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Properties of large-amplitudes vibrations in dynamical systems with discrete symmetry. Geometrical aspects by Chechin, George; Ryabov, Denis is a scholarly article available to read on EtoBox.

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The research group from the Rostov State University has been developing the theory of bushes of nonlinear normal modes (NNMs) in Hamiltonian systems with discrete symmetry since the late 90s of the last century. Group-theoretical methods for studying large-amplitude atomic vibrations in molecular and crystal structures were developed. Each bush represents a certain collection of vibrational modes, which do not change in time despite the time evolution of these modes, and the energy of the initial excitation remains trapped in the bush. Any bush is characterized by its symmetry group, which is a subgroup of the system's symmetry group. The modes contained in the given bush are determined by symmetry-related methods and do not depend on the interatomic interactions in the considered system. The irreducible representations of the point and space groups are essentially used in the theory of the bushes of NNMs, and this theory can be considered as a generalization of the well-known Wigner classification of the small-amplitude vibrations in molecules and crystals for the case of large-amplitudes vibrations. Since using of the irreducible representations of the symmetry groups can be an o

Author

Chechin, George; Ryabov, Denis

Published

2020

Language

EN