In a disordered system, because of the presence of impurities or of other forms of structural disorder, the interactions between the degrees of freedom are given by frozen random variables. At low temperature, certain disordered systems, such as spin glasses, display slow dynamics which is due to a complex energy landscape with many metastable states. Such slow dynamics prevent the system from reaching a Boltzmann thermal equilibrium during the time it is observed. It thus keeps a certain memory of its history: we say that it ages. During the last decade, numerous works have been devoted to non-equilibrium systems: the structure of excitations and chaos in spin glasses, the violation of the fluctuation-dissipation theorem, the concept of effective temperature, the study of exactly soluble kinetic models, the statistics of metastable states, the extrema and saddle points of random energy landscapes, etc.
Condensed matter physics displays remarkable quantum phenomena: superconductivity, the fractional Hall effect, Bose-Einstein condensation, the Kondo effect... Field theory can be used to study the behavior of real systems: vortex models for the description of superconducting properties of mesoscopic systems, as well as Laughlin quasi-particles carrying fractional electric charge; dimer lattice models for the description of incompressible quantum liquids with topological order and fractional excitations. Supersymmetric models can describe phase diagrams of certain strongly correlated electron systems in which both fermionic metallic phases and bosonic magnetic phases coexist (e.g. a Kondo impurity in a metal). Various out-of-equilibrium quantum systems are also studied, ranging from the formation of a Bose-Einstein condensate to the dynamics of quantum dots in which a small number of electrons are trapped by potential barriers.
Polymers are physical realizations of stochastic processes such as Brownian motion or self-avoiding random walks. Certain universal aspects of membranes (flexible films, biological membranes) are related to random geometries which are studied in string theory and quantum gravity. When the objects are charged (poly-electrolytes, charged membranes) or when they possess internal degrees of freedom, their physical and geometric properties are deeply modified: new phases appear. The physics of disordered systems governs the complex interactions between chemically different monomers in biological polymers. One can study this way the denaturation of DNA or the folding of proteins and of RNA. The classification of the possible forms of the latter can be made with the help of topological tools (the Euler characteristic or the genus). At a more macroscopic scale, the interactions of proteins and genes are modeled with the help of biological lattices, and the study of their connectivity properties yields a better understanding of cellular metabolism.
The study of hydrodynamic instabilities allows us to understand the mechanisms which can lead to turbulence. Thermal convection is a typical instability present in our environment. Alone, or coupled to other mechanisms, it creates motion in the atmosphere and in oceans. The modeling of the dynamo effect aims at understanding of the generation and the maintenance of the magnetic field inside the earth, the planets and stars. Shearing flow modes, the instabilities of which are modified by rotation or stratification, are studied in relation to laboratory experiments and as possible sources of turbulence in accretion disks and in astrophysics.