Mathematical Physics
Coordinator : Christoph Kopper
- Permanent staff :
Jean-René Chazottes
Razvan Gurau
Philippe Mounaix
- PhD students:
- Post-Doc:
- Senior Researcher (emeritus) :
Amitabha Chakrabarti
Pierre Collet (Emérite)
Jacques Magnen (Emérite)
Research activities
Statistical Physics, Field Theory
Our work in field theory is largely based on the concepts of the renormalization group and the functional integral, either in constructive or in perturbative approach.
Recent progress concerns fractional stochastic calculus with the aid of the functional integral, the convergence of Wilson's operator product expansion obtained with the flow equations of the renormalization group, and the 1/N expansion of random tensor models which generalize those for random matrix ones.
In statistical physics recent results are: i) examples of nonconvergence for lattice Gibbs measures when temperature tends to zero, in any dimension; ii) exponential lower bounds on the speed of memory loss for generic Markov chains; iii) convergence towards a pointlike Poisson process for the times of entrance into small spheres for nonuniformly hyperbolic dynamical systems.
There has also been progress concerning discrete dynamical systems and cellular automata, and their integrability detectors. The analysis of the ultra-discrete sine-Gordon equation in d=2 has led to interesting unexpected results. We have also obtained rigorous results which link the large norm concentrations of a Gaussian random field to the Bose-Einstein-condensation, and on the approach to equilibrium for the stochastic nonlinear Schrödinger equation.
Further results concern the geometry of conjugate surfaces and engrenages.