Laboratoire de Physique Théorique et Hautes Energies

Théorie de la renormalisation

Pietro Slavich — 2012-11-15T14:25:16Z

En construction (voir version anglaise).

Matière Condensée et Physique Statistique

Damien Brémont — 2012-11-07T18:01:14Z

Quantum out of equilibrium dynamics

Damien Brémont — 2012-11-06T22:38:38Z

Besides their experimental relevance and possible technological application,
the behavior of quantum systems out of equilibrium is a topic of fundamental
interest, the understanding of which is still at an early stage.
Some techniques of classical dissipative systems have been generalized to the quantum case but important questions remain to be answered such as which would be the meaning of the effective temperature appearing in fluctuation-dissipation relations out of equilibrium.
The time-dependent (second and higher order) correlation functions and the (linear and non-linear) responses of systems evolving close to equilibrium satisfy a number of model independent relations. In classical dynamics these fluctuation-dissipation theorems are Ward identities of a symmetry of the, generically non-Markovian, dynamic generating functional. The quantum version is work in progress. We studied the effect of a drive, realized in the form of the coupling to
two fermion reservoirs at different chemical potentials, on the phase transition and coarsening dynamics of coupled quantum rotors. In experimental systems the coupling to an environment is usually unavoidable. We studied the effect of a non-Ohmic classical bath on the critical (Langevin) dynamics of the classical —phi-4, O(N) model in the large N limit by using the dynamic renormalization-group. We showed that although the critical temperature and critical dimensions
are not altered by the bath, the dynamic critical exponent is, for sufficiently sub-Ohmic baths. As a step towards understanding impurity motion in one dimensional ultra cold quantum liquids, we derived the non equilibrium correlation function of a quantum Brownian particle with general Gaussian
non-factorizing initial conditions. We studied the possible emergence of thermal behavior long after the quench of a closed quantum system by studying fluctuation-dissipation relations in which parameters replace the equilibrium temperature. We analyzed these relations in the stationary regime after a quench in the transverse field of the quantum Ising chain.
The lack of thermalization to a Gibbs ensemble became apparent with this approach.

Dynamics through phase transitions

Damien Brémont — 2012-11-06T22:33:51Z

Sub-critical coarsening is the process whereby a macroscopic system in contact with an equilibrium reservoir orders after a rapid change in a parameter that takes it from a disordered phase into an ordered one in its equilibrium phase diagram. Closely related is critical coarsening, the process whereby a critical state is approached by quenching a disordered system right to the critical point.
One of our goals is to characterize the geometry of coarsening phenomena in distribution. We studied analytically the statistical and geometric properties of ordered structures in planar curvature driven coarsening. The results provide the first analytic proof of dynamic scaling in more than one dimension for a finite dimensional order parameter. We studied numerically 2d phase separation, domain growth
in the random bond ferromagnetic Ising model and the Potts model. Experiments in a liquid crystal -film confirmed our predictions and demonstrated that monitoring the time-evolution of structures can be a very efficient way to determine the dynamic universality class. More recently, we analyzed these same questions after a quench to a critical point. We studied the relaxation of the 2d kinetically constrained spiral model. We showed that any unblocked state de-correlates in -finite times in the full phase diagram and we proved that the dynamics occur via coarsening of vacancy lines.
Quenches at very slow rates attracted a lot of attention in the cosmology and the condensed matter communities. A proposal for the cooling-rate dependence is given by the Kibble-Zurek (KZ) mechanism. We revisited these ideas in phase ordering systems across a second order phase transition and we revealed the limitations of the KZ mechanism. Next, we extended the analysis to the KT transition in the 2d XY model.

Fluctuations in glassy systems

Damien Brémont — 2012-11-06T22:28:54Z

Glassy dynamics occur out of equilibrium with special properties such as physical aging, memory effects and dynamic heterogeneities, that is to say, regions of particles rearranging cooperatively at the nanometer scale, at very different rates compared with the bulk. Such features have been observed in a wide variety of
materials including vortex matter in high-Tc superconductors.
The symmetry that captures the universal fluctuating aging dynamics of glassy systems should be the invariance of an effective dynamical action under uniform reparametrizations of the time-scales.
This scenario was put to the test with Monte Carlo simulations of the 3d
Edwards-Anderson spin-glass, the 3d random field Ising model, and confocal
microscopy data on dense (super-cooled liquid and glassy) colloidal suspensions.
We constructed restricted averages to obtain objects with a better statistics than the
completely fluctuating ones. The outcome of these studies is that while truly glassy systems conform to the consequences of the hypothesis, simple coarsening does not with time-reparametrization invariance being reduced to time rescaling at the heart of the difference. This result suggests that the fluctuations are intimately related to the global effective temperature.
A directed elastic manifold in random media is a system with many glassy aspects due to the competition between elasticity and disorder. The study of the Edwards-Wilkinson and a disordered elastic line, confirmed the growth of a coherence length that controls the scaling properties of averaged observables. A set of regimes going from normal diffusive aging to saturation -a la Family-Vicsek for finite-length lines passing through activated aging have been exhibited. The fluctuations of two-time quantities behave has also been analyzed.
As a first step towards a successful field theory of Brownian particles in interaction, we studied exactly the Brownian gas. Even though the particles do not interact, the field theory contains an interaction term that enforce the constraint of a strictly positive density field. In this paper we determined non-perturbatively the Poissonian nature of the ground state.

Electronic systems in low dimensions.

