Moving nonlinear localized vibrational modes for a one-dimensional homogenous lattice with quartic anharmonicity

Moving nonlinear localized vibrational modes (i.e. discrete breathers) for the one-dimensional homogenous lattice with quartic anharmonicity are obtained analytically by means of a semidiscrete approximation plus an integration. In addition to the pulse-envelope type of moving modes which have been found previously both analytically and numerically, we find that a kink-envelope type of moving mode which has not been reported before can also exist for such a lattice system. The two types of modes in both right- and left-moving form can occur with different carrier wavevectors and frequencies in separate parts of the plane. Numerical simulations are performed and their results are in good agreement with the analytical predictions. Received 13 October 1999 and Received in final form 15 May 2000     

Anharmonic excitations in the FPU and FK models

The properties of vibrational localized (breathers) and traveling (anharmonic phonons) waves are discussed in an infinite, one-dimensional, monoatomic crystal for the Fermi-Pasta-Ulam and Frenkel-Kontorova models. The shooting and finite difference schemes have been implemented to reckon the displacement fields of breathers and anharmonic phonons, respectively. These tools provide localized and traveling waves proving to be indefinitely stable in simulations carried out by solving the equations of motion. The emphasis is laid on the role of the cubic and quartic terms of the anharmonic potential which turn out to oppose and to shore up the restoring force, respectively. The case of vibrational modes arising in an anharmonic crystal subject to a soft phonon induced instability is also addressed. Received 7 November 2001 and Received in final form 5 February 2002 Published online 6 June 2002     

Nonlinear Gap Modes in a 1D Alternating Bond Monatomic Lattice with Anharmonicity

We analytically study the nonlinear localized gap modes in a one-dimensional atomic chain with uniform atomic mass but two periodically alternating force constants between the nearest neighbors by means of a quasi-continuum approximation. This model simulates a row of atoms in the <111> direction of a diamond-structure type of crystals or molecular crystals with alternating double and single bonds. For this lattice system, we find that the harmonic plus quartic anharmonic terms of inter-site potential produce a new type of nonlinear localized gap modes with a slightly asymmetry distribution of atomic displacements. These localized gap modes are somewhat different from widely studied localized gap modes with a symmetry atomic displacement distribution in diatomic ion lattices.     

一维金刚石结构晶格的非线性局域模

用多重尺度法研究了质量均匀相互作用力交替变化的原子链形成的非线性局域振动模式,这 种原子链模拟了金刚石结构晶格沿〈111〉晶向或一维分子链的振动,通过多重尺度展开分 析得出,原子位移分布服从微扰的非线性Schrdinger方程,求得了相应的定态解和传播解 ,其结果与相互作用力相同质量交替分布的另一种形式的一维双原子晶格的结果有所不同, 其原因是金刚石结构晶格的对称性相对差些. 关键词： 金刚石结构 非线性局域模 多重尺度法     

Standing wave instabilities, breather formation and thermalization in a Hamiltonian anharmonic lattice

Modulational instability of travelling plane waves is often considered as the first step in the formation of intrinsically localized modes (discrete breathers) in anharmonic lattices. Here, we consider an alternative mechanism for breather formation, originating in oscillatory instabilities of spatially periodic or quasiperiodic nonlinear standing waves (SWs). These SWs are constructed for Klein-Gordon or Discrete Nonlinear Schr?dinger lattices as exact time periodic and time reversible multibreather solutions from the limit of uncoupled oscillators, and merge into harmonic SWs in the small-amplitude limit. Approaching the linear limit, all SWs with nontrivial wave vectors (0 < Q < π) become unstable through oscillatory instabilities, persisting for arbitrarily small amplitudes in infinite lattices. The dynamics resulting from these instabilities is found to be qualitatively different for wave vectors smaller than or larger than π/2, respectively. In one regime persisting breathers are found, while in the other regime the system thermalizes. Received 6 October 2001 / Received in final form 1st March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: mjn@ifm.liu.se     

