Grégory Schehr (LPTMS Orsay)

Finite temperature free fermions and the Kardar-Parisi-Zhang equation at finite time


I will consider a system of N one-dimensional free fermions confined by a harmonic well. At zero temperature (T=0), this system is intimately connected to random matrices belonging to the Gaussian Unitary Ensemble. In particular, the density of fermions has, for large N, a finite support and it is given by the Wigner semi-circular law. Besides, close to the edges of the support, the quantum fluctuations are described by the so-called Airy-Kernel (which plays an important role in random matrix theory). What happens at finite temperature T ? I will show that at finite but low temperature, the fluctuations close to the edge, are described by a generalization of the Airy kernel, which depends continuously on temperature. Remarkably, exactly the same kernel arises in the exact solution of the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions at finite time. 
I will also discuss recent results for fermions in higher dimensions.

André Thiaville (LPS Orsay)

Topology in magnetism

After recalling what topology is, the seminal work by Ernst Feldtkeller [1] introducing topology in magnetism will be described. His arguments were generalized and systematized, first by Maurice Kléman and coworkers [2], into what is now known as the topological theory of defects, for all types of order parameter and samples’ dimensionality and topology [3]. The tools of this theory can be also used to define topologically stable continuous magnetic structures, also called topological solitons, prominent examples being the vortex and the skyrmion. The associated topological number will be recalled and its signification discussed through examples. The distinct role of chirality, compared to topology, will be stressed. We shall then describe the links of topology with magnetization dynamics. The electrical transport through magnetic textures with non-trivial topology will also be discussed. Finally, the energy cost of “breaking the topology” will be discussed, through the following questions: what is the energy of the singular Bloch point, how large is the energy barrier to reverse a vortex or to delete a magnetic skyrmion ?

[1] E. Feldtkeller, Mikromagnetisch stetige und unstetige Magnetisierungskonfigurationen, Z. angew. Phys. 19, 530-536 (1965). English translation IEEE Trans. Magn. 53, 0700308 (2017).

[2] G. Toulouse, M. Kléman, Principles of a classification of defects in ordered media, J. Physique Lett. 37, L149-151 (1976).

[3] N.D. Mermin, The topological theory of defects in ordered media, Rev. Mod. Phys. 51, 591-648 (1979); M. Kléman, Points, lines and walls (Wiley, New York, 1983).

André Thiaville (LPS Orsay)

Magnétisme et topologie [titre provisoire]

Christina Kurzthaler (Univ. Innsbruck)

Spatiotemporal dynamics of active agents

Various challenges are faced when microorganisms or artificially synthesized self-propelled particles move autonomously in aqueous media at low Reynolds number. These active agents are intrinsically out of equilibrium and exhibit peculiar dynamical behavior due to the complex interplay of stochastic fluctuations and directed swimming motion. In particular, these particles display fascinating physics ranging from the run-and-tumble motion of bacteria to the noisy circular trajectories of biological or artificial microswimmers due to hydrodynamic couplings in the vicinity of interfaces or chiral body shapes. Here, we provide a theoretical analysis of the spatiotemporal dynamics of different types of active particles in terms of the experimentally accessible intermediate scattering function. Our analytical predictions characterize the spatiotemporal dynamics of catalytic Janus particles, a paradigmatic class of synthetic active agents, from the smallest length scales where translational Brownian motion dominates, up to the largest ones, which probe the randomization of the swimming direction due to rotational diffusion. We also show that our theoretical framework finds application in different areas such as polymer physics.