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Hamiltonian Lattice Dynamical Systems |
Hamiltonian
lattice dynamical systems form a special but important class of models in the
physical sciences. They arise naturally in the study of crystals in solid state
physics, as many-particle models for statistical mechanics, as spatial discretisations of partial differential equations, modeling
coupled oscillators in engineering and as idealizations of DNA molecules in the
biological sciences. An important example of such a Hamiltonian lattice
dynamical system is the Fermi- Pasta-Ulam chain,
which was introduced 50 years ago. Its - at the time – surprising non-ergodicity properties strongly influenced the development
of KAM theory, chaos and solitons. Our understanding
of integrability and stochasticity
in the Fermi-Pasta-Ulam chain is far from
satisfactory, but recent progress on the role of symmetry, periodic and
quasi-periodic behavior and integrable approximations
is bound to lead to a better understanding of the process of energy equipartition and transport among vibrational
excitations in lattice dynamical systems. In particular, the recent interest in
nanoparticles and nanodevices,
optical lattices and transport through molecules makes such an understanding
highly desirable. This workshop
aims at bringing together two groups of researchers: 1. Mathematicians that work on lattice
dynamical systems, in particular the Fermi-Pasta-Ulam
problem, and related topics such as KAM theory, bifurcation theory and variational methods. 2. Physicists and numerical experimentalists
with an interest in lattice dynamical systems and their applications. Among the main
topics to be addressed during this workshop are: 1. Integrability,
near-integrability and KAM theory for Hamiltonian
lattices. 2. Special solutions (solitary waves, rotating
waves, breathers, etc.) and their bifurcations in a Hamiltonian framework. 3. Energy transport and ergodicity
of Hamiltonian lattices. 4. Formal asymptotic methods and numerics. Confirmed Invited
Speakers are: Serge Aubry (Saclay) [Back] |