A theory is developed to describe the effect of an intrinsic localized mode (ILM) on small vibrations in a monatomic chain with hard quartic anharmonicity. One prediction is the appearance in the chain of linear local modes nearby the ILM. To check this result, MD calculations of vibrations under strong local excitation are carried through with high precision. The results fully confirm the prediction.
In this paper an analytical and numerical study of anharmonic vibrations of monatomic chain and graphene in transverse (perpendicular) with respect to the chain/plane direction is presented. Due to the lack of odd anharmonicities and presence of hard quartic anharmonicity for displacements in this direction, there may exist localized anharmonic transverse modes with the frequencies above the spectrum of the corresponding phonons. Although these frequencies are in resonance with longitudinal (chain) or in-plane (graphene) phonons, the modes can decay only due to a weak anharmonic process. There…
A theory of intrinsic localized modes (ILMs) in anharmonic lattices is developed, which allows one to reduce the original nonlinear problem to a linear problem of small variations of the mode. This enables us to apply the Lifshitz method of the perturbed phonon dynamics for the calculations of ILMs. In order to check the theory, the ILMs in monatomic chain are considered. A comparison of the results with the corresponding molecular dynamics calculations shows an excellent agreement.
Moving self-localized vibration of large size (vibrational soliton) in monatomic chain with cubic and quartic anharmonicities is considered. Two types of motion of such vibrations are found: the subsonic and the supersonic ones. First type of motion is possible for chains with hard quartic anharmonicity supposing that cubic anharmonicity is weak. This motion was earlier observed in numerical simulations. For the second type of motion the cubic anharmonicity plays the decisive role: the moving mode is stabilized by co-moving deformation of the lattice caused by this anharmonicity. The quartic a…
It is found that in some metals an intrinsic localized mode may exist with frequency above the top of the phonon spectrum. The necessary condition, requiring sufficiently high ratio of quartic to cubic anharmonicity may be fulfilled because of screening of the interaction between ions by free electrons. Starting from the known literature values of the pair potentials we have found that in Ni and Nb the derived localized mode condition is fulfilled. MD simulations of the nonlinear dynamics of Ni and Nb confirmed that high frequency ILMs may exist in these metals.
The possibility of thermal excitation of intrinsic localized modes (ILMs) arising from anharmonicity in ionic perfect crystals is studied numerically for realistic model systems in one and three dimensions. Implications are discussed for an interesting high-temperature feature seen in earlier inelastic neutron scattering experiments on single crystal NaI. The general conclusion is that ILM formation energies are far too large for thermal excitation of ILMs to account for the observed feature in a pure crystal.
Recent neutron and x-ray scattering measurements show intrinsic localized modes (ILMs) in metallic uranium and ionic sodium iodide. Here, the role ILMs play in the behavior of these materials is examined. With the thermal activation of ILMs, thermal expansion is enhanced, made more anisotropic, and, at a microscopic level, becomes inhomogeneous. Interstitial diffusion, ionic conductivity, the annealing rate of radiation damage, and void growth are all influenced by ILMs. The lattice thermal conductivity is suppressed above the ILM activation temperature while no impact is observed in the elect…
MD simulations of recoil processes following the scattering of X-rays or neutrons have been performed in ionic crystals and metals. At small energies (<10 eV) the recoil can induce intrinsic localized modes (ILMs) and linear local modes associated with them. As a rule, the frequencies of such modes are located in the gaps of the phonon spectrum. However, in metallic Ni, Nb and Fe, due to the renormalization of atomic interactions by free electrons, the frequencies mentioned are found to be positioned above the phonon spectrum. It has been shown that these ILMs are highly mobile and can efficie…
Deep level transient spectroscopy shows that defects created by alpha irradiation of germanium are annealed by low energy plasma ions up to a depth of several thousand lattice units. The plasma ions have energies of 2-8eV and therefore can deliver energies of the order of a few eV to the germanium atoms. The most abundant defect is identified as the E-center, a complex of the dopant antimony and a vacancy with and annealing energy of 1.3eV as determined by our measurements. The inductively coupled plasma has a very low density and a very low flux of ions. This implies that the ion impacts are …
We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of Jacobian elliptic functions. These include one, two and three spin excitations. All these solutions have smooth anticontinuum limits. Their linear stability and semiclassical quantization are also discussed briefly.
