Parametrically Driven Solitons in a Chain of Nonlinear Coupled Pendula with an Impurity

The system consisting of a chain of parametrically driven and damped nonlinear coupled pendula with a mass impurity is studied by means of a discrete version of the envelope function approach. An analogue of the parametrically driven damped nonlinear Schodinger equation with an impurity term is derived from the original lattice equation. Analytical solutions of impurity pinned high-frequency breathers and kinks are obtained. The results show that the mass impurity has striking influence on the high-frequency modes. In addition, we perform numerical simulations, showing that the light mass impurity has a stabilizing effect on the chain. The breathers seeding chaos in the homogeneous chain are pinned on a suitable light impurity to pull the chain from the chaotic state.     

A renormalization scheme for calculating the spectrum of a vibronic system occurring in molecules or impurities in insulators

An iteration scheme which makes use of a numerical renormalization group approach is used to calculate the spectrum of vibronic levels. This spectrum resulted from dynamic effects occurring in certain molecules or impurities in insulators.The Hamiltonian of these systems is expressed in the matrix form, using products of suitable electron-phonon states as a basis. In applying this method to multimode electron-phonon systems, phonon modes are coupled in a chain-like fashion. Then a finite chain calculation in terms of Hubbard X-operators is explored by setting up the vibronic Hamiltonian.Calculations are based on Lanczos algorithm, in which only the nearest neighbor matrix elements along the chain need to be taken into account. The iterative scheme is then applied to a two-level electronic system coupled to phonons. A single-particle Green's function corresponding to a two-level system is applied to calculate the spectral density of states, which, coupled to single mode is carried out. The strength of lines in density of states is affected by the coupling constant as well as the temperature dependence of some measurable quantities.     

Potentials induced by the electron-optical-phonon interaction in a quantum well

The potential induced by the electron-optical-phonon interaction in a quantum well (QW) is investigated by means of the perturbation theory. We consider the interactions of an electron with both bulklike confined longitudinal optical (LO) phonons and four branches of interface optical (IO) phonons. The spatial distributionV _i(z) of the induced potential for QW structures with different heterolayer compositions and different well widths is calculated in detail. The numerical results show that the heterolayer composition of the QW plays an important role in determining the shape ofV _i(z) and that the existence of IO-phonons is important to the electronic states in QWs.     

On the path length of an excess electron interacted with optical phonons in a molecular chain

We show that in a molecular chain with dispersionless phonons at zero temperature, a “quasistationary” moving soliton state of an excess electron is possible. As the soliton velocity vanishes, the path length of the excess electron exponentially tends to infinity. It is demonstrated that in the presence of dispersion, when the soliton initial velocity exceeds the maximum group velocity of the chain, the soliton slows down until it reaches the maximum group velocity and then moves stationarily at this maximum group velocity. A conclusion is made of the fallacy of some works were the existence of moving polarons in a dispersionless medium is considered infeasible.     

Neutron scattering study of the intermolecular vibrations in solid C60

We present a detailed account of an inelastic neutron scattering study of the intermolecular vibrations in solid C₆₀ above and below the structural phase transformation. Assignment of the observed phonon peaks to modes of translational and librational character is discussed on the basis of lattice dynamical calculations using phenomenological intermolecular potentials. A new bond charge model is presented which reproduces the observed phonon branches very well. However, the apparently small influence of the orientational disorder on the librational excitations remains to be understood.     

Lattice dynamics of sapphire (Al2O3)

Using inelastic neutron scattering we have determined all the dispersion branches of the ₁, ₂ and ₃ representations along the three-fold axis as well as the 2 times 15 branches of ₁ and ₂ symmetry along the -A-direction plus some branches along the -D-direction. The experimental data are analyzed using various rigid ion, polarizable ion and shell models. The shell models give a very satisfactory account of the dispersion curves as well as the scattering intensities. Special attention is given to the investigation of dielectric constants and equilibrium conditions.     

Microscopic foundation of the phenomenological few-level approach to coherent semiconductor optics

We present the results of inelastic neutron scattering experiments for Cr₂O₃ carried out using the single-crystal time-of-flight spectrometer PRISMA at ISIS (U.K.) as well as the three-axis spectrometer TAS-1 at JAERI(J). The collected data are analysed on the basis of phenomenological shell models showing convincing agreement between calculation and experiment both for the frequencies and intensities. All together the dispersion relations of 12 out of 20 phonon branches along the three-fold axis are determined. By a comparison with the Cr₂O₃ iso-type sapphire (Al₂O₃) it is found that the dynamical response of the oxygen ion is only little affected by the ionic substitution. The chromiumd electrons find their expression mainly in a strengthening of the metal-oxygen bonding. The problem of ionic polarizabilities is addressed in detail both for the oxygen and chromium ions.     

