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Dispersive and long‐time behavior of oscillations in lattices
Author(s) -
Path Carsten,
Mielke Alexander
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610232
Subject(s) - gravitational singularity , nearest neighbour , lattice (music) , statistical physics , k nearest neighbors algorithm , physics , harmonic , classical mechanics , quantum mechanics , computer science , artificial intelligence , acoustics
We study the long‐time dynamics of oscillations in lattices of infinitely many particles interacting via harmonic springs and adumbrate how decay rates for the displacements are proved analytically applying methods for oscillatory integrals. After recapitulating the results of an infinite chain with nearest‐neighbour interaction, we highlight the differences to the case of next‐nearest‐neighbour interaction. Finally we give an outlook on the two dimensional lattice with nearest‐neighbour interaction where more complicated singularities occur. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)