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     

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     

High-order vibrational relaxation: a nonperturbative theory

A nonperturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the positive frequency part of the time-dependent non-stationary displacement correlation function of atoms. The nonlinear integral equation for this function is derived and solved numerically. We have found that the rate exhibits a critical behavior: it sharply increases near a specific (critical) value(s) of the interaction; the corresponding dependence is characterized by the critical index k - 1, where k is the number of the created phonons. Received 2 May 2002 Published online 31 July 2002     

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     

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     

Localized modes in a one-dimensional sphalerite-structure lattice with anharmonicity

The nonlinear localized vibrational modes of a one-dimensional atomic chain with two periodically alternating masses and force constants are analytically investigated using a discrete multiple-scale expansion method. This model simulates a row of atoms in the <1 1 1>-direction of sphalerite, or zinc blende, crystals. Owing to the structural asymmetry, the vibrational amplitude is governed by a perturbed nonlinear Schr?dinger equation instead of the standard one found in one-dimensional lattices with two alternating masses but uniform force constant. Although the stationary localized modes with carrier wavevector at the Brillouin-zone boundary are similar to those of ionic lattices, the moving localized modes with wavevectors within the zone are different owing to the perturbation. The calculation shows that the height of the moving localized modes in this lattice dampens with time. Received 14 May 2001 and Received in final form 12 July 2001     

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     

Periodic, Quasiperiodic and Chaotic Discrete Breathers in a Parametrical Driven Two-Dimensional Discrete Klein-Gordon Lattice

We study a two-dimensional lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the two-dimensional Klein-Gordon lattice with hard on-site potential. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers and chaotic discrete breathers by changing the amplitude of the driver.     

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     

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     

Picosecond X-ray diffraction studies of laser-excited acoustic phonons in InSb

We have employed time-resolved X-ray diffraction with picosecond temporal resolution to measure the time-dependent rocking curves of laser-irradiated asymmetrically cut single InSb crystals. Coherent acoustic phonons were excited in the crystals by irradiation with 800-nm, 100-fs laser pulses at irradiances between 0.25 and 12 mJ/cm². The induced time-dependent strain profiles (corresponding to the coherent phonons) were monitored by diffracting collimated, monochromatic pulses of X-rays from the irradiated crystals. Recording of the diffracted radiation with a fast low-jitter X-ray streak camera resulted in an overall temporal resolution of better than 2 ps. The strain associated with the coherent phonons modifies the rocking curve of the crystal in a time-dependent manner, and the rocking curve is recorded by keeping the angle of incidence of the X-rays upon the crystal fixed, but varying the energy of the incident X-rays around a central energy of 8.453 keV (corresponding to the peak of the rocking curve of the unperturbed crystal). The observed time-dependent diffraction from the irradiated crystals is in reasonable agreement with simulations over a wide range of energies from the unperturbed rocking-curve peak. Received: 22 March 2002 / Revised version: 25 March 2002 / Published online: 6 June 2002     

Moving breather collisions in Klein-Gordon chains of oscillators

We investigate the collisions of moving breathers, with the same frequency, in three different Klein-Gordon chains of oscillators. The on-site potentials are: the asymmetric and soft Morse potential, the symmetric and soft sine-Gordon potential and the symmetric and hard φ⁴ potential. The simulation of a collision begins generating two identical moving breathers traveling with opposite velocities, they are obtained after perturbing two identical stationary breathers which centers are separated by a fixed number of particles. If this number is odd we obtain an on-site collision, but if this number is even we obtain an inter-site collision. Apart from this distinction, we have considered symmetric collisions, if the colliding moving breathers are vibrating in phase, and anti-symmetric collisions, if the colliding moving breathers are vibrating in anti-phase. The simulations show that the collision properties of the three chains are different. The main observed phenomena are: breather generation with trapping, with the appearance of two new moving breathers with opposite velocities, and a stationary breather trapped at the collision region; breather generation without trapping, with the appearance of new moving breathers with opposite velocities; breather trapping at the collision region, without the appearance of new moving breathers; and breather reflection. For each Klein-Gordon chain, the collision outcomes depend on the lattice parameters, the frequency of the perturbed stationary breathers, the internal structure of the moving breathers and the number of particles that initially separates the stationary breathers when they are perturbed.     

Anharmonic dynamical behaviour in bcc zirconium

We present inelastic neutron scattering measurements of the low energy and strongly damped phonons in the high temperature bcc phase of zirconium. These phonons were investigated at different scattering vectors but equivalent phonon wave vectors in different Brillouin zones or along different but equivalent paths in the same Brillouin zone. Neither the observed differences in intensity nor in line shapes can be explained by the coherent one-phonon scattering law . This leads to an apparent violation of the fundamental symmetry of lattice dynamics. Taking into account the strong anharmonicity of these phonons, interferences between one- and multi-phonon scattering are held responsible for these effects. Measurements in different scattering planes reveal that due to the symmetry of the bcc lattice, these effects can only be observed in certain directions. Received: 24 December 1997 / Received in final form: 9 March 1998 / Accepted: 19 March 1998     

Breather trapping and breather transmission in a DNA model with an interface

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur. The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy. Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.     

Discrete moving breather collisions in a Klein-Gordon chain of oscillators

We study the collisions of moving breathers with the same frequency, traveling with opposite directions within a Klein-Gordon chain of oscillators. Two types of collisions have been analyzed: symmetric and non-symmetric, head-on collisions. For low enough frequency the outcome is strongly dependent of the dynamical states of the two colliding breathers just before the collision. For symmetric collisions, several results can be observed: breather generation, with the formation of a trapped breather and two new moving breathers; breather reflection; generation of two new moving breathers; and breather fusion bringing about a trapped breather. For non-symmetric collisions some possible results are: breather generation, with the formation of three new moving breathers; breather fusion, originating a new moving breather; breather trapping with breather reflection; generation of two new moving breathers; and two new moving breathers traveling as a bound state. Breather annihilation has never been observed.     

Raman and infrared spectroscopical investigation of the optical vibrational modes in GaSb/AlSb superlattices

The vibrational spectrum of ultra-thin layer GaSb/AlSb superlattices was investigated in detail by infrared (IR) and Raman spectroscopies. The effect of confinement of the transverse and longitudinal optical phonons in both types of the layers was studied. The dispersions of optical phonons of the GaSb and the AlSb obtained from the analysis of the Raman and IR spectra are in a good accordance with the theoretical data and results of neutron scattering experiments. First- and second-order Raman spectroscopy indicates the presence of intermixture of atoms at the interfaces in the GaSb/AlSb superlattices. Received: 11 May 1998 / Accepted: 21 July 1998     

On symmetric breather collisions in lattices with saturable nonlinearity

Symmetric collisions of two discrete breathers in the lattice with saturable nonlinearity are investigated. The strong correlation of the collision properties and the parameters of colliding breathers (power, velocity, and phase difference), lattice parameters and position of the collision point is found. This is related to the internal structure of the colliding breathers and energy exchange with the phonon background. The type of collision changes from elastic to the inelastic (the breathers merging, multi-bounce interactions, breather creation etc.) with the increasing of the colliding breather power. Collision of high power breathers always results in the breather fusion. The elastic and inelastic collisions are related to the periodic and quasi-periodic colliding breathers, respectively.     

Low-frequency breathers in polyethylene crystal

It is shown both analytically and numerically that three-dimensional low-frequency (acoustic) breathers identified as localized coupled bend and twist nonlinear waves can exist in polyethylene (PE) crystal. Their motion along the chain is accompanied by the simultaneous excitation of both (“zig” and “zag”) sub-chains forming PE macromolecule.In the region of a breather one can observe intensive out-of-plane motion of carbon atoms and relatively small displacements in the plane of the zigzag. In spite of this smallness, the “secondary” nonlinear effects turn out to be crucial for the existence of breathers.Both the existence and stability of low-frequency breathers in free motion are confirmed by computer simulation, using the Molecular Dynamics (MD) procedure. The stability of breathers with respect to thermal excitations as well as to mutual collisions and collisions with optical breathers is also discussed. We study also the breathers’ formation in different conditions. It turns out that the frequencies and extensions of the breathers can be varied in very narrow regions predicted by our analytical solution.     

Melting of the cooperative Jahn-Teller distortion in LaMnO 3 single crystal studied by Raman spectroscopy

We have studied the behavior of the Raman phonons of a stoichiometric LaMnO₃ single crystal as a function of temperature in the range between 77 K and 900 K. We focus on the three main phonon peaks of the Pbnm structure, related to the tilt, antisymmetric stretching (Jahn-Teller mode) and stretching modes of Mn-O octahedra. The phonon frequencies show a strong softening that can be fit taking into account their renormalization because of three phonon anharmonic effects in the pseudoharmonic approximation. Thermal expansion effects, in particular the variation of Mn-O bond lengths with temperature, are not relevant above 300 K. On the contrary, phonon width behavior deviates from the three phonon scattering processes well bellow T _c . The correlation between the magnitude of the cooperative Jahn-Teller distortion, that disappears at 800 K, and the amplitude of the Raman phonons in the orthorhombic phase is shown. Nevertheless, Pbnm phonons are still observable above this temperature. Phonon width and intensity behavior around T _c can be explained by local melting of the orbital order that begins quite below T _c and by fluctuations of the regular Mn-O octahedra that correspond to dynamic Jahn-Teller distortions. Received 25 January 2001 and Received in final form 14 March 2001     

Coherent and incoherent phonon processes in artificial atoms

Carrier-phonon interaction in semiconductor quantum dots leads to three classes of phenomena: coherent effects (spectrum reconstruction) due to the nearly-dispersionless LO phonons, incoherent effects (transitions) induced by acoustical phonons and dressing phenomena, related to non-adiabatic, sub-picosecond excitation. Polaron spectra, relaxation times and dressing-related decoherence rates are calculated, in accordance with experiment. Received 30 August 2002 / Received in final form 25 November 2002 Published online 28 January 2003