The main aim of this talk is to introduce and review some of the recent developments in the theoretical and mathematical aspects of the non-equilibrium statistical mechanics of geophysical flows. This domains, at the intersection between statistical mechanics, turbulence and climate applications is a wonderful new playground for theoretical and mathematical physicists. Path integrals, instanton theory, semiclassical approximations, large deviation theory, and diffusion Monte-Carlo algorithms are at the core of our approach. Many natural and experimental turbulent flows display a bistable behavior: rare and abrupt dynamical transitions between two very different subregions of the phase space. The most prominent natural examples are probably the Earth magnetic field reversals (over geological timescales), the Kuroshio current bistability. Recent results show that a similar bistability occurs also in the turbulent dynamics of atmosphere jets, for instance on Jupiter's troposphere. Those abrupt transitions are extremely rare events that change drastically the nature of the flow and are thus of paramount importance. We will discuss those phenomena from a theoretical physics point of view, mainly in relation with large deviation theory.

In this talk, I discuss our recent work on the Higgs-Yukawa model, as relevant to BSM physics, using lattice simulations and the approach of the constraint effective potential. After an introduction to the lattice method for such calculations, without going into numerical details, I concentrate on the inclusion of a dimension-six operator as the prototype of new physics. In particular, I discuss the effect of such an operator on the Higgs boson mass. Exploratory result for finite-temperature phase transition will also be shown.

Correlation functions of local gauge-invariant operators are natural observables in any conformal quantum field theory. In N=4 SYM a particular role is played by the multipoint supercorrelators of the stress-tensor multiplet. Their chiral truncation in the light-cone limit coincides with the scattering superamplitudes. We propose a novel approach to calculating such correlators based on reformulation of the theory in Lorentz harmonic chiral superspace which introduces an infinite number of auxiliary higher-spin fields and pure gauges. This technique enables us to obtain the integrands of all such supercorrelators, including the non-chiral sector, at any loop order.

l est bien connu que divers solides amorphes ont de nombreuses propriétés universelles. L'une d'entre elles est la variation de la conductivité thermique en fonction de la température. Cependant, le mécanisme microscopique du transfert de chaleur dans le domaine de température supérieure à 20 K est encore mal compris. Simulations numériques récentes du silicium et de la silice amorphes montrent que les modes de vibration dans la gamme de fréquences correspondante (dits «diffusons») sont délocalisés. En même temps ils sont complètement différents des phonons acoustiques de basse fréquence.
Dans ce travail, nous présentons un modèle stable de matrice aléatoire d'un solide amorphe. Dans ce modèle, on peut faire varier le degré de désordre allant du cristal parfait jusqu'au milieu mou extrêmement désordonné sans rigidité macroscopique. Nous montrons que les solides amorphes réels sont proches du deuxième cas limite, et que les diffusons occupent la partie dominante du spectre de vibration. La fréquence de transition entre les phonons acoustiques et diffusons est déterminée par le critère Ioffe-Regel. Fait intéressant, cette fréquence de transition coïncide pratiquement avec la position du pic boson. Nous montrons également que la diffusivité et la densité d'états de vibration de diffusons sont pratiquement constantes en fonction de la fréquence. Par conséquent, la conductivité thermique est une fonction linéaire de la température dans le domaine allant à des températures relativement élevées, puis elle sature. Cette conclusion est en accord avec de nombreuses données expérimentales.
En outre, nous considérons un modèle numérique de matériaux de type de silicium amorphe et étudions le rôle du désordre pour les vibrations longitudinales et transverses. Nous montrons aussi que la théorie des matrices aléatoires peut être appliquée avec succès pour estimer la densité d'états vibrationnels des systèmes granulaires bloqués.

Nearly 20 years ago Zudov et al. experimentally discovered huge microwave-induced resistance oscillations (MIRO) in high-mobility two-dimensional electron gas at low temperatures and moderate magnetic fields. This spectacular phenomenon has attracted a lot of interest. The mainstream theories describe MIRO as a quantum phenomenon and deal with quantum transitions between Landau levels in the presence of different types of disorder. In contrast, we show that MIRO is a purely classical memory effect caused by re-collisions of electrons with scattering centers after a cyclotron period. We develop a novel Drude-like approach to magneto-transport in presence of a microwave field, taking account of memory effects, and find an excellent agreement between numerical simulations, analytical results, and experiment.

