Intrinsic Localized Modes Research Articles

Quantum breathers and intrinsic localized excitations in an isotropic ferromagnet with octupole–dipole interaction

A numerical and analytical work on quantum breathers and intrinsic localized excitations in an isotropic ferromagnet with octupole–dipole interaction are reported. For the case with two bosons, we find many interesting and unusual features. For examples, the energy spectrum is composed of two symmetric continuums interconnected by two isolated bands that are sharply merged in a double continuum bands. These continuum bands are surrounded by two symmetric isolated bands and are also symmetric with respect to the degenerated point localized at the center of the Brillouin zone. When the value of octupole–dipole parameter increases, the shape of the continuum band undergoes grave changes and looks like a superposition of two continuum bands, but merged and becomes non degenerated at the center of the Brillouin zone. The eigenfunctions of the corresponding bound states are analyzed and their existences as quantum breathers are proved. The intrinsic localized excitation analysis, show that the bright and dark type intrinsic localized modes (ILMs) can exist in the system. The accuracy of the analytical solutions is tested by numerical simulations. Further more, we have proved that the increasing value of the coupling strength can lead the decreasing intensity of localization of the bright ILMs whereas the opposite behavior appears for the dark ILMs case.

Delocalization of phonons and energy spectrum in disordered nonlinear systems

We study phonon delocalization in disordered media in the presence of nonlinearity. By considering the Fermi-Pasta-Ulam $\ensuremath{\beta}$-model, we show that regardless of whether the initial state of the linear system is localized or not, the final state will be an extended mode after turning on the nonlinear term. We report on the results of an extensive dynamical simulation of a disordered nonlinear system, which show that, independent of the initial mode frequency, in the final state the energy spectrum is excited according to the Kolmogorov spectrum $E(\ensuremath{\omega})\ensuremath{\sim}{\ensuremath{\omega}}^{\ensuremath{-}5/3}$. Finally, we show that disorder will not cause delocalization of intrinsic localized modes.

Spherically localized discrete breathers in bcc metals V and Nb

Discrete breathers (DBs), also called intrinsic localized modes (ILMs), are spatially localized, large-amplitude vibrational modes in nonlinear lattices. Rod-like discrete breathers (DBs) have been reported in fcc Ni and bcc Nb by Haas et al. in 2011 based on molecular dynamics simulations. Here we use a general approach to find new type DBs in bcc V and Nb. In this approach, we firstly find the lattice symmetry dictated exact solutions to the equations of atomic motion in the form of delocalized nonlinear vibrational modes (DNVMs). Secondly, a localizing function with spherical symmetry is imposed over the DNVMs. Parameter of the localizing function is chosen such that the obtained DB has a long lifetime. The results presented in this work demonstrate that pure metals can support a variety of DBs. Interatomic potentials have a strong effect on the DB lifetime. Maximal DB lifetime in V is two orders of magnitude larger than that in Nb. The results of this study are interesting for the theory of DBs, and also they will help to better understand the impact of DBs on the physical properties of metals.

Modulational instability in addition to discrete breathers in 2D quantum ultracold atoms loaded in optical lattices

The modulational instability associated with discrete breathers in 2D quantum ultracold atoms is studied by using the Glauber’s coherent state combined with a semi-discrete approximation and multiple-scale methods. The linear stability analysis exhibits an intriguing threshold amplitude and instability regions associated with modulational growth rate. In addition, we demonstrate a coexistence of two bright intrinsic localized modes namely, the radial symmetric and bilateral symmetric modes, at the center and at the edges of the Brillouin zone, respectively, by alternating the on-site parameter interaction. Numerical investigations reveal a good agreement with the theoretical analysis.