MOVING NONLINEAR LOCALIZED MODES FOR ONE-DIMENSIONAL KLEIN－GORDON DIATOMIC LATTICE

We study analytically the moving nonlinear localized vibrational modes (discrete breathers) for a one-dimensional Klein－Gordon diatomic lattice in the whole ω(q) plane of the system by means of a semi- discrete approximation, in which the carrier wave of the modes is treated explicitly while the envelope is described in the continuum approximation. We find that both pulse and kink envelope moving modes for this lattice system can occur with certain carrier wave vectors and vibrational frequencies in separate regions of the ω(q) plane. However, the kink envelope moving modes have not been reported previously for this lattice system.     

Magnetic order in the Shastry-Sutherland model

We investigate the influence of energetic disorder, viscous damping and an external field on the electron transfer (ET) in DNA. The double helix structure of the λ-form of DNA is modeled by a steric oscillator network. In the context of the base-pair picture two different kinds of modes representing twist motions of the base pairs and H-bond distortions are coupled to the electron amplitude. Through the nonlinear interaction between the electronic and the vibrational degrees of freedom localized stationary states in the form of standing electron-vibron breathers are produced which we derive with a stationary map method. We show that in the presence of additional energetic disorder the degree of localization of such breathers is enhanced. It is demonstrated how an applied electric field initiates the long-range coherent motion of breathers along the bases of a DNA strand. These moving electron-vibron breathers, absorbing energy from the applied field, sustain energetic losses due to the viscous friction caused by the aqueous solvent as well as the impact of a moderate amount of energetic disorder. Moreover, it is illustrated that with the choice of the amplitude and frequency of the external field, the breather can be steered to a desired lattice position achieving control of the ET. Received 5 July 2002 Published online 29 November 2002     

Ab initio calculation of local vibrational modes by the Green’s function method. Application to GaAs:C and GaN:As

We present an ab initio technique for the calculation of vibrational modes at deep defects in semiconductors outside and inside the host-phonon bands. The dynamical matrix is calculated using density-functional theory in the local density approximation. In the results presented here all interatomic harmonic forces up to the eleventh nearest neighbour of a particular atom of the perturbed or unperturbed crystal are included. The Green's function method is used to obtain the difference of the density of phonon states between the perturbed and the perfect crystal. This technique is applied to calculate the split-off mode at the C impurity at As site in GaAs and its isotope shifts, which are in good agreement with Raman scattering experiments. It is demonstrated that the impurities generate resonances and localized modes inside the host-phonon bands. The resonances arise at specific energies of the density of phonon states of the perfect crystal which are practically independent of the chemical nature of the defect, whereas the localized modes show distinct impurity or ligand isotope shifts. Our calculations of GaAs and cubic GaN lead to the assignment of a number of low energy Raman-scattering peaks between 7.2 meV and 31.0 meV, observed at a layer of cubic GaN on a GaAs substrate, to resonances inside the phonon bands of GaAs and GaN. Received 5 March 1999     

Discrete nonlinear Schrödinger breathers in a phonon bath

We study the dynamics of the discrete nonlinear Schr?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 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. Received 21 January 1999 and Received in final form 20 September 1999     

The vibrational modes around the soliton lattice with next neighbor hopping interactions in highly doped trans-(CH) x

Starting from the extended SSH model that includes an external Coulomb potential arising from interchain charged solitons and counterions, the intrachain e-e interaction and the next neighbor hopping interactions, eight localized vibrational modes around the soliton lattice have been found for the doping levels from 3.33 at.% to 13.33 at.%. Among them three are infrared active and they can be used to interpret the three observed infrared absorption lines at 487, 1284 and 1362 cm^–1. Furthermore, the frequencies of localized modes are decreased and their localizations are weakened when the dopant concentrations increase.     

