Louise DELZESCAUX & Pierre RIZKALLAH

- Louise DELZESCAUX : Nonperturbative renormalization group approach to flat polymerized membrane bilayers
Doctorante en 2ème année, sous la supervision de Dominique Mouhanna

Phase transition is a key concept in physics. It is a physical process of transition between two states of a system, induced by a parameter which can be the temperature, a magnetic field, etc. This phenomenon is present in different areas of physics such as condensed matter or particle physics. The Mermin-Wagner Theorem states that there is no symmetry breaking in continuous system with short-range interactions of dimension equal or less than 2. However, polymerized membranes are 2d systems that display a crumpling transition between a high-temperature, crumpled, phase and a low temperature, flat, phase. In this seminar, I will talk about the flat phase of polymerized membranes - which, for instance, is relevant for graphene - and present briefly the renormalization group, the technique we use to study the fluctuations and the behavior of this phase. I will also introduce polymerized membrane bilayers, which is the system I am working on with Dominique Mouhanna for my Phd.

- Pierre RIZKALLAH : Microscopic models and hydrodynamic description for single-file diffusion

The situation where an active particle (called a tracer) diffuses in a complex environment arises in many biological systems (molecular motors, bacteria, micro-swimmers, algae...), but also in soft matter experiments with active colloids. When particles are confined in a one dimensional geometry like pores or narrow channels, the situation is called single-file diffusion because particles cannot bypass each other.
This strong geometrical constraint leads to an anomalous scaling ∼ √t for the mean and variance of the displacement of a driven tracer particle. Many microscopic models have been considered to describe this situation. We focus first on the paradigmatic simple exclusion process with a symmetric tracer and its description in terms of fluctuating hydrodynamics. We explain how we can obtain an exact expression for the tracer’s cumulant generating function and its correlations with its environment [1]. Then, we show how the hydrodynamic description can be adapted to describe single-file diffusion with a biased tracer. [2]

[1] Exact closure and solution for spatial correlations in single-file diffusion. A. Grabsch, A. Poncet, P. Rizkallah, P. Illien, O. Bénichou
Science Advances 8, eabm5043 (2022)
[2] Driven tracer in the Symmetric Exclusion Process: linear response and beyond. A. Grabsch, P. Rizkallah, P. Illien, O. Bénichou
arXiv:2207.13079. (accepted in Phys. Rev. Lett.)