The reason for existence of discrete breathers in 2D and 3D Morse crystals

Abstract

It is known that crystals can support discrete breathers (DBs) -periodic in time and spatially localized vibrational modes. DB does not radiate energy, as its frequency does not lie within the spectrum of small-amplitude traveling waves (phonons). DB frequency can leave the spectrum of low-amplitude oscillations due to the nonlinearity of the interatomic potentials, as it is well known that the frequency of a nonlinear oscillator depends on the amplitude. Theoretically, it was shown that DB cannot exist in a one-dimensional chain of identical point masses interacting with each other through the Toda, Born-Mayer, Lennard-Jones or Morse potential. The reason of non-existence of DB is the softness of the considered potentials, which does not allow to form a spatially localized mode with frequency above the phonon spectrum. On the basis of this rigorous result, it was concluded that because of the softness of the interatomic interactions in crystals with a simple structure (e.g., in pure metals) existence of DB is very unlikely. Attention should be paid to crystals with a gap in phonon spectrum. In such crystals localized vibrational modes may have frequencies decreasing with amplitude and entering the gap of the phonon spectrum. The first successful attempt to excite a gap DB in alkali halide NaI crystal dates back to 1997, for this purpose, the method of molecular dynamics was used. However, in 2011 DBs with frequencies higher than the phonon spectrum were discovered in pure metals, which poses the question about the conditions of the existence of DBs in crystals with realistic interatomic potentials. In this paper we show that the dimension of the crystal is important, and the Morse crystals of dimension higher than one can support DBs with frequencies above the phonon spectrum. Известно, что кристаллы могут поддерживать существование дискретных бризеров (ДБ) -периодических во вре-мени пространственно-локализованных колебательных мод. ДБ не излучают энергию, так как их частота не лежит в спектре малоамплитудных бегущих волн (фононов). Выход частоты ДБ из спектра малоамплитудных колебаний происходит за счет нелинейности во взаимодействии атомов, ведь известно, что частота нелинейных осцилляторов зависит от амплитуды колебаний. Теоретически было показано, что ДБ не могут существовать в одномерной це-почке одинаковых точечных масс, взаимодействующих друг с другом посредством потенциалов Тоды, Борн-Маера,

Stationary Modes and Localized Metastable States in a Triangular Lattice of Active Particles

“…In this paper we consider the dynamics of one of the examples of active matter -a lattice of active particles with potential interaction. There exists a large body of literature on different localized excitations in conservative lattices (see, e.g., [25][26][27][28][29][30][31][32][33][34][35]). In those works it has been found that solitons and mobile discrete breathers of different configurations can propagate in two-dimensional lattices.…”