES
11/1979
A4
15 f.
FR
TEXTE
PREPUBLICATION
P_79_310.pdf
1979
The Density at infinity of a discrete group of hyperbolic motions
THEORIE ERGODIQUE
THEORIE DE LA MESURE
TRANSFORMATIONS
SURFACES DE RIEMANN
GROUPES DE KLEIN
Dedicated to Rufus Bowen
SULLIVAN
M/79/261
IHES
03/1979
A4
27 f.
EN
TEXTE
PREPUBLICATION
M_79_261.pdf
1979
The Ergodic theory of axiom a flows
THEORIE ERGODIQUE
ENTROPIE
AXIOMES
RUELLE
BOWEN
P/74/78
IHES
03/1974
A4
38 f.
EN
TEXTE
PREPUBLICATION
P_74_78.pdf
1974
The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb Gas
SPIN
PHYSIQUE NUCLEAIRE
GAZ
DENSITE
TRANSFORMATIONS
ELECTROSTATIQUE
FROHLICH
SPENCER
P/81/25
IHES
1981
A4
77 f.
EN
TEXTE
PREPUBLICATION
P_81_25.pdf
1981
The Present Status of CP, T and CPT Invariance
PHYSIQUE NUCLEAIRE
PARTICULES
SYMETRIE
INVARIANTS
Introduction :
Last time I came to Sweden, cars were drivent on the left side of the roads. This week most cars I saw were driven on the right side. I am very grateful to the Nobel Foundation for this opportunity to observe this P violation. I may have found the cause of this P violation by looking at buses or trucks with the same inscription on both sides ; they are not symmetrically written.
I have also made a couter-experiment to verify this theory. In Tokyo I found an equal probability for cars to be driven on the left side or the right side of the streets and I did observe that identical texts were placed symmetrically on buses and trucks : the first character is near the front part on both sides so the same text must be read from left to right on one side and from right to left on the other side.
Since I have never been yet in a car undergoing a spontaneous CP transformation, I will be able to give you today my report on CP, T and CPT invariance.
MICHEL
P/68/31
IHES
[06/1968]
A4
18 f.
EN
TEXTE
PREPUBLICATION
P_68_31.pdf
1968
The States of classical statistical mechanics
MECANIQUE STATISTIQUE
Abstract : a state of an infinite system in classical statistical mechanics is usually described by its correlation functions. We discuss here other description in particular as 1) a state on a B*-algebras, 2) a collection of density distributions, 3) a field theory 4) a mesure on a space of configurations of infitely many particles. We consier the relations between these various descriptions and prove under very general conditions an integral representation of a state as superposition of extremal invariant states corresponding to pure thermodynamical phases.
RUELLE
P/66/02
IHES
1966
A4
31 f.
EN
TEXTE
PREPUBLICATION
P_66_02.pdf
1966
Von Neumann algebra automorphisms and time-thermodynamics relation in general covariant quantum theoies
ALGEBRES DE VON NEUMANN
AUTOMORPHISMES
THEORIE QUANTIQUE
THERMODYNAMIQUE
TEMPS
GRAVITATION
CONNES
ROVELLI
M/94/36
IHES
06/1994
A4
14 f.
EN
TEXTE
PREPUBLICATION
M_94_36.pdf
1994