Damien Brémont — 2012-11-06T22:25:02Z

1) One-dimensional interacting electrons. An important class of multi-loop diagrams (beyond the Dzyaloshinskii-Larkin theorem) has been related to the equilibration of one-dimensional interacting electrons. The remarkable result is the derivation of a T3-law for the energy relaxation of thermal carriers.

2) Reduced quantum electrodynamics (RQED). We have computed radiative corrections, up to 2 loop, for a general RQED. Remarkable results have been found : when the gauge -field is four-dimensional, its beta function is zero (as in the Luttinger liquid case). Moreover, the 2-loop interaction correction numerical constant to the polarization operator (conductivity) has been computed. It's smallness may be an indication that interaction correction are (still) diff-cult to observe experimentally for (non-relativistic) graphene.

3) Skyrmion lattices for integer quantum Hall systems. We have studied quantum Hall ferromagnets with topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a d-component complex spinor field.
In particular we have computed analytically the complete low-lying excitation spectrum, which separates into d^2-1 gapless acoustic magnetic modes and a magnetophonon.

Publications du LPTHE sur INSPIRE

Damien Brémont — 2011-10-06T15:58:22Z

- Publications du LPTHE sur INSPIRE

Propositions de thèses au LPTHE

Damien Brémont — 2009-02-10T08:33:11Z

Fedor Smirnov : Approche algebro-géométrique à la quantification des modèles intégrables.

Les modèles intégrables trouvent plusieurs applications dans la physique
mathématique moderne. Ils servent de source indispensable à des formules exactes qui sont nécessaires pour dépasser les limites de la théorie des perturbations. Les méthodes de la géométrie algébrique jouent un rôle décisif dans l'étude des modèles intégrables classiques. Récemment il a été démontré dans le travaux de Jimbo, Miwa, Smirnov que certaines déformations des objets de géométrie algébrique étaient importantes pour l'étude de modèles intégrables quantiques. Il est nécessaire de
mieux comprendre la relation entre les méthodes de la géométrie algébrique pour le cas classique et le cas quantique. En particulier, il faut trouver un analogue classique de la description fermionique de l'espace des observables locales. C'est le problème le plus important que je propose de considérer.

Karim Benakli : Modèles de secteurs de Higgs étendus

La détermination de la nature de la brisure de la symétrie électro-faible, et la recherche d'un boson de Higgs associé, constituent l'objectif premier des expériences conduites au LHC dans les prochaines années. Les extensions non-minimales du modèle standard introduisent de nouveaux états qui couplent aux champs de Higgs et modifient par conséquent les signatures expérimentales de la brisure de la symétrie électrofaible. L'objet de cette thèse est l'étude de telles extensions et leurs implications.

Laurent Baulieu : Aspects geometriques dans les theories de jauge, la supersymmetrie et la gravite

Des progres recents dans la renormalisation des theories supersymetriques et de la supergravite et l'existence des theories topologiques suggerent l'existence de nouvelles formulations qui pourront modifier profondement notre comprehension de la structure interne des theories avec des symetries de jauge, y compris la gravite. L'objet de cette proposition de these est d'explorer ces domaines.. Pour plus de precisions sur les methodes utilisees, les candidats interesses sont invites a consulter les deux dernieres theses que j'ai dirige dans ces domaines, celles de G. Bossard et A. Martin, ainsi que les articles qui y sont associes (sur les archives electroniques).

Boris Pioline : Formes automorphes et supercordes

Bien que très prometteuse pour l'unification des interactions fondamentales dans un cadre quantique cohérent, la théorie des cordes ne possède pas à l'heure actuelle de formulation non perturbative satisfaisante. Cependant de nombreux indices laissent à penser qu'une telle théorie existe (la théorie M), et qu'elle est invariante sous un groupe de symétries discrètes infini (le groupe de U-dualité). Dans le cas le plus simple des compactifications sur un tore T^d, ce groupe est un sous groupe arithmétique du groupe exceptionnel E_d dans la forme réelle déployée.
Ceci implique en particulier que les amplitudes de diffusion sont des fonctions sur K\backslash E_d invariantes par Gamma, i.e. des fonctions automorphes de Gamma. Le but de la thèse est de construire de tels objets, en s'appuyant sur et en généralisant des constructions mathématiques connues, et d'étudier leur interprétation en termes d'effets non-perturbatifs instantoniques. Les fonctions automorphes apparaissent également lors du comptage des micro-états des trous noirs
supersymétriques, ces deux problèmes étant fortement reliés puisqu'un trou noir en dimension D donne lieu à un instanton en dimension D-1.

D'autres propositions de thèse seront annoncées prochainement.

partie de

Damien Brémont — 2008-04-24T15:59:22Z

Le laboratoire fait partie

de l'ILP
(Institut Lagrange de Paris)

Le laboratoire fait partie

de la FRIF
(Fédération de Recherche Interactions Fondamentales)

Dernières publications

Damien Brémont — 2008-04-24T15:38:49Z

Dernières publications

Kerr/CFT, dipole theories and nonrelativistic CFTs
El-Showk, Sheer ; Guica, Monica
Frozen into stripes : fate of the critical Ising model after a quench
Blanchard, Thibault ; Picco, Marco
Connectivities of Potts Fortuin-Kasteleyn clusters and time-like Liouville correlator
Picco, Marco ; Santachiara, Raoul ; Viti, Jacopo ; Delfino, Gesualdo
Q-discrete Painlevé equation and associated linear problem
Shi, Yang
Rankin-Selberg methods for closed strings on orbifolds
Angelantonj, Carlo ; Florakis, Ioannis ; Pioline, Boris