An analytical expression for Eg and Ag modes of pyrochlores

A general analytical expression has been derived for E_g and A_1g modes in terms of stretching and bending force constant for cubic pyrochlore structure compounds. The expression has been applied to different pyrochlore oxides accounting six stretching and four bending force constants. The calculation of E_g and A_1g mode has been carried out by using the earlier reported values of force constants for titanates, hafnates and stannates. The analytical expression can be applied to any pyrochlore structure compounds for evaluating and assigning E_g and A_1g mode if the interatomic force constants are already known.     

Quasicontinuum approximation and iterative method for envelope solitons in anharmonic chains

For solitary waves on a monoatomic chain with nearest neighbor interactions the continuum approximation has a limited validity range and exhibits certein mathematical problems. For pulse solitons these problems are overcome by the Quasicontinuum Approach (QCA), and the validity range is considerably extended. We generalize the QCA to oscillatory excitations and derive analytic expressions for bright and dark envelope solitons, limiting ourselves to a polynomial interaction potential with harmonic, cubic and quartic terms. Moreover we describe and apply a numerical iteration procedure in Fourier space in order to take into account discreteness effects in a systematic way. This procedure yields envelope solitons with a width in the order of the lattice constant. In the case of zero velocity these solutions can be compared with intrinsic localized modes derived by other authors. The stability and accuracy of all our solutions are tested by numerical simulations.     

Existence and Stability of Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains

Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft Ф^4 potential but also in hard Ф^4 potential and K4 chains. The measurements of compact-like discrete breathers＇ core in soft and hard Ф^4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers＇ core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice.     

Phonon Dispersion in Equiatomic Li-Based Binary Alloys

The computations of the phonon dispersion curves （PDC） of four equiatomic Li-based binary alloys, namely Li0.5Na0.5, Li0.5K0.5, Li0.5Rb0.5 and Li0.5Cs0.5, to second order in the local model potential is discussed in terms of the real-space sum of Born von Karman central force constants. Instead of the concentration average of the force constants of metallic Li, Na, K, Rb and Cs, the pseudo-alloy atom （PAA） is adopted to compute directly the force constants of four equiatomic Li-based binary alloys. The exchange and correlation functions due to Hartree （H） and Ichimaru-Utsumi （IU） are used to investigate the influence of screening effects. The phonon frequencies of four equiatomic Li-based binary alloys in the longitudinal branch are more sensitive to the exchange and correlation effects in comparison with the transverse branches. However, the frequencies in the longitudinal branch are suppressed due to IU-screening function than the frequencies due to static H-screening function.     

Lattice Dynamics and Superconductivity of RuB2: A First-Principles Study

We report the first-principles linear response calculations on lattice dynamics and electron-phonon coupling （EPC） of superhard material RuB2. Phonon frequencies and eigenvectors are obtained throughout the whole Brillouin zone. The calculated EPC paracneters for the optical phonon modes at F indicate that the d electrons of transition metal play the most important role in deciding the superconducting behaviour, and there are sizeable contributions from B p electrons to EPC. Our calculated EPC constant is 0.41, and the estimated superconducting transition temperature Tc is 1.6K using the Coulomb pseudopotential u^＊ = 0.12, in excellent agreement with the experimental ones.     

Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices

Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generalized discrete two-dimensional monatomic model. It is proven that the two- dimensional compact-like discrete breathers exist not only in two-dimensional soft Φ4 potentials but also in hard two-dimensional Φ4 potentials and pure two-dimensional K4 lattices. The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Φ4 potential are determined by coupling parameter K4, while those in pure two-dimensional K4 lattices have no coupling with parameter K4. The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.     

Coherent phonon excitation in bismuth

Ultrafast time-resolved reflectivity of a bismuth thin film evaporated on a silicon substrate is measured to investigate coherent phonons in bismuth. The reflectivity result is analyzed by a linear chirp approximation to obtain the time dependent frequencies of coherent phonons. Not only the optical modes are detected, which are generated by a combination of impulsive stimulated Raman scattering and displacive excitation of coherent phonon, acoustic phonon modes are also observed, which are emitted by the A_1g optical phonon.     

Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.     

Two-Dimensional Discrete Gap Breathers in a Two-Dimensional Diatomic β Fermi--Pasta--Ulam Lattice

We study the existence of two-dimensional discrete breathers in a two-dimensional face-centred square lattice consisting of alternating light and heavy atoms, