Description du sujet de thèse

Statistical physics of nonequilibrium mixtures: tracer diffusion and complex interactions

Transport of soft matter at small scales is at the heart of many modern scientific challenges, such as the design of new nanomaterials or nanofluidic devices, or the understanding of intracellular self-organization. The hallmarks of these systems are their strong heterogeneity, and their nonequilibrium nature. From a theoretical perspective, the interplay between these two features makes the analytical description of such systems particularly difficult, and the available models are generally restricted to single species systems, with simple pair interactions between the constituents.

Recently, we focused on properties associated with tracer particles in model nonequilibrium suspensions (that include multi-temperature thermostats, or non-reciprocal interactions) that were introduced recently, and that have received a lot of attention in the scientific community. Analytical calculations, relying on linearized stochastic field theories, coupled with Brownian dynamics simulations, revealed how the nonequilibrium nature of the mixtures could lead to enhanced diffusion and to the formation of pairs of particles that self-propel.


The goal of the thesis is two-fold: (i) the student will first extend the analytical results, that were obtained within a perturbative approach, to confined geometries. the project will also open the way to more complex models, where long-ranged interactions (chemotactic or electrostatic) between the constituents will be incorporated. ; (ii) in parallel, the student will work on more fundamental aspects of the stochastic field theory that was employed so far. In particular, an objective will be to go beyond the linear and Gaussian approximation employed so far, and to incorporate the effect of hardcore repulsive interactions. The work will essentially be analytical: the candidate must have an taste for stochastic processes, statistical field theory and perturbative methods.

Required skills:
- fluent English
- excellent background in fundamental physics (master degree in theoretical physics)
- skills in written and oral communication

Contexte de travail

The thesis will be carried out within the MEM (Modelling and Multi-scale Experiments) team of the PHENIX laboratory.
The financial support for the thesis is provided by the ANR TRANONEQ project led by Pierre Illien. This support will enable the candidate to benefit from a workstation and to finance missions (schools, conferences, etc.).
The candidate will benefit from the laboratory's computing resources. High-performance computing equipment will enable him/her to carry out most of his/her work. If necessary, the shared resources of Sorbonne Université (MESU supercomputer) can be used.

Contraintes et risques

None.