Inelastic neutron measurements of the high-temperature lattice excitations in NaI show that in thermal equilibrium at 555 K an intrinsic mode, localized in three dimensions, occurs at a single frequency near the center of the spectral phonon gap, polarized along [111]. At higher temperatures the intrinsic localized mode gains intensity. Higher energy inelastic neutron and x-ray scattering measurements on a room-temperature NaI crystal indicate that the creation energy of the ground state of the intrinsic localized mode is 299 meV.
Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state softens in frequency and its amplitude grows as the upper frequency bifurcation point is approached, similar to the soft mode kinetic transition for a single driven Duffing resonator. A lower frequency bifurcation point occurs when the four-wave-mixing partner of this same phase mode intercepts the top of the extended wave branch, initiating a second kinetic tran…
This experimental study of driven intrinsic localized modes (ILMs) in an electronic circuit lattice with saturable nonlinearity follows the theoretical work of Hadzievski and coworkers. They proposed that a saturable nonlinearity could introduce transition points where localized excitations in nonintegrable lattices would move freely. In our experiments MOS capacitors provide the saturable nonlinearity in an electric lattice. Because of the soft nonlinearity driver locked, auto-resonance stationary ILMs are observed below the bottom of a linear frequency band of the lattice. With decreasing dr…
Locked intrinsic localized modes (ILMs) and large amplitude lattice spatial modes (LSMs) have been experimentally measured for a driven 1-D nonlinear cyclic electric transmission line, where the nonlinear element is a saturable capacitor. Depending on the number of cells and electrical lattice damping a LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum an LSM can be continuously converted into ILMs and visa versa. The differences in pattern formation between simulations and experimental findings are due to a low con…
The experimental properties of intrinsic localized modes (ILM) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest neighbor intersite potentials. Here it is shown for a 1-D lumped electrical transmission line a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis the nonlinear inductive current equations are transformed to flux transmission line equations with analogue onsite hard potential nonlinearities. Approxima…
In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrodinger equation model, to the case of two-component systems. We consider all the different combinations of "up" (zero phase) and "down" (π phase) site excitations and are able to compute not only the corresponding existence curves, but also the eigenvalue dependences of the small eigenvalues potentially responsible for instabilities, as a function of the nonlinear parameters of the model representing the self/cross …
It is well known that a moving intrinsic localized mode (ILM) in a nonlinear physical lattice looses energy because of the resonance between it and the underlying small amplitude plane wave spectrum. By exploring the Fourier transform (FT) properties of the nonlinear force of a running ILM in a driven and damped 1D nonlinear lattice, as described by a 2-D wavenumber and frequency map, we quantify the magnitude of the resonance where the small amplitude normal mode dispersion curve and the FT amplitude components of the ILM intersect. We show that for a traveling ILM characterized by a specific…
We study intrinsic localized modes (ILMs), or solitons, in arrays of parametrically-driven nonlinear resonators with application to microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). The analysis is performed using an amplitude equation in the form of a nonlinear Schroedinger equation with a term corresponding to nonlinear damping (also known as a forced complex Ginzburg-Landau equation), which is derived directly from the underlying equations of motion of the coupled resonators, using the method of multiple scales. We investigate the creation, stability, and interaction…
Intrinsic Localized Modes (ILMs) or Discrete Breathers (DBs) are produced through a non-linear vibration localization phenomenon. While Anderson localization is due to lattice defects, the nonlinearity of lattices provides the basis for ILM excitation. Over the past two decades, these ILMs have been realized in a wide range of physical systems including photonic crystals, nonlinear atomic lattices, anti-ferromagnets, coupled Josephson junction arrays and coupled cantilevers. This paper brings out the feasibility of exciting ILMs in a standalone mechanical resonator. Through piezoelectric drivi…
