Attention : désormais les séminaires ont lieu tous les lundis à 10h45 en salle 523 du LPTMC - Tour 12-13
SALLE INHABITUELLE: Salle de séminaire de l'INSP, couloir 23-22, pièce 3-17
Benoit Douçot (LPTHE)
Introduction à la classification des isolants et supraconducteurs topologiques (1ère partie)
Peu de temps après la découverte fondamentale par Kane et Mele en 2005 de modèles réalistes d’isolants topologiques invariants par symétrie de renversement du temps, et la confirmation expérimentale de l’existence de la phase d’effet Hall quantique de spin par Molenkamp et collaborateurs, est apparue une impressionnante classification des isolants et supraconducteurs topologiques pour des Hamiltoniens quadratiques de fermions. Cette classification résulte de la confluence remarquable entre deux domaines de recherche a priori très éloignés. Le premier est l’étude de la localisation d’ Anderson due au désordre en présence de symétries discrètes, comme le renversement du temps, éventuellement étendue au cas supraconducteur. En 1996, M. Zirnbauer a montré qu’il existe 10 classes de symétries discrètes possibles pour de tels systèmes. En suivant ce fil conducteur,Schnyder, Ryu, Furasaki et Ludwig ont identifié en 2008 lesquelles de ces classes, en fonction de la dimension de l’espace, permettent de stabiliser des états de bord échappant à la localisation d’Anderson. Le deuxième domaine de recherche impliqué est l’étude de la topologie des états de Bloch pour des systèmes invariants par translation. En 2009, A. Kitaev a compris comment incorporer les contraintes provenant des symétries discrètes sur cette topologie, et il a abouti à une classification identique à la précédente ! Le but de ces deux cours est de donner un aperçu de cette classification, d’expliquer certaines des idées mathématiques sous-jacentes, et de montrer comment elle peut être utilisée. Un prérequis utile (mais non nécessaire) est d’avoir suivi les cours récents de Jean-Noël Fuchs et Tristan Cren sur les isolants et supraconducteurs topologiques.
Nicolas Wschebor (Université de la République d'Uruguay, Montevideo)
Proving conformal invariance in critical scalar theories in any dimension
Conformal invariance in three dimension has a tremendous renewed interest due to the surprisingly good results obtained by using the “conformal bootstrap” in last five years. In this talk, the interest of this symmetry is reviewed and its existence in critical (scale invariant) theories in any dimension is discussed. In particular, using Wilson renormalization group, we show that if no integrated vector operator of scaling dimension −1 exists in a given model, then scale invariance implies conformal invariance. By using the Lebowitz inequalities, we prove that this necessary condition (or another similar necessary condition proposed by Polchinski many years ago) is fulfilled in all dimensions less than four for the Ising universality class. This shows, in particular, that scale invariance implies conformal invariance for the three-dimensional Ising model. Finally, the extension of this result to other critical systems is discussed.
Alessandro Codello (INFM Bologna, Italie)
Functional perturbative RG and CFT data in the e-expansion
I will show how the use of standard perturbative RG in dimensional regularization allows for a renormalization group based computation of both the spectrum and a family of coefficients of the operator product expansion (OPE) for the whole family of scalar multi-critical universality classes.
The task is greatly simplified by a straightforward generalization of perturbation theory to a functional perturbative RG approach. I illustrate the procedure in the e-expansion by obtaining the next-to-leading corrections for the spectrum and the leading corrections for the OPE coefficients of Ising and Lee-Yang universality classes and then give several results for the whole family of renormalizable multi-critical models.
Whenever a comparison is possible our RG results explicitly match the ones recently derived using a combination of CFT constraints, Schwinger-Dyson equation and the free theory behavior at the upper critical dimension.
Julien Cividini (Weizmann institute, Israël)
Driven tracer with absolute negative mobility
Instances of negative mobility, where a system responds to a perturbation in a way opposite to naive expectation, have been studied theoretically and experimentally in numerous nonequilibrium systems. After reviewing part of the literature on the topic, we will consider a simple one-dimensional lattice model of a driven tracer in bath. We will show that contrary to previous expectations, Absolute Negative Mobility (ANM), whereby current is produced in a direction opposite to the drive, occurs around an equilibrium state. We derive analytical predictions for the mobility in the linear response regime. The high density regime will help us elucidate the mechanism leading to ANM. The lattice model can be seen as a toy model for hard Brownian discs in a narrow planar channel. Molecular dynamics studies show that the hard discs model exhibits Negative Differential Mobility (NDM), but no ANM.
Vittore Scolari (Institut Pasteur, Paris)
Kinetic signature of cooperativity in the irreversible collapse of a polymer
We investigated the kinetics of a polymer collapse due to the formation of irreversible crosslinks between its monomers. We use the contact probability as a function of the monomeric distance as a scale dependent order parameter and show in simulations the emergence of acooperative pearling instability. This produces a sharp conformational transition in time, inducing a crossover between short and long distance behaviour due to the formation of pearls. The size of pearls and the transition time depends on the equilibrium dynamics of the polymer and the rate at which cross links are formed. We finally confirm experimentally the existence of this transition using a chromosome conformation capture experiment.