Attention : désormais les séminaires ont lieu tous les lundis à 10h45 en salle 523 du LPTMC - Tour 12-13
Bertrand Delamotte (LPTMC)
Groupe de renormalisation fonctionnel et généralisation du théorème central limite à des variables aléatoires fortement corrélées
Cette série de deux séminaires, faits en grande partie au tableau, a comme but d'introduire de la façon la plus pédagogique et élémentaire possible la notion de généralisation du théorème de la limite centrale (TCL) et de la relation entre probabilités et (groupe de) renormalisation. Après un rappel de ce qui est bien établi sur le TCL et de ses généralisations aux lois de Lévy stables, sera expliquée la difficulté inhérente au cas où les variables aléatoires sont corrélées. Le groupe de renormalisation fonctionnel (GRF) sera alors introduit et il sera montré que la notion de loi stable en probabilité est très proche (même si pas identique) de la notion de point fixe en renormalisation. Enfin, toutes ces notions seront explicitées sur l'exemple du modèle d'Ising en trois dimensions où l'on montrera que la famille infinie de distributions de probabilité de l'aimantation à la criticalité est reproduite de façon très précise par l'implémentation la plus simple du GRF.
Aleksandra Walczak (ENS)
Learning from mice and birds: active (?) matter and collective (?) behaviour.
Interacting systems in biology often exhibit interesting dynamics, such as coexistence of multiple time scales, manifested by the fat tails in the distribution of waiting times. While existing tools in statistical inference, such as the maximum entropy models, have been powerful to reproduce the empirical steady state distribution, it remains challenging to learn a good model for the dynamics. Inspired by experiments, I will discuss a generalized Glauber dynamics approach that tunes dynamics of an interacting system, while keeping the steady state distribution fixed. I will also use the entropy production rate to quantify the departure from equilibrium of a flock of birds, showing how the irreversibility condition imposes asymmetries on the steady state distribution of the system.
Silvia Pappalardi (ENS)
Quantum bounds and fluctuation dissipation theorem
In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and deriva- tion of quantum bounds on the transport coefficients or on the chaos rate. However, the physical meaning and the mechanism enforcing such bounds is still an open question. In this talk, I will discuss the quantum fluctuation-dissipation theorem (the KMS conditions) as the principle underlying bounds on correlation time scales. By restating the problem in a replicated space, I will show that the quantum bound to chaos is a direct consequence of the KMS condition, as applied to a particular pair of two-time correlation and response functions. Encouraged by this, I will describe how quantum fluctuation-dissipation relations act in general as a blurring of the time-dependence of correlations, which can imply bounds on their decay rates. Thinking in terms of fluctuation-dissipation opens a direct connection between bounds and other thermodynamic properties.
Francesco Mori (LPTMS)
Stochastic resetting: from geometric properties to optimal control
"When in a difficult situation, it is sometimes better to give up and start all over again''. While this empirical truth has been regularly observed in a wide range of circumstances, quantifying the effectiveness of such a heuristic strategy remains an open challenge. In this talk, I will first consider the minimal model of a single diffusive particle that is reset to its starting position with a constant rate. I will present recent results on the geometrical properties of this process, including the convex hull  and the number of visited sites . Then, I will introduce a novel framework that allows to optimally control a very general class of dynamical systems through restarts . This approach, analog to the celebrated Hamilton-Jacobi-Bellman equation, is successfully applied to simple settings and provides the basis to investigate realistic restarting strategies across disciplines.
 S. N., Majumdar, F. Mori, H. Schawe, and G. Schehr, Phys. Rev. E 103, 022135 (2021).
 M. Biroli, F. Mori, and S. N. Majumdar, preprint arXiv:2202.04906 (2022).
 B. De Bruyne and F. Mori, preprint arXiv:2112.11416 (2021).
Xhek Turkeshi (Collège de France)
Measurement-induced phase transitions in random circuits
I will discuss what happens to a quantum many-body system when its unitary evolution is interspersed with local measurements. The tension between unitary dynamics (generating entanglement) and measurements (localizing information) resolves in a dynamical phase transition between one phase where dominated by scrambling and another one in which frequent measurements constraint the state on a reduced manifold. In this talk, I will consider the minimal model for the transition, where the unitary dynamics is generated by random circuits. I will discuss how the measurement-induced phase transition is encoded in structural facets of the system wave-function, which is analyzed through the lens of participation entropy. Large-scale numerical simulations and the investigation of a variety of models identify a robust order parameter for the transition.