## A semiclassical perspective to study quantum interacting particles

### Rémy Dubertrand (Université de Liège, Belgique)

Quantum chaos have had a great success to describe various types of one-particle quantum systems in the semiclassical regime (e.g. large quantum numbers). I will describe how these techniques can be used to describe quantum systems of interacting particles. For example I contributed to look at Bose Hubbard model and justify why the spectral statistics agrees with RMT for a certain regime of the ratio between onsite interaction and hopping energies. I will discuss in a more general framework how fruitful a semiclassical approach can be to study such systems of interacting particles.

## Effect of crowding and hydrodynamic interactions on the dynamics of fluctuating systems

### Pierre Illien (EC2M laboratory, ESPCI Paris)

Describing the interactions of a fluctuating object with its environment is an ubiquitous problem of statistical physics. I will first focus on the dynamics of a driven particle in a host medium which hinders its motion through crowding interactions. Going beyond the usual effective descriptions of the environment of the active tracer, we propose a lattice model which takes explicitly into account the correlations between the dynamics of the tracer and the response of the bath and for which we determine analytically exact and approximate solutions, that reveal intrinsically nonlinear and nonequilibrium properties.

I will then present recent results that reveal how the diffusivity of enzymes can be enhanced when they are catalytically active. In order to identify the physical mechanisms at stake in this phenomenon, we perform measurements on the endothermic and relatively slow enzyme aldolase. We propose a new physical paradigm, which reveals that the diffusion coefficient of a model enzyme hydrodynamically coupled to its environment increases significantly when undergoing changes in conformational fluctuations in a substrate concentration dependent manner, and is independent of the overall turnover rate of the underlying enzymatic reaction.