Discrete breathers with hard and soft type of nonlinearity in 1D Morse lattices with long-range interactions

Abstract

1Мирнинский политехнический институт (филиал) Северо-Восточного федерального университета, ул. Тихонова 5/1, 678175, Мирный, Россия 2 Институт проблем сверхпластичности металлов РАН, ул. Степана Халтурина 39, 450001, Уфа, Россия † sash-alex@yandex.ru, ‡ elena.a.korznikova@gmail.com В последнее время в области изучения дискретных бризеров наблюдается переход от теоретических исследований, связанных с доказательством их существования в упрощенных нелинейных системах, к поиску долгоживущих бри-зеров в реальных объектах, например, в кристаллических решетках. Изучение дискретных бризеров в различных физических системах требует учета различных факторов. Атомы в кристалле обычно взаимодействуют не только с ближайшими соседями, ввиду чего важным представляется учет дальнодействующих межатомных взаимодей-ствий. При наличии последних, не представляется возможным использовать потенциалы в виде разложения в ряд Тейлора до третьей или четвертой степени, как это делалось в подавляющем большинстве теоретических работ. В данной работе обсуждаются различные виды дискретных бризеров (точнее квазибризеров), которые могут быть возбуждены в одномерных моно-и биатомных решетках с дальнодействующим морзевским взаимодействием и си-нусоидальным локальным потенциалом. Данная модель описывает на качественном уровне дискретные бризеры в чистых металлах и упорядоченных сплавах. Recently the focus of studies on discrete breathers has arguably shifted from the mathematical proof of their existence in simplified nonlinear lattices towards the search for the long-lived quasi-breathers in real systems, e.g., in crystal lattices. In each particular field, different factors should be taken into account. Atoms in crystals typically interact not only with the nearest neighbors and thus, the effect of long-range interatomic forces is an important issue. When the long-range forces are involved, the tails of the interatomic potentials contribute essentially to the dynamics of the system and in these circumstances one cannot use truncated Taylor expansions of the potentials such as cubic or quartic. In this work we discuss various discrete breathers (more precisely, quasi-breathers) that can be excited in 1D monatomic and diatomic Morse lattices with long-range interactions and sinusoidal on-site potential. This model describes at a qualitative level discrete breathers in pure metals and ordered alloys.

Highly symmetric discrete breather in a two-dimensional Morse crystal

“…We considered the value α = 5, for which the equilibrium interatomic distance is a = 0.98813 at the potential cutoff radius of 5.5a. We note that the Morse potential was often used for the simulation of different properties of discrete breathers in crystals [23][24][25][26][27][28][29][40][41][42][43][44][45][46].…”

“…The authors of [38] could excite only the discrete breathers with the soft type of nonlinearity, considering a diatomic chain with a gap in the phonon spectrum. It was shown later that discrete breathers with the hard type of nonlinearity can exist in two-and threedimensional crystals with Morse interaction [39][40][41][42][43][44][45][46]. The reason is that the effect of the increase in the average interatomic distances in the core of the discrete breathers can be suppressed to some extent in crystals of dimension higher than unity and, thus, the hard core of the interatomic potential makes a larger contribution to the dynamics of the system than the soft tail.…”

Effect of the Morse Potential Stiffness on the Properties of Discrete Breathers in 2D close Packed Crystal

“…However, in [6] a possibility of existence of DB with hard type of nonlinearity and with frequencies above the phonon spectrum was demonstrated by means of molecular dynamics modeling for Ni and Nb. Later the possibility of the existence DB above the phonon spectrum of the crystal was confirmed in our works [7][8][9][10][11][12] for the case of two-dimensional (2D) monoatomic crystal with Morse interaction potential. The aim of this work is to investigate the effect of the rigidity of the Morse potential on the properties of DB in 2D monoatomic crystal model.…”

Effect of the interatomic potential stiffness on the properties of gap discrete breathers in 2D biatomic Morse crystal

“…By now, a large volume of works has been performed to analyze properties of DB in various crystalline materials, particularly, the results of the molecular dynamics studies have been reported in . Several works have been devoted to the study of DB in model crystals with Morse interatomic potentials [4][5][6][7], while other works to the study of DB in graphene and related materials [8][9][10]. In the work [8], for the first time, DB in a crystalline body has been studied with the help of DFT theory, using graphane as an example.…”