Both low frequency and high frequency impurity modes have been produced in a SiN micromechanical cantilever array by illumination with either an infrared or visible laser. When such laser-induced impurities are placed near a driven intrinsic localized mode (ILM) it is either repelled or attracted. By measuring the linear response spectrum for these two cases it was found that vibrational hopping of the ILM takes place when the natural frequency of the ILM and an even symmetry linear local mode are symmetrically located about the driven ILM frequency so that parametric excitation of these two l…
We investigate the mobility of nonlinear localized modes in a generalized discrete Ginzburg-Landau type model, describing a one-dimensional waveguide array in an active Kerr medium with intrinsic, saturable gain and damping. It is shown that exponentially localized, traveling discrete dissipative breather-solitons may exist as stable attractors supported only by intrinsic properties of the medium, i.e., in absence of any external field or symmetry-breaking perturbations. Through an interplay by the gain and damping effects, the moving soliton may overcome the Peierls-Nabarro barrier, present i…
Intrinsic localized modes, also called discrete breathers, can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external harmonic excitations. In this work, we have studied experimentally the efectiveness of generic periodic excitations of variable waveform at generating discrete breathers in such lattices. We have found that this generation phenomenon is optimally controlled by the impulse transmitted by the external excitation (time integral over two consecutive zeros
A method is presented for realizing logic operations in a micromechanical cantilever array based on the timed application of a lattice disturbance to control the properties of intrinsic localized modes (ILMs). The application of a specific inhomogeneous field destroys a driver-locked ILM, while the same operation can create an ILM if initially no-ILM exists. Logic states "1" and "0" correspond to "present" or "absent" ILM.
We report the observation of spontaneous localization of energy in two spatial dimensions in the context of nonlinear electrical lattices. Both stationary and traveling self-localized modes were generated experimentally and theoretically in a family of two-dimensional square, as well as hon- eycomb lattices composed of 6x6 elements. Specifically, we find regions in driver voltage and frequency where stationary discrete breathers, also known as intrinsic localized modes (ILM), exist and are stable due to the interplay of damping and spatially homogeneous driving. By introduc- ing additional cap…
Lugiato-Lefever (LL) equations in one and two dimensions (1D and 2D) accurately describe the dynamics of optical fields in pumped lossy cavities with the intrinsic Kerr nonlinearity. The external pump is usually assumed to be uniform, but it can be made tightly focused too -- in particular, for building small pixels. We obtain solutions of the LL equations, with both the focusing and defocusing intrinsic nonlinearity, for 1D and 2D confined modes supported by the localized pump. In the 1D setting, we first develop a simple perturbation theory, based in the sech ansatz, in the case of weak pump…
We demonstrate experimentally and corroborate numerically that an electrical lattice with nearest-neighbor and second-neighbor coupling can simultaneously support long-lived coherent structures in the form of both standard intrinsic localized modes (ILMs), as well as resonant ILMs. In the latter case, the wings of the ILM exhibit oscillations due to resonance with a degenerate plane-wave mode. This kind of localized mode has also been termed nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmoni…
We consider the localized nonlinear breathing modes that emerge in heterogeneous granular configurations of two materials with a periodicity of three and four beads. We examine as characteristic examples chains with 1 steel and 2 alumnium beads, as well as ones with 1 steel and three aluminum beads. We analyze the higher order gaps that emerge in such settings and explore the intrinsic localized modes that bifurcate from the edge of the upper bands. A generic surprising feature of such states is that they appear to be more robust than their counterparts bifurcating from the edges of the lower …
We present a systematic study of the existence and stability of discrete breathers that are spatially localized in the bulk of a one-dimensional chain of compressed elastic beads that interact via Hertzian contact. The chain is diatomic, consisting of a periodic arrangement of heavy and light spherical particles. We examine two families of discrete gap breathers: (1) an unstable discrete gap breather that is centered on a heavy particle and characterized by a symmetric spatial energy profile and (2) a potentially stable discrete gap breather that is centered on a light particle and is characte…
We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected N-th neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability …
