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Hamiltonian dynamics of dense chains and lattices: or how to correct the continuum. (English) Zbl 1076.70505

Summary: We discuss the problems involved in deriving correct quasi-continuum approximations of Hamiltonians describing the motion of dense lattices directly from the underlying discrete Hamiltonian. This assures that the resulting equations of motion have a Hamiltonian structure and are free from ultra-violet instabilities.

MSC:

70H05 Hamilton’s equations
82B21 Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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