Présidents de session
Systemes integrables
- Eric Ragoucy (LAPTh)
Systemes integrables
- Eric Ragoucy (LAPTh)
Description
The notion of integrability is based on an essential property, namely the existence of an "adequate" number of conserved quantities in the system. This "adequate" number then allows for the full resolution of the model, i.e., to calculate exactly (without using approximations or perturbative techniques) all its physical quantities, such as energies, momenta, correlation functions, etc... Analytical and algebraic developments have grown in the 80s (starting with the study of spin chains) and there exists now a huge arsenal of mathematical tools to study such systems. Of course, not all systems are integrable, but, surprisingly enough, there are many integrable systems in physics, even if integrable techniques are not always used to solve them.
Integrable systems take place in many areas, in physics or in mathematics. In physics, they are involved in field theory and symmetries (especially in elementary particle physics, in string theories and in supersymmetric Yang-Mills theories), in statistical mechanics (for example in so-called ASEP models, for asymmetric exclusion principle), or condensed matter physics (e.g. in models used to describe nano-technology materials such as carbon nano-tubes). In mathematics, integrable systems are themselves the basis for the development of a particularly rich set of new mathematical structures (quantum groups, deformed algebras, Hopf and quasi-Hopf structures, etc...).
