Centre de Physique Théorique


May 2019

Friday 3 May 14:00-15:00, Amphi 5 CPT

Inflation and non-gaussianities in the case of analytic infinite derivative (AID) gravity.

Alexey Koshelev (Universidade da Beira Interior)

From 5 to 11 May, IESC, Cargèse

Hot topics in Modern Cosmology Spontaneous Workshop XIII

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Spontaneous Workshop (SW) brings together specialists on recent insights in Particle Physics, Astrophysics and Cosmology. The aim is to stimulate debate on common topics in views of providing us with innovating ideas on emerging problems. The workshop’s organization is based on an optimal number of concise presentations and with enough space for discussions in order to favour interactions among participants. Postdocs and PhD students are encouraged to attend.

Tuesday 7 May 11:00-12:00, Amphi 5 du CPT

Order and symmetry-breaking in the fluctuations of nonequilibrium diffusive systems.

Nicolás Tizón Escamilla

Abstract: Understanding the statistics of macroscopic fluctuations in nonequilibrium systems remains as one of the major challenges of theoretical physics. This interest is rooted in the prominent role that fluctuations play in equilibrium, where their statistics is directly linked to the relevant thermodynamic potentials. Similarly, it is nowadays expected that a deeper understanding of nonequilibrium fluctuations will pave the way to a sound definition of nonequilibrium potentials. In recent years, a macroscopic fluctuation theory (MFT) has been formulated to study dynamic fluctuations in systems far from equilibrium, offering detailed predictions for the large deviation functions associated to the distribution of fluctuations which acts as a marginal of the nonequilibrium analog of thermodynamic potential. MFT also determines the optimal path to a fluctuation shedding light on e.g. the reasons behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions and new symmetries.

In this talk, I will focus on the emergence of dynamic phase transitions at a fluctuating level, studying the current statistics of an archetypal two-dimensional (2d) driven diffusive system, the weakly asymmetric simple exclusion process (WASEP), characterizing its properties using MFT. The complex interplay among the external field, anisotropy and currents in 2d leads to a rich phase diagram, with different symmetry-broken fluctuation phases. Order in the form of coherent jammed states emerges, revealing a deep connection between rare events and self-organized structures which enhance their probability, an observation of broad implications.

Thursday 9 May 11:00-12:00, Amphi 5 du CPT

Numerical simulation of dry foam and biological tissues.

Francesca Zaccagnino (Aberystwyth University, UK)

We present a numerical model to study the rheology of two-dimensional dry foams. In a foam flowing at high velocity, the tangential component of the velocity associated with the gradient of surfactant concentration is not negligible. We develop a non quasi-static model to investigate the influence of viscoelastic parameters on the film evolution. In particular, we consider the surfactant transport and the resulting surface tension variation along each film. Since, experiments on a foam between two parallel plates suggest that the diffusion of curvature along the film can not be neglected, we merge our surfactant transport (ST) model with the two-dimensional Viscous Froth (VF) model[1]. The VF+ST model is validated by fitting experimental data for the evolution of the length of a film after a topological rearrangement (T1). Extending the VF model, which allows us to estimate the drag coefficient, our VF+ST model predicts two additional parameters, the Gibbs elasticity and the surface viscosity. The VF+ST model allow us to fit experimental data for foams containing either anionic surfactants or proteins [2].
Furthermore, we apply the VF+ST model to predict the rheological parameters of a flowing two-dimensional dry foam. We implement hexagonal ordered and disordered foams subjected to simple shear or oscillating strain. We highlight how the viscoelastic parameters of our model affect the distribution of topological rearrangements in the foam. Additionally, we calculate the shear stress, which offers a qualitative description of the transition of the foam from a solid-like to a liquid-like behaviour. Hence, starting from the stress-strain curves at different shear rates we predict the elastic shear modulus and the yield stress of the foam. In the case of oscillating strain we investigate how the foam behaviour depends on the frequency or the amplitude of the applied strain and we calculate the storage and loss moduli. Overall, we analyse the effect of the viscoelastic parameters of our model on the rheological properties of a foam.
Finally, the model is applied to investigate the morphology of biological tissues. Well known analogies between fluids and biological tissue make possible the application our model to simulate experiments presented by Bonnet et al[3]. They carried out an annular ablation on Drosophilapupa dorsal thorax epithelium. In agreement with the experimental results, we find that after severing the cells, the anisotropy in the tissue increases with the age of the Drosophilapupa. In the simulation the ageing of the tissue is implemented by applying an initial pre-strain. As before, we investigate the effect of our viscoelastic parameters on the tissue. We propose our model as a tool for further investigations on tissue morphology.

[1] Kern, N., Weaire, D., Martin, A., Hutzler, S., and Cox, S. J.,Two-dimensional viscous froth model for foam dynamics, Physical Review E, 70(4), 041411, (2004).
[2] Zaccagnino, F., Audebert, A. and Cox, S. J.,Simulation of surfactant transport during the rheological relaxation of two-dimensional dry foams, Physical Review E, 98(2), 022801, (2018).
[3] Bonnet, I., Marcq, P., Bosveld, F., Fetler, L., Bellaıche, Y., and Graner, F., Mechanical state, material properties and continuous description of an epithelial tissue, Journal of The RoyalSociety Interface, 9(75), 2614-2623, (2012)

Friday 10 May 14:00-15:00, CPT, Amphi 5

Gauge vs. boundaries: a geometric field-space perspective

Aldo Riello

Wednesday 22 May 14:00-15:00, CPT, Amphi 5

Graphes quantiques, trou spectral et optimisation de formes

Guillaume Levy (CMLS, Ecole Polytechnique)


Dans cet exposé, on considère le laplacien unidimensionnel agissant sur des fonctions définies sur un graphe métrique. En guise de condition aux sommets, analogue dans ce cadre des conditions au bord, on impose les conditions de Neumann, qui traduisent la conservation du courant à travers les sommets. Pour un graphe de départ donné, on s’autorise à faire varier les longueurs des arêtes tout en conservant la longueur totale du graphe. On cherche ensuite des bornes explicites sur la première valeur propre non nulle de cet opérateur (égale au trou spectral ici) en fonction de paramètres métriques, topologiques et combinatoires du graphe sous-jacent, que l’on souhaite optimales, ainsi que les graphes atteignant les valeurs extrêmes. On résout ainsi complètement le problème du minimum et l’on apporte également des réponses partielles au problème du maximum. On conclut en présentant une conjecture sur la forme générale des maximiseurs. Ce travail a été réalisé en collaboration avec Ram Band, du Technion (Haïfa).

Wednesday 22 May 15:30-17:00, Amphi 5

Quantum cellular automata, computability and universality.

Pablo Arrighi (LIS, Aix-Marseille Université)

I will draw a distinction between finite-dimensional quantum evolutions ("automata") and infinite-dimensional evolutions ("operators"), and then explore their consequences upon two well-established concepts in Computer Science : computability and universality. Most of the results I will mention will rely on a decomposition of quantum operators, into quantum automata---which is based upon the tacit assumption of a fixed partial order. Time-allowing, I will try to touch on the topical question of quantum partial orders.

Friday 24 May 14:00-15:00, Amphi 5

Fundamental strong dynamics beyond the Standard Model in the electroweak sector

Aldo Deandrea (Université Claude Bernard Lyon and CNRS)

Models that arise from a new strong interaction can be defined in terms of a simple, confining, gauge group and a number of fundamental fermions which form bound states allowing a more fundamental explanation of weak interactions and of the Higgs sector of the Standard Model. I will discuss some of the key features of these models and their phenomenology, namely the presence of a larger scalar sector than in the standard model as well as the presence of vector-like fermions and spin-1 resonances.

Wednesday 29 May 14:00-16:00, CPT, Amphi 5

Contre-exemples explicites réfutant la conjecture de Schäffer

Rachid Zarouf (Université d'Aix-Marseille)


Schäffer a prouvé en 1970 que pour toute norme matricielle induite
et toute matrice $n\times n$ inversible $T$, l’inégalité
[|det(T)||T^-1|\leq\mathcalS |T|^n-1]
est vérifiée avec $\mathcalS=\mathcalS(n)\leq\sqrten$. Il a
conjecturé que le meilleur $\mathcalS$ était en fait borné. Ceci a été
réfuté par Gluskin-Meyer-Pajor et les contributions ultérieures de
J. Bourgain et H. Queffélec qui ont successivement amélioré les minorations
correspondantes de $\mathcalS$, s’appuyant sur une inégalité de
Bourgain. La construction de contre-exemples explicites réfutant cette
conjecture reste ouverte depuis 22 ans, l’inégalité de Bourgain reliant
cette question à la théorie des sommes de puissances de nombres complexes
et à certains problèmes de P. Turán. Nous démontrons une analogue
de l’inégalité de Bourgain nous conduisant à la construction des premiers
contre-exemples explicites réfutant la conjecture de Schäffer. Il
s’agit d’une suite explicite de matrices $n\times n$ de Toeplitz
de spectre fixe et arbitraire ${\lambda}\subset\mathbbD-{0}$
satisfaisant $\mathcalS\geq c(\lambda)\sqrtn$.

Un élément clé de notre approche sera d’étudier sur les normes $l_p$
des coefficients de Fourier de la puissance $n$-ième d’un automorphisme
du disque unité, sujet initié par J-P. Kahane.

En cours de route, nous déterminons sur l’intervalle $]-1,1[$, le
comportement asymptotique des polynômes de Jacobi dont le premier
paramètre varie, sujet initié par G. Darboux.