Restricted normal mode analysis and chaotic response of p-mode intrinsic localized mode

Nonlinearities in arrays of discrete oscillators can cause energy localizations called intrinsic localized modes (ILMs). Two spatial physical manifestations of localization within the array are the ST-mode ILM (a symmetric mode) and the P-mode ILM (an asymmetric mode). The free response and forced response of the asymmetric vibratory P-mode are discussed within this paper, with particular attention given to the linear coupling between the oscillators. The free, undamped response is studied by means of the restricted normal mode approach, which gives the amplitude profile of the P-mode ILM. The initial P-mode ILM amplitude profile, as calculated from the restricted normal mode approach, is capable of creating both forced and unforced persistent ILMs. For the unforced and undamped free response, the P-mode ILM is stable with and without linear coupling, and its response frequency is incommensurate with the response of the surrounding oscillators. It was found that the frequency of oscillation of this mode has a strong relationship to the amplitude of vibration. Moreover, the amplitude profiles generated by the restricted normal mode approach are used to generate initial conditions for the forced, damped case. The existence of the damped and forced P-mode ILM is strongly dependent upon the linear coupling term. It is shown that if linear coupling does not exist, then this mode is persistent but chaotic. To the author’s knowledge, this is the first pinned and persistent chaotic ILM to be observed, which is not predicted from local analysis.

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity.

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.

Intrinsic anharmonic localization in thermoelectric PbSe

Lead chalcogenides have exceptional thermoelectric properties and intriguing anharmonic lattice dynamics underlying their low thermal conductivities. An ideal material for thermoelectric efficiency is the phonon glass–electron crystal, which drives research on strategies to scatter or localize phonons while minimally disrupting electronic-transport. Anharmonicity can potentially do both, even in perfect crystals, and simulations suggest that PbSe is anharmonic enough to support intrinsic localized modes that halt transport. Here, we experimentally observe high-temperature localization in PbSe using neutron scattering but find that localization is not limited to isolated modes – zero group velocity develops for a significant section of the transverse optic phonon on heating above a transition in the anharmonic dynamics. Arrest of the optic phonon propagation coincides with unusual sharpening of the longitudinal acoustic mode due to a loss of phase space for scattering. Our study shows how nonlinear physics beyond conventional anharmonic perturbations can fundamentally alter vibrational transport properties.

Induced localized nonlinear modes in an electrical lattice

Intrinsic localized modes, also called discrete breathers (DBs), can exist under certain conditions in one-dimensional nonlinear electrical lattices driven by external periodic excitations (PEs). In this work, we have studied experimentally the effectiveness of some PEs of variable waveform at generating DBs in such lattices. We have found that this generation phenomenon is optimally controlled by the strength of the fundamental harmonic of the driving.

Experimental and numerical observation of dark and bright breathers in the band gap of a diatomic electrical lattice.

We observe dark and bright intrinsic localized modes (ILMs), also known as discrete breathers, experimentally and numerically in a diatomic-like electrical lattice. The experimental generation of dark ILMs by driving a dissipative lattice with spatially homogenous amplitude is, to our knowledge, unprecedented. In addition, the experimental manifestation of bright breathers within the band gap is also novel in this system. In experimental measurements the dark modes appear just below the bottom of the top branch in frequency. As the frequency is then lowered further into the band gap, the dark ILMs persist, until the nonlinear localization pattern reverses and bright ILMs appear on top of the finite background. Deep into the band gap, only a single bright structure survives in a lattice of 32 nodes. The vicinity of the bottom band also features bright and dark self-localized excitations. These results pave the way for a more systematic study of dark breathers and their bifurcations in diatomic-like chains.

Nonlinear acoustic metamaterials

Acoustic metamaterials (AMM) have become a very active topic for research in numerous domains of engineering and science because of their promise to create materials, structures, and devices that can control acoustic wave propagation in ways that exceed the capabilities of naturally occurring or conventional composite materials. The majority of AMM research has been focused on linear behavior such as negative dynamic effective stiffness and density, cloaking, and negative refraction. One drawback of the focus on linear behavior is the restriction of the effective material properties of interest to narrow frequency bands that cannot be changed with external stimulus. Nonlinearity has been explored as a means of increasing the bandwidth of performance by enabling tunable band gaps and material configurability. Other recent work has investigated nonlinear AMM to access phenomena such as harmonic generation, non-reciprocity, enhanced energy absorption, solitons, mode hopping and conversion, chaos, and intrinsic localized modes. This talk will provide an overview of nonlinear AMM, starting with a background on AMM, then surveying existing research on the topic and its relationship to seminal works in nonlinear acoustics, and finally discussing promising avenues of future research. [Work supported by the National Science Foundation EFRI program and ARL:UT.]

