Crucial role of 'non-essential' multifield approximations in lattice dynamics and dynamic phase transitions
Résumé
Relevant scales of length and time in lattice dynamics depend on both, the structure of atomic interactions and the nature of the observed phenomenon. In this work we are interested in building a continuum description of mass-spring systems which is capable of capturing at least some microscopically fast and microscopically localized phenomena that cannot be handled correctly by the classical continuum theories relying on a single displacement field. Our approach is based on a non-essential multilattice description of a mass-spring system with nearest neighbor interactions and its multi-field long wavelength approximations. The outcome is a non-classical quasi-continuum elas-todynamics with non-trivial inertia whose complexity depends on the scale of frequencies intended to be captured. The advantage of the multi-field approach is that we can deal in the same framework with both quasi-continuum (atomically diffuse) and anti-continuum (atomically localized) phenomena. Possible extensions for the mass-spring models with nonlocal interactions will be discussed as well.