Attention : désormais les séminaires auront lieu tous les lundis à 11h00 en salle 523 du LPTMC - Tour 12-13
I will first start with a general introduction on theoretical ecology, stressing the
reasons that make connections with statistical physics interesting and timely.
I will then focus on Lotka-Volterra equations, which provide a general model to study large assemblies of strongly
interacting degrees of freedom in many different fields: biology, economy and in particular ecology.
I will present our analysis of Lotka-Volterra equations as model of ecosystems formed by a
large number of species and show the different phases that emerge. Two of them are particularly
interesting: when interactions are symmetric we find a regime characterised by an exponential
number of multiple equilibria, all poised at the edge of stability for a large number of species.
For non symmetric interactions, this phase is replaced by a chaotic one.
I will then conclude discussing relationships with experiments and general consequences of our works.
Tin Sulejmanpasic (LPT-ENS)
Fractionalization between the vacua: from QCD to quantum magnetism
Quantum Chromodynamics (QCD) -- the theory of strong nuclear forces -- has baffled the physics community and remains one of the poorly understood parts of the standard model. Its quintessential property: the confinement of quarks into protons, neutrons and mesons, while verified both experimentally and numerically, remains an elusive theoretical problem. The various cousins of QCD are however possible to understand to varying degrees and precision. In some of these theories the vacuum state is degenerate, and hence allows for domain walls -- a surface excitation which interpolates between two vacua of the theory. These domain walls have a remarkable property that quarks become liberated on them, and the domain wall excitation spectrum is very different from that of the bulk. Such QCD cousins are, unfortunately, not the physical theory, and they do not occur in nature. QCD however has another unlikely cousin: the Valence Bond Solid (VBS) state of the quantum anti-ferromagnet, where spin 1/2 excitations (or spinons) are bound into spin 1 excitations by a mechanism very similar to confinement of quarks. Perhaps surprisingly the low energy theory describing the behavior of the VBS phase is virtually identical to its QCD cousins under certain conditions. Further the VBS phase may have multiple vacua, and thus support domain walls, which in turn support liberated spinon excitations absent in the bulk. This has been verified numerically in the so-called J-Q model. These domain wall modes can in fact be seen as edge modes akin to those of the symmetry protected topological state. A multidisciplinary effort is slowly emerging to understand such phenomena, from the theoretical aspects of fundamental and condensed matter physics, to the numerical efforts in trying to understand QCD and quantum magnets.
Xia-qing Shi (Soochow university & SPEC, CEA Saclay)
Recent results on dense bacterial suspensions
This talk will show that bacterial suspensions, beyond their intrinsic, dominating importance in biology, are also excellent systems to explore and test theoretical results on active matter, I will present recent experimental results on dense bacterial suspensions obtained in the groups of Masaki Sano (University of Tokyo), Yilin Wu (Chinese University of Hong Kong), and Hepeng Zhang (Shanghai Jiaotong University). I will put them in context, situating them within our current knowledge of active matter, stressing differences and similarities. Particular attention will be paid to the modeling efforts already deployed or to be developed in order to understand the fascinating large-scale phenomena observed by these 3 groups.
Raphaël Chétrite (Laboratoire J. Dieudonné, Nice)
On Gibbs-Shannon Entropy
This talk will focus on the question of the physical contents of the Gibbs-Shannon entropy outside equilibrium.
Article : Gavrilov-Chetrite-Bechhoeffer : Direct measurement of weakly nonequilibrium system entropy is consistent with Gibbs-Shannon form. PNAS 2017.
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.