Anna RITZ ZWILLING & Jérémie KLINGER & Brieuc BENVEGNEN

- Anna RITZ ZWILLING : Partition function for string-net models
Doctorante en 1ère année, sous la supervision de Jean-Noël Fuchs et Julien Vidal

The discovery of the fractional quantum Hall effect brought into light a new realm of phases of matter, called topologically-ordered phases. In two dimensions, these phases are characterized by exotic emergent excitations, known as anyons, with fractional quantum numbers and anyonic exchange statistics (i.e. neither bosonic nor fermionic). Another fundamental property of topologically-ordered phases is that the ground-state degeneracy depends on the surface topology (i.e. whether the system resides on a sphere, a torus, a pretzel...). The robustness of this degeneracy against local perturbations makes these systems promising candidates for topological quantum computation. Motivated by the latter, recent work has been dedicated to studying the fate of topological order at finite temperature.

In this talk, I will introduce a prominent exactly solvable toy-model for topologically-ordered phases, called string-net model, and present the calculation of its partition function.


- Jérémie KLINGER : Splitting Probabilities of Jump Processes
Doctorant en 3ème année, sous la supervision d'Olivier Bénichou

We derive a universal asymptotic form of the splitting probability of symmetric jump processes which quantifies the probability that the process crosses x before 0 starting from a given position 0 <= x0 <= x. Due to the discrete nature of the process, we show that this probability is non vanishing for the initial condition x0 = 0 and proves to be particularly relevant in applications to light scattering in heterogeneous media in realistic 3D slab geometries.


- Brieuc BENVEGNEN : Flocking in one dimension
Doctorant en 3ème année, sous la supervision d'Alexandre Solon

We study flocking in 1d using the active Ising model, a stochastic lattice gas in which particles self-propel in the direction controlled by the Ising spin they carry. Contrary to the passive Ising model, we observe an ordered phase where particles aggregate and move collectively. Symmetry is not broken though because the aggregate reverses stochastically its direction of motion due to the prominent effect of fluctuations. I will rationalize this behavior by explaining the dynamics of the aggregates and their reversals. At lower temperature, we observe static asters which are amenable to an analytic treatment.