|During the last years, significant efforts have been devoted to the study of dynamical properties of (classical and quantum) open systems. In particular, through the study of noisy or forced dissipative systems, or Hamiltonian systems with a large number of degrees of freedom, our understanding of the mathematical structure of nonequilibrium statistical mechanics has greatly improved. The aim of this meeting is to present the latest results and discuss the possible future directions of research in this area. The following topics will be discussed:
- Axiomatic approaches: Under appropriate hypotheses on the ergodic properties of the underlying dynamical system (chaotic hypothesis, asymptotic abelianness, etc), it is possible to prove various predictions of nonequilibrium thermodynamics (linear response, Kubo formula, Onsager's relations, etc.). This approach also lead to unexpected results, like the Gallavotti-Cohen fluctuation theorem.
- Specific models: Modern techniques (quantum field theory, algebraic quantum dynamical systems, spectral analysis, renormalization group, etc.) have been successfully applied to the study of various models (spin-boson, spin-fermion, Pauli-Fierz, Lorentz-gas, etc.). Elementary physical properties like return to equilibrium or existence and structural properties of nonequilibrium steady states, have been obtained in this way. More difficult questions, like the emergence of the Fourier law, are currently under investigation.
- Markovian Dynamics: It gives a natural mathematical framework to study the dynamics of various nonequilibrium processes: Hamiltonian systems coupled to reservoirs, exclusion processes on the lattice, noisy extended systems.
The program includes short courses to be given by H. Araki (Kyoto), B. Derrida (École Normale), J. Froehlich (ETH), J.-P. Eckmann (Geneva) (*). The workshop is being held in conjunction with the preceeding one (Workshop on Spectral Theory of Schrödinger Operators), and many participants will be attending both.
H. Araki (Kyoto), J. Bellissard (Atlanta), P. Blanchard (Bielefeld),
L. Bruneau (Warsaw), T. Chen (Courant), S. De Bievre (Lille),
J. Derezinski (Warsaw), B. Derrida (Paris), J.-P. Eckmann (Geneva),
G. Elliott (Toronto), A.C. D van Enter (Groningen), L. Erdös (Münich), B. Helffer (Paris), G-M. Graf (ETH), M. Griesemer (Alabama), C. Jäkel (Münich), G. Jona - Lasinio (Rome), A. Knauf (Erlangen), R. Livi (Florence), M. Merkli (Montreal), T. Matsui (Kyushu), B. Nachtergaele (Davies), K. Netocny (Groningen), F. Nier (Rennes), Y. Ogata (Tokyo), Y. Pautrat (Montreal), L. Rey-Bellet (Amherst), R. Seiringer (Princeton), D. Spehner (Essen), S. Starr (Montreal), L. Thomas (Virginia), A. Verbeure (Leuven), H.T. Yau (Stanford), L.-S. Young (Courant), V. Zagrebnov (Marseille).