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## Systems far from equilibrium

Many-particles systems reach an equilibrium state after sufficiently large time. These equilibrium states have been studied for long and are relatively well understood by now. However, many situations encountered in nature are far from equilibrium, and the causes may be diverse. A system can be driven out of equilibrium when it is exposed to an external perturbation such as a voltage difference, a heat flow or a particle flux. Alternatively, the system may be initially placed in a state far from equilibrium, and relax so slowly towards its equilibrium state that it may be found in various different non-equilibrium states, which are interesting by themselves. From a theoretical point of view the usual techniques to study equilibrium systems cannot be applied to far from equilibrium situations and new concepts are required, such as stochastic methods based on Fokker-Planck, Langevin or master equations. The researchers at LPMMC investigate various aspects of this theme.

One research activity is dedicated to the study of critical phenomena occuring in systems far from equilibrium. For instance, a moving interface, formed by a fluid propagating in a porous medium, or by a (flameless) combustion front burning a paper, generically becomes rough as it grows. The profile of the interface then develops large fluctuations which lead to scale invariance. This phenomenon, called kinetic roughening, is a critical phenomenon driven by the dynamics, which occurs without fine-tuning any external parameter such as the temperature. The physics of kinetic roughening is captured by a stochastic equation of evolution (Langevin type), originally derived by Kardar, Parisi and Zhang. The theoretical characterization of the KPZ critical interface is a non-equilibrium, non-linear, and non-perturbative problem, which requires to devise suitable techniques.

Another line of research concerns Bose condensation of polaritons in semiconductor micro-cavities. Cavity polaritons are hybride excitations resulting from strong coupling between micro-cavity photons and excitons in the semiconductor. They have a finite lifetime so their population must necessarily be supplied by an external pump and the system is intrinsically out of equilibrium. At sufficiently large power, polaritons undergo a Bose-Einstein condensation (or ’polariton laser’ transition, characterized by a macroscopic population of a single quantum state. We explore theoretically the coherence properties of this condensate, taking into account the effects of disorder and the non-equilibrium nature of the system. Our activites are in close connection with ongoing experiments at the Neel Institute.

## Some recent results

We have studied kinetic roughening using a field-theoretic based method, called the Non-Perturbative Renormalization Group. This approach has enabled us to calculate the correlation and response functions associated with the KPZ growth in the strong-coupling regime corresponding to the rough phase. We have showed that these functions generically take scaling forms, that we have computed. They compare precisely to exact results available for one-dimensional interfaces and constitute the first analytical predictions for two and three dimensional interfaces.

Experiments at Néel Institute have realized Bose-Einstein condensates of polaritons in ZnO microcavities in a one-dimensional geometry. We have explored the origin of the decay of first-order coherence observed in the experiment. The modelization yields information on the disorder amplitude and interaction strength, and brings insight into the interplay of disorder and interactions in polariton gases.

## Selected publications

*Physical Review B*

**88**, 121407(R) (2013)