Survival condition for low-frequency quasi-one-dimensional breathers in a two-dimensional strongly anisotropic crystal (original) (raw)
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Journal of Physics a Mathematical and General, 2002
We investigate the resonance mechanisms for discrete breathers in finite-size Klein-Gordon lattices, when some harmonic of the breather frequency enters the linear phonon band. For soft on-site potentials, the second-harmonic resonances typically result in the appearance of solutions with non-zero tails, phonobreathers. However, these tails may be very weak, and for small systems where the phonon frequencies are sparsely distributed, we identify 'phantom breathers' as being practically localized solutions, existing with frequencies in-between the phonon frequencies. For particular parameter values the tails completely vanish, and the phantom breathers decay exponentially over the whole system. We also describe briefly a first-harmonic resonance with a constant-amplitude wave and the generation of phonobreathers for hard potentials.
Discrete breathers in anharmonic models with acoustic phonons
Annales De L Institut Henri Poincare-physique Theorique, 1998
Nous demontrons l'existence de « breathers » pour une large classe de modeles constitues d'un reseau de molecules anharmoniques couplees par des phonons acoustiques harmoniques. En plus de l'hypothese usuelle selon laquelle la frequence des « breathers » ainsi que ses harmoniques ne se situent pas les bandes de phonons, nous imposons l'hypothese essentielle a notre resultat, que la vitesse du son ne s'annule pas. Nous sommes conduit a distinguer les « breathers » piezoactifs generant une contrainte dans le cristal s'annulant a l'infini comme le champ electrique d'une charge Coulombienne, de ceux qui ne le sont pas et engendrant une contrainte analogue au champ electrique d'un dipole. Une consequence est que la preuve d'existence s'etend a des « multi-breathers » ne comportant qu'un nombre fini de « breathers » piezoactifs mais un nombre infini et des configurations arbitraires de « breathers » non piezoactifs. Dans ces modeles, l'a...
Breather$ndash$phonon resonances in finite-size lattices: lquotlquotlquotphantom breathers$rquot$?
Journal of Physics A: Mathematical and General, 2002
We investigate the resonance mechanisms for discrete breathers in finite-size Klein-Gordon lattices, when some harmonic of the breather frequency enters the linear phonon band. For soft on-site potentials, the second-harmonic resonances typically result in the appearance of solutions with non-zero tails, phonobreathers. However, these tails may be very weak, and for small systems where the phonon frequencies are sparsely distributed, we identify 'phantom breathers' as being practically localized solutions, existing with frequencies in-between the phonon frequencies. For particular parameter values the tails completely vanish, and the phantom breathers decay exponentially over the whole system. We also describe briefly a first-harmonic resonance with a constant-amplitude wave and the generation of phonobreathers for hard potentials.
Discrete nonlinear Schr�dinger breathers in a phonon bath
Eur Phys J B, 2000
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.
Nucleation of Breathers via Stochastic Resonance in Nonlinear Lattices
Physical Review Letters, 2009
By applying a staggered driving force in a prototypical discrete model with a quartic nonlinearity, we demonstrate the spontaneous formation and destruction of discrete breathers with a selected frequency due to thermal fluctuations. The phenomenon exhibits the striking features of stochastic resonance (SR): a nonmonotonic behavior as noise is increased and breather generation under subthreshold conditions. The corresponding peak is associated with a matching between the external driving frequency and the breather frequency at the average energy given by ambient temperature. PACS numbers: 63.20.Pw, 05.45.Yv, 05.45.Xt, Intrinsic localized modes, often referred to as discrete breathers, have been the focus of a number of theoretical studies (for a recent review see e.g. [1]). One of the main reasons for the large interest in these modes is the fact that they provide a natural setup for energy localization, a paradigm of interest to many areas of physics as well as chemistry and biology. Such discrete breathers have been rigorously proven to exist as time-periodic localized excitations in nonlinear Hamiltonian lattices . Ever since, they have been experimentally observed in a wide variety of different media, ranging from optical waveguides and photorefractive crystals to micromechanical cantilever arrays and Josephson junctions, as well as in Bose-Einstein condensates and layered antiferromagnets, among many others .
Discrete breathers above phonon spectrum
Letters on Materials, 2016
It is shown that in some metals (Ni, Nb, Fe, Cu) may exist discrete breathers with frequencies above the top of the phonon spectrum. These excitations are mobile: they may propagate along the crystallographic directions transferring energy of > 1 eV over large distances. The discrete breathers with the frequencies above the top of the phonon bands may also exist in covalent crystals (diamond, Si and Ge). It is also found that in monatomic chains and planes (e.g. in graphene), the transverse discrete breathers may be excited above the spectrum of corresponding phonons. Although these vibrations are in resonance with longitudinal (chain) or in-plane (graphene) phonons the lifetime of them may be very long.
Discrete nonlinear Schrödinger breathers in a phonon bath
The European Physical Journal B, 2000
We study the dynamics of the discrete nonlinear Schrödinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this non-Gibbsian state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather.
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
We investigate the long-time evolution of weakly perturbed single-site breathers (localized stationary states) in the discrete nonlinear Schrodinger equation. The perturbations we consider correspond to time-periodic solutions of the linearized equations around the breather, and can be either (i) spatially localized or (ii) spatially extended. For case (i), which corresponds to the excitation of an internal mode of the breather, we find that the nonlinear interaction between the breather and its internal mode always leads to a slow growth of the breather amplitude and frequency. In case (ii), corresponding to interaction between the breather and a standing-wave phonon, the breather will grow provided that the wave vector of the phonon is such that the generation of radiating higher harmonics at the breather is possible. In other cases, breather decay is observed. This condition yields a limit value for the breather frequency above which no further growth is possible. We also discuss...
Kink-breather solution in the weakly discrete Frenkel-Kontorova model
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 2000
The discrete Frenkel-Kontorova model, having the sine-Gordon equation as the continuous analog, was investigated numerically at a small degree of discreteness. Interaction between a kink and a breather in a discrete system was compared with the exact three-soliton solution to the continuous sine-Gordon equation. Nontrivial effects of discreteness were found numerically. One is that a kink and a breather in the discrete system are mutually attractive quasiparticles, so they can be regarded as a three-soliton oscillatory system. The other is the energy exchange between a kink and a breather when their collision takes place in a vicinity of a separatrix solution to the continuous sine-Gordon equation. We have estimated numerically the kink-breather binding energy EB and the maximum possible exchange energy EE for different breather frequencies omega. The results suggest that there is a threshold breather frequency for the "spontaneous" breaking up of the three-soliton oscilla...
Journal of Statistical Physics, 2006
For low density gases the validity of the Boltzmann transport equation is well established. The central object is the one-particle distribution function, f , which in the Boltzmann-Grad limit satisfies the Boltzmann equation. Grad and, much refined, Cercignani argue for the existence of this limit on the basis of the BBGKY hierarchy for hard spheres. At least for a short kinetic time span, the argument can be made mathematically precise following the seminal work of Lanford. In this article a corresponding program is undertaken for weakly nonlinear, both discrete and continuum, wave equations. Our working example is the harmonic lattice with a weakly nonquadratic on-site potential. We argue that the role of the Boltzmann f -function is taken over by the Wigner function, which is a very convenient device to filter the slow degrees of freedom. The Wigner function, so to speak, labels locally the covariances of dynamically almost stationary measures. One route to the phonon Boltzmann equation is a Gaussian decoupling, which is based on the fact that the purely harmonic dynamics has very good mixing properties. As a further approach the expansion in terms of Feynman diagrams is outlined. Both methods are extended to the quantized version of the weakly nonlinear wave equation.