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 [1] and the number of visited sites [2]. Then, I will introduce a novel framework that allows to optimally control a very general class of dynamical systems through restarts [3]. 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.

[1] S. N., Majumdar, F. Mori, H. Schawe, and G. Schehr, Phys. Rev. E 103, 022135 (2021).

[2] M. Biroli, F. Mori, and S. N. Majumdar, preprint arXiv:2202.04906 (2022).

[3] 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.