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UFN, 2016, Volume 186, Number 5, Pages 471–488 (Mi ufn5376)  

This article is cited in 62 scientific papers (total in 62 papers)

REVIEWS OF TOPICAL PROBLEMS

Discrete breathers in crystals

S. V. Dmitrievab, E. A. Korznikovaa, Yu. A. Baimovaca, M. G. Velarded

a Institute for Metals Superplasticity Problems, Russian Academy of Sciences, Ufa
b Research Laboratory for Mechanics of New Nanomaterial, Peter the Great Saint-Petersburg Polytechnic University
c Mikheev Institute of Metal Physics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
d Instituto Pluridisciplinar, Universidad Complutense, Madrid

Abstract: It is well known that periodic discrete defect-containing systems, in addition to traveling waves, support vibrational defect-localized modes. It turned out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Since the nodes of the system are all on equal footing, it is only through the special choice of initial conditions that a group of nodes can be found on which such a mode, called a discrete breather (DB), will be excited. The DB frequency must be outside the frequency range of the small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically conserve its vibrational energy forever provided no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery in them of DBs was only a matter of time. It is well known that periodic discrete defect-containing systems support both traveling waves and vibrational defect-localized modes. It turns out that if a periodic discrete system is nonlinear, it can support spatially localized vibrational modes as exact solutions even in the absence of defects. Because the nodes of the system are all on equal footing, only a special choice of the initial conditions allows selecting a group of nodes on which such a mode, called a discrete breather (DB), can be excited. The DB frequency must be outside the frequency range of small-amplitude traveling waves. Not resonating with and expending no energy on the excitation of traveling waves, a DB can theoretically preserve its vibrational energy forever if no thermal vibrations or other perturbations are present. Crystals are nonlinear discrete systems, and the discovery of DBs in them was only a matter of time. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite definitive evidence for the existence of DBs in crystals, their role in solid-state physics remains unclear. This review addresses some of the problems that are specific to real crystal physics and which went undiscussed in the classical literature on DBs. In particular, the interaction of a moving DB with lattice defects is examined, the effect of elastic lattice deformations on the properties of DBs and the possibility of their existence are discussed, and recent studies of the effect of nonlinear lattice perturbations on the crystal electron subsystem are presented.

Funding Agency Grant Number
Russian Science Foundation 14-13-00982
14-12-10175
Ministry of Education and Science of the Russian Federation MK-5283.2015.2
The work was supported by the Russian Science Foundation (grant No. 14-2-10175), grant MK-5283.2015.2 of the President of the Russian Federation for Young Scientists, and grant no. 14-13-00982 of the Russian Science Foundation.


DOI: https://doi.org/10.3367/UFNr.2016.02.037729

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English version:
Physics–Uspekhi, 2016, 59:5, 446–461

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PACS: 05.45.-a, 05.45.Yv, 63.20.-e
Received: July 27, 2015
Revised: January 30, 2016
Accepted: February 9, 2016

Citation: S. V. Dmitriev, E. A. Korznikova, Yu. A. Baimova, M. G. Velarde, “Discrete breathers in crystals”, UFN, 186:5 (2016), 471–488; Phys. Usp., 59:5 (2016), 446–461

Citation in format AMSBIB
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