Reviews of topical problems

Discrete breathers in crystals

 a, b,  b,  c, b,  d
a Tomsk State University, prosp. Lenina 36, Tomsk, 634050, Russian Federation
b Institute for Metals Superplasticity Problems of RAS, Khalturina st. 39, Ufa, 450001, Russian Federation
c Institute of Metal Physics, Ural Division of the Russian Academy of Sciences, ul. S Kovalevskoi 18, Ekaterinburg, 620219, Russian Federation
d Instituto Pluridisciplinar, Universidad Complutense, Paseo Juan XXIII, 1, Madrid, 28040, Spain

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. Experimental studies of DBs encounter major technical difficulties, leaving atomistic computer simulations as the primary investigation tool. Despite the definitive evidence for the existence of DBs in crystals, their role in solid state physics still 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, how elastic lattice deformations influence the properties of DBs and the possibility of their existence is discussed, recent studies of the effect of nonlinear lattice perturbations on the crystal electron subsystem are presented, etc.

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Keywords: crystal lattice, nonlinear oscillations, discrete breather, crystal lattice defect
PACS: 05.45.−a, 05.45.Yv, 63.20.−e (all)
DOI: 10.3367/UFNe.2016.02.037729
Citation: Dmitriev S V, Korznikova E A, Baimova J A, Velarde M G "Discrete breathers in crystals" Phys. Usp. 59 446–461 (2016)
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Received: 27th, July 2015, revised: 30th, January 2016, 9th, February 2016

Оригинал: Дмитриев С В, Корзникова Е А, Баимова Ю А, Веларде М Г «Дискретные бризеры в кристаллах» УФН 186 471–488 (2016); DOI: 10.3367/UFNr.2016.02.037729

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