Infrared spectra and lattice vibrations of the spin-chain compound LiCuVO 4

The infrared spectra of the one-dimensional antiferromagnet LiCuVO₄ are measured in the frequency range from 10 cm^-1 to 10 000 cm^-1 and at temperatures from 2 K to 300 K, for the electric field vector E of the radiation polarized either along the a- or along the b-crystallographic directions. For each polarization six infrared active phonon modes are observed in accordance with factor group analysis of the crystal structure of LiCuVO₄. The theoretical group analysis of the possible spinel low-symmetry phases is performed within the framework of Landau's theory of phase transitions. The parameters of several phonon lines show noticeable anomalies around 150 K where the magnetic correlations appear in the copper chains, which may indicate a finite interaction between the phonon and the magnon subsystems in LiCuVO₄. Received 19 February 2001 and Received in final form 26 June 2001     

Envelope solitary waves on two-dimensional lattices with in-plane displacements

We investigate envelope solitary waves on square lattices with two degrees of freedom and nonlinear nearest and next-nearest neighbor interactions. We consider solitary waves which are localized in the direction of their motion and periodically modulated along the perpendicular direction. In the quasi-monochromatic approximation and low-amplitude limit a system of two coupled nonlinear Schr?dinger equations (CNLS) is obtained for the envelopes of the longitudinal and transversal displacements. For the case of bright envelope solitary waves the solvability condition is discussed, also with respect to the modulation. The stability of two special solution classes (type-I and type-II) of the CNLS equations is tested by molecular dynamics simulations. The shape of type-I solitary waves does not change during propagation, whereas the width of type-II excitations oscillates in time. Received: 4 December 1997 / Revised: 6 June 1998 / Accepted: 7 July 1998     

Soliton dynamics in chiral molecular chains with first- and third-neighbour interactions

We investigate the propagation and interaction of solitons associated with circularly polarized vibrations in gyrotropic media. The chirality of the structure yields different dispersion laws and hence different phase and group velocities for the left- and right-handed modes. The helical arrangement of the monomers is modelled through first- and third-neighbour interactions. The dynamics of the excitations is governed by a system of coupled discrete nonlinear Schr?dinger equations which is studied both analytically and numerically. Depending on the initial conditions and the interaction constants, different evolutionary patterns are obtained corresponding to unbound or bound one- and two-soliton solutions. The results can be applied to the process of energy transfer in helical polymers. Received 1st October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: krad@issp.bas.bg     

Crowdion dynamics in a nonuniformly deformed three-dimensional crystal

The problem of crowdion motion is formulated and analyzed as a dynamical problem of a three-dimensional crystal lattice formed by atoms of several kinds, which interact with each other by means of short-range pair potentials. It is explained that in order for the the crowdion excitations of the close-packed atomic rows to be distinguishable against the background of small dynamic deformations of the crystal as a whole, the microscopic parameters of the crystal structure must meet certain stated requirements. The equation of motion of a crowdion in an arbitrary elastic strain field of the crystal is derived in the Lagrangian formalism. Expressions are obtained which relate the effective mass and the rest energy of a crowdion with the geometric and force parameters of the crystal lattice. Received 4 October 2001 / Received in final form 27 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nazarenko@ksame.kharkov.ua     

Next-nearest neighbor interaction and localized solutions of polymer chains

We study localization in polymer chains modeled by the nonlinear discrete Schr?dinger equation (DNLS) with next-nearest-neighbor (n-n-n) interaction extending beyond the usual nearest-neighbor exchange approximation. Modulational instability of plane carrier waves is discussed and it is shown that localization gets amplified under the influence of an enhanced interaction radius. Furthermore, we construct exact localized solitonlike solutions of the n-n-n interaction DNLS. To this end the stationary lattice system is cast into a nonlinear map. The homoclinic orbits of unstable equilibria of this map are attributed to standing solitonlike solutions of the lattice system. We note that in comparison with the standard next-neighbor interaction DNLS which bears only one type of static soliton-like states (either staggering or unstaggering) the one with n-n-n interaction radius can support unstaggering as well as staggering stationary localized states with frequencies lying above respectively below the linear band. Generally, the stronger the n-n-n interaction on the DNLS lattice the smaller are the maximal amplitudes of the standing solitonlike solutions and the less rapid are their exponential decays. Received 4 October 2000     

