Discrete breathers in crystals: achievements and open problems

С. Дмитриев1,2
1Институт проблем сверхпластичности металлов РАН, Уфа
2Национальный исследовательский Томский государственный университет, Томск
Аннотация
It has long been known that periodic discrete systems containing defects, in addition to traveling waves, allow for the existence of vibrational modes localized on defects. It turned out that if a periodic discrete system is nonlinear, it can support exact solutions in the form of spatially localized vibrational modes even in the absence of defects. Since all the nodes of the system are identical, only a special choice of initial conditions can distinguish the group of nodes, on which such localized mode, called discrete breather (DB),will be excited. Frequency of DB must lie outside the spectrum of small-amplitude traveling waves. Do not resonating with traveling waves and do not losing energy to their excitation, theoretically DB can maintain its vibrational energy forever, in the absence of thermal vibrations and other perturbations. Crystals are nonlinear discrete systems and discovery of DB in them was only a matter of time. Experimental studies of DB run into considerable technical difficulties, and the main tool of their study is by far the atomistic computer simulations. Having gained confidence in the existence of DB in crystals, we still poorly understand their role in solid state physics. This review covers issues specific to the physics of real crystals, which were not considered in the classical works on DB.
Принята: 30 марта 2016
Просмотры: 108   Загрузки: 38
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Цитирования
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Захаров П.В., Старостенков М.Д., Ерёмин А.М., Фундаментальные проблемы современного материаловедения 13(2), 223-229 (2016).