Localized nonlinear, soliton-like waves in two-dimensional anharmonic lattices (original) (raw)
Related papers
Nonlinear soliton-like excitations in two-dimensional lattices and charge transport
The European Physical Journal Special Topics, 2013
We study soliton-like excitations and their time and space evolution in several two-dimensional anharmonic lattices with Morse interactions: square lattices including ones with externally fixed square lattice frame (cuprate model), and triangular lattices. We analyze the dispersion equations and lump solutions of the Kadomtsev-Petviashvili equation. Adding electrons to the lattice we find solectron bound states and offer computational evidence of how electrons can be controlled and transported by such acoustic waves and how electron-surfing occurs at the nanoscale. We also offer computational evidence of the possibility of long lasting, fast lattice soliton and corresponding supersonic, almost loss-free transfer or transport of electrons bound to such lattice solitons along crystallographic axes.
Properties of nano-scale soliton-like excitations in two-dimensional lattice layers
Physica D: Nonlinear Phenomena, 2011
Nano-scale soliton-like supersonic, intrinsic localized excitations in two-dimensional atomic anharmonic lattice layers are here considered. We study the propagation, the velocity and other soliton-like features at head-on collisions of such lattice excitations created by using suitable initial mechanical and thermal conditions. Noteworthy is that narrow, highly-energetic solitons moving along one lattice row are very robust, accompanied by weak anti-phase oscillations in the lateral direction.
Soliton-like excitations and solectrons in two-dimensional nonlinear lattices
The European Physical Journal B, 2011
We discuss here the thermal excitation of soliton-like supersonic, intrinsic localized modes in two-dimensional monolayers of atoms imbedded into a heat bath. These excitations induce local electrical polarization fields at the nano-scale in the lattice which influence electron dynamics, thus leading to a new form of trapping. We study the soliton-mediated electron dynamics in such systems at moderately high temperatures and calculate the density of embedded electrons in a suitable adiabatic approximation.
Chaos, CNN, Memristors and Beyond, 2013
We study the thermal excitation of intrinsic localized modes in the form of solitons in 1d and 2d anharmonic lattices at moderately high temperatures. Such finite-amplitude fluctuations form long-living dynamical structures with lifetime in the pico-second range thus surviving a relatively long time in comparison to other thermal fluctuations. Further we discuss the influence of such long-living fluctuations on the dynamics of added excess free electrons. The atomic lattice units are treated as quasi-classical objects interacting by Morse forces and stochastically moving according to Langevin equations. In 2d the atoms are initially organized in a triangular lattice. The electron distributions are in a first estimate represented by equilibrium adiabatic distributions in the actual polarization fields. Computer simulations show that in 2d systems such excitations are moving with supersonic velocities along lattice rows oriented with the cristallographic axes. By following the electron distributions we have also been able to study the excitations of solectron type (electron-soliton dynamic bound states) and estimate their life times.
Localized versus traveling waves in infinite anharmonic lattices
Physics Letters A, 2002
Localized and traveling modes are worked out for an infinite anharmonic atomic chain by implementing a shooting algorithm and the finite difference and Newton procedures, respectively. These methods unlike the other currently used ones yield exact solutions in simulations carried out by integrating the equation of motion under the relevant initial conditions. (J. Szeftel). 0375-9601/02/$ -see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 -9 6 0 1 ( 0 2 ) 0 0 3 7 3 -0
Solitons in nonlinear lattices
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are also surveyed, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation. The solitons are considered in one, two, and three dimensions. Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of one-dimensional solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for theoretical and experimental studies alike. In both the one-dimensional and two-dimensional cases, the mechanism that creates solitons in NLs in principle is different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.
Energy self-localization and gap local pulses in a two-dimensional nonlinear lattice
Physical Review B, 1993
We study the formation of localized states, mediated by modulationa1 instability, on a twodimensional lattice with nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal surface, for example. The basic equations of the motion governing the dynamics of the lattice are derived from the model Hamiltonian. In the low-amplitude approximation and sernidiscrete limit these equations can be approximated by a two-dimensional nonlinear Schrodinger equation. The modulational instability conditions are calculated; they inform us about the selection mechanism of the wave vectors and growth rate of the instabilities taking place both in the longitudinal and transverse directions. The dynamics of the lattice is then investigated by means of numerical simulations; due to modulational instability an initial steady state that consists of a plane wave with low amplitude modulated by very weak noise, evolves into an oscillating localized state, inhomogeneously distributed on the lattice. These nonlinear localized modes, which move slowly, present the remarkable properties of gap modes. Their amplitude is large and they pulsate at a low frequency that lies inside the lower linear gap of the lattice.
Publisher’s Note: Solitons in nonlinear lattices [Rev. Mod. Phys. 83, 247 (2011)]
Reviews of Modern Physics, 2011
This article offers a comprehensive survey of results obtained for solitons and complex nonlinear wave patterns supported by purely nonlinear lattices (NLs), which represent a spatially periodic modulation of the local strength and sign of the nonlinearity, and their combinations with linear lattices. A majority of the results obtained, thus far, in this field and reviewed in this article are theoretical. Nevertheless, relevant experimental settings are surveyed too, with emphasis on perspectives for implementation of the theoretical predictions in the experiment. Physical systems discussed in the review belong to the realms of nonlinear optics (including artificial optical media, such as photonic crystals, and plasmonics) and Bose-Einstein condensation (BEC). The solitons are considered in one, two, and three dimensions (1D, 2D, and 3D). Basic properties of the solitons presented in the review are their existence, stability, and mobility. Although the field is still far from completion, general conclusions can be drawn. In particular, a novel fundamental property of 1D solitons, which does not occur in the absence of NLs, is a finite threshold value of the soliton norm, necessary for their existence. In multidimensional settings, the stability of solitons supported by the spatial modulation of the nonlinearity is a truly challenging problem, for the theoretical and experimental studies alike. In both the 1D and 2D cases, the mechanism which creates solitons in NLs is principally different from its counterpart in linear lattices, as the solitons are created directly, rather than bifurcating from Bloch modes of linear lattices.