Nonlinear electron-lattice interaction on excited states in polythiophene

In consideration of the effects of the square term of the electron-lattice interaction and the bond-bending term, the energy spectra and the localized vibrational modes around a bipolaron of the polythiophene are investigated based on the one-dimensional and two-dimensional extension SSH model. The results show that, with the influence of the square term, the energy gap increases, the frequencies of all the localized vibrational modes around a bipolaron decrease and their localizations also shift. It is noted that, an even-parity mode has been found which corresponds to absorption peak at 1220 cm⁻¹. When the bond-bending term is considered, the frequencies of the localized modes increase and five new localized modes appear. Among them, one Raman active mode and three infrared active modes may correspond the observed RRS absorption peaks at 1047 cm⁻¹ and three infrared absorption peaks at 370, 1020, 1120 cm⁻¹ in the experiments.     

Optical investigation of CdS quantum dots in Langmuir–Blodgett films

Structures with CdS quantum dots produced by the Langmuir–Blodgett (LB) technique were investigated by Raman, IR, and UV spectroscopies. The confinement effect of longitudinal optical (LO) phonons in CdS quantum dots was investigated by Raman spectroscopy. Surface vibrational modes of CdS quantum dots were observed in IR spectra. It was shown experimentally that the frequency of the surface vibrational modes depends on the properties of the surrounding media. An average size of CdS quantum dots of about 3–6.4 nm was obtained from the analysis of UV measurements. Received: 1 February 1999 / Accepted: 1 April 1999 / Published online: 19 May 1999     

One-dimensional delocalizing transitions of matter waves in optical lattices

We investigate, both analytically and numerically, the conditions for the occurrence of the delocalizing transition phenomenon of one-dimensional localized modes of several nonlinear continuous periodic and discrete systems of the nonlinear Schrödinger type. We show that either non-existence of solitons in the small amplitude limit or the loss of stability along existence branches can lead to delocalizing transitions, which occur following different scenarios. Examples of delocalizing transitions of both types are provided for a class of equations which describe single component and binary mixtures of Bose-Einstein condensates trapped in linear and nonlinear optical lattices.     

Localized vibrational modes in an <Emphasis Type="Italic">A</Emphasis><Subscript>3</Subscript><Emphasis Type="Italic">B</Emphasis> two-dimensional perfect crystal

The possibility of existence of nonlinear localized vibrational modes in an A₃B two-dimensional crystal with pairwise interatomic bonds is demonstrated. Such modes are easily realized when the difference between masses of atoms A and B is significant and the spectrum of small-amplitude crystal vibrations has a sufficiently wide gap. The influence of the uniform tension/compression deformation on the small-amplitude crystal vibration spectrum and on the existence of nonlinear localized modes is investigated. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–79, August, 2008.     

Resonance effects in nonlinear lattices

We study a class of one-dimensional nonlinear lattices with nearest-neighbour interactions described by a potential of the binomial type. This potential contains a free parameter which can be chosen to reproduce a variety of models, such as the Toda, the Fermi-Pasta-Ulam and the Coulomb-like lattices. Carrying out essentially numerical experiments, the effects of soliton propagation on a lattice with defects are investigated. In particular, the properties of the localized mode, generated by the propagation of the soliton through the defect, are discussed with respect to the defect mass and the potential parameter, in the light of a simple theoretical model. Furthermore, an interesting phenomenon is observed: the amplitude of the speed of the mass defect shows a sequel of resonance peaks in terms of the mass defect. The positions of these peaks appear to be independent of the potential parameter. Received 16 August 1999 and Received in final form 3 February 2000