We study the metal-insulator transition in a narrow impurity band with small degree of disorder. The critical concentration is shown to be lower than predicted by the Mott-Anderson criterion. As a result, a band of delocalized states appears in the middle of the impurity band. However, the Fermi level lies below the band of delocalized states. Thus, at low temperatures the transport is due to activation from the Fermi level.  The theory is in agreement with experimental data for AlGaAs/GaAs quantum wells.
We also explain the breakdown behavior observed experimentally. The concept of the virtual Anderson transition allows to explain ferromagnetism observed in AlGaAs/GaAs structures, doped with Mn at very low concentrations.

I will describe experiments using soap films and soap bubbles to illustrate the interest of these common objects to some fluid mechanics problems. The flow in the very thin layer of these films is basically two dimensional and this property brings fundamental differences with fluid flows in three dimensions as well as experimental simplification. I will use three examples for this talk: the interaction between a flow and different structures in fast flowing soap films, the measurement of viscous drag in turbulent soap film channels, and thermal convection in soap bubbles. In all these cases, the two dimensional nature of the flow allows to capture some of the key features of the underlying dynamics such as a symmetry breaking mechanism leading to locomotion of passive objects in the first case, the role of the structure of the turbulence on the scaling of the viscous drag in the second case, and the appearance of large scale vortices in the last case.

Despite its chemical simplicity, boron trioxyde appears a puzzling system, as it does not crystalles under normal conditions of temperature and pressure. It was hypothesized, based on DFT calculation in the GGA approximation, that this 'crystallization anomaly' resulted from the existence of a 'hidden' low energy polymorphism (see Ref. 1).
In a previous work, we showed that including dispersion effects was critical for an accurate description of the volume and energetics of SiO2 polymorphs (see Ref. 2). SiO2 and B2O3 being the two textbook examples of network forming oxydes, it is to be expected that dispersion effects also play a crucial role in the ab initio description of B2O3's hidden polymorphism. We consequently use van der Waals corrected density functional theory and Quantum Monte Carlo to investigate B2O3 polymorphs. We show that some conclusions of Ref. 1 must be modified, and we use this methodology to predict the properties of the newly found polymorphs. It is demonstrated that most structures have interesting mechanical properties, including high porosity, strong anisotropy, and negative linear compressibility.

Ref. 1 : 'Hidden polymorphs drive vitrification in B2O3', Guillaume Ferlat, Ari Paavo Seitsonen, Michele Lazzeri & Francesco Mauri,Nature Materials 11, 925-929 (2012).

Ref. 2: 'Dispersion effects in SiO2 polymorphs: An ab initio study', Henri Hay, Guillaume Ferlat, Michele Casula, Ari Paavo Seitsonen, and Francesco Mauri, Phys. Rev. B 92, 144111 (2015)

The study of out-of-equilibrium thermodynamics has received a significant thrust thanks to the experimental advances in the control and manipulation of microscopic systems. Work, an ubiquitous concept in traditional thermodynamics, assumes in this context the role of a stochastic variable whose fluctuations can be ingeniously related to equilibrium properties, as is the case of the celebrated Jarzynski equality. In this talk, I will revise these concepts and discuss a feasible experimental scheme to directly measure work in cold atomic setups. I will show that the interaction between atoms and the light polarisation of a probe laser, as in atomic ensembles experiments, allows us to implement such POVM. In this way the work done on or extracted from the atoms after a given process is encoded in the light quadrature that can be measured with a standard homodyne detection. The protocol allows one to verify fluctuation theorems and study properties of the non-unitary dynamics of a given thermodynamic process [1]. A second scheme allows one to measure the work done on an atomic BEC in a double well potential when the atomic self-interaction is varied. I will discuss strategies based on optimal control techniques to reduce the irreversible work production.

References
G. De Chiara, A. J. Roncaglia, J. P. Paz, New J. Phys. 17, 035004 (2015)