Transverse to longitudinal mode conversion via nonlinear inertial effects in a locally resonant metamaterial plate

Acoustic and elastic metamaterials have potential for tailoring wave propagation in ways beyond the capabilities of conventional materials and have been shown to exhibit a myriad of rich dynamical effects, such as negative effective properties, cloaking, extreme damping, and non-reciprocity. However, most of the existing literature has been focused on linear dynamics in which these behaviors are restricted to narrow frequency bands. More recently, nonlinearity has been investigated as a method of increasing this bandwidth, as well as a means to broaden the palette of available dynamics. Past studies on nonlinear acoustic and elastic metamaterials have demonstrated effects not easily accessible in the linear regime, including harmonic generation, mode hopping and conversion, tunable band gaps, chaos, and intrinsic localized modes. In this work, we present a model for a nonlinear elastic plate metamaterial that exhibits mode conversion between transverse and longitudinal waves. The mode conversion is enabled by cantilevered beam attachments undergoing large-angle out-of-plane oscillations. By analyzing the unit cell of this locally-resonant plate, we interpret the transverse-longitudinal coupling as a nonlinear, anisotropic effective mass density. The mode conversion effect is demonstrated via direct numerical simulations. [Work supported by NSF and ARL:UT.]

Numerical analysis of intrinsic localized modes in two-dimensional hexagonal Fermi-Pasta-Ulam lattice

Numerical analysis of intrinsic localized modes in two-dimensional hexagonal Fermi-Pasta-Ulam lattice

Resonant localized modes in electrical lattices with second-neighbor coupling

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 plane-wave mode of the same frequency. This kind of localized mode has also been termed a nanopteron. Here we show experimentally and using realistic simulations of the system that the nanopteron can be stabilized via both direct and subharmonic driving. In the case of excitations at the zone center (i.e., at wave number $k=0$), we observed stable ILMs as well as a periodic localization pattern in certain driving regimes. In the zone boundary case (of wave number $k=\ensuremath{\pi}/a$, where $a$ is the lattice spacing), the ILMs are always resonant with a plane-wave mode, but they can nevertheless be stabilized by direct (staggered) and subharmonic driving.

Surface discrete breathers in Pt3Al intermetallic alloy

It is known that defect-free crystals can support spatially localized, large amplitude vibrational modes with frequencies outside the linear phonon spectrum. Such excitations are called discrete breathers (DB) or intrinsic localized modes. So far, for 3D crystals DB were considered only in the bulk. In the present molecular dynamics study, for the first time, we demonstrate that DB can be excited at the low Miller indices surfaces of the Pt3Al intermetallic alloy. It is shown that properties of the DB depend essentially on the surface orientation and termination, as well as on DB polarization. The study of DB at crystal surfaces is important because they can localize energy of order of 1 eV, which can reduce the potential barrier for local structure transformation or a chemical reaction.

Quantum breathers and intrinsic localized excitation associated with the modulational instability in 1D Bose–Hubbard chain

In this work, the energy spectrum and intrinsic localized modes associated with the modulational instability of boson chains is described by a Bose–Hubbard model. By using of number states method combined with the numerical diagonalization, we show that the energy spectrum of the system exhibits bound states signature. With the help of multiple scales method in addition to a quasidiscreteness approximation, we obtain bright and dark type intrinsic localized modes at the center and at the edges of the Brillouin zone respectively and their appearance conditions. We found that the inclusion of interaction of two bosons at the same site can influence the appearance conditions of bright and dark soliton solutions. Considering the fact that nowadays, the forthright way to predict the formation of intrinsic localized modes in nonlinear systems is the modulational instability. We investigate analytically, through the linear stability of plane wave solutions, the existence of localized structures in the Bose–Hubbard chain. It is found that the shape of the region of modulational instability and the instability growth rates of the plane wave can be more affected dramatically when the interaction of two bosons at the same site is involved in the system. Furthermore, we calculate the instability growth rates of plane wave at the center and at the edge of the Brillouin zone for different values of the interaction of two bosons to analyze their formation conditions which are in full agreement with the method of multiple scale in addition to a quasi-discreteness approximation analysis.

Phase dynamics of discrete breathers periodically tunneling in weakly coupled nonlinear chains

We present a brief discussion of the phase-coherent dynamics of discrete breathers (intrinsic localized modes) in a system of two weakly coupled nonlinear chains and its comparison with periodic tunneling of quantum particles in a double-well potential and with macroscopic quantum tunneling of two weakly linked Bose–Einstein condensates. We consider the dynamics of relative phase of classically-tunneling discrete breathers in two weakly coupled nonlinear chains and show that the dynamics of the relative phase in the π/2 tunneling mode coincides with the experimentally observed dynamics of the relative phase of quantum particles, periodically tunneling in a double-well potential, both for noninteracting and strongly repulsively interacting particles. The observed coincidence demonstrates the correspondence between the dynamics of classical localized excitations in two weakly coupled nonlinear chains and tunneling dynamics of quantum object in the double-well potential. We show that in both π/2 and winding tunneling modes the relative phase experiences periodic jumps by π in the instants of complete depopulation of one of the weakly coupled chains or potential wells. The connection of the observed phase dynamics with the non-quantum uncertainty principle is discussed.

Experimental demonstration of excitation and propagation of intrinsic localized modes in a mass–spring chain

Excitation and propagation of nonlinear localized oscillations are demonstrated experimentally by using a mass–spring chain to emulate those in the celebrated Fermi–Pasta–Ulam chain of β type. Two types of experiments are performed, one corresponding to a boundary-value problem and the other to an initial-value one. In the former experiment, one end of the chain is driven sinusoidally in the direction of the chain above a cut-off frequency. In the latter experiment, only a number of weights centered around the weight in the middle of the chain are held displaced initially and released suddenly. The experimental results show quantitatively good agreements with the numerical ones. Two videos linked also show visually mobile and stationary localized oscillations.

Discrete breathers in an electric lattice with an impurity: Birth, interaction, and death.

We have simulated aspects of intrinsic localized modes or discrete breathers in a modulated lumped transmission line with nonlinear varactors and a defect unit cell. As the inductance or capacitance of this cell is increased, a transition from instability to stability takes place. Namely, there exist threshold values of the inductance or capacitance of a lattice impurity for a breather to be able to attach to. A resistive defect can also anchor a breather. Moreover, by either gradually lowering all the source resistances, or else increasing the modulation frequency, multiple secondary ILMs can be spontaneously generated at host sites (with only a single inductive or capacitive defect). Further, if two impurities are subcritically spaced (the separation increasing with the amplitude of the modulation voltage), a breather can pop up midway, with no breathers at the impurity sites themselves. Finally, an ILM can pull closer its neighbors on both sides, only to perish once these ILMs have gotten sufficiently close. To our knowledge, these effects have not been reported for any discrete nonlinear system.

Experimentally observed evolution between dynamic patterns and intrinsic localized modes in a driven nonlinear electrical cyclic lattice

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 an LSM of fixed shape can be tuned across the modal spectrum. Interestingly, by tuning the driver frequency away from this spectrum the LSM can be continuously converted into ILMs and vice versa. The differences in pattern formation between simulations and experimental findings are due to a low concentration of impurities. Through this novel nonlinear excitation and switching channel in cyclic lattices either energy balanced or unbalanced LSMs and ILMs may occur. Because of the general nature of these dynamical results for nonintegrable lattices applications are to be expected. The ultimate stability of driven aero machinery containing nonlinear periodic structures may be one example.

Molecular dynamics analysis of stability of intrinsic localized mode in deformed carbon nanotubes

In this paper, structures and dynamics of intrinsic localized modes (ILMs) in carbon nanotubes (CNTs) are investigated by molecular dynamics (MD) simulation. Systematic study of ILM with tensile deformation is performed. Moreover, lifetime of ILMs is estimated by numerical results of MD simulation. It is found that the bigger the tensile strain is, the longer the lifetime of ILM is. From these results, by changing the tensile condition, the stability (lifetime) of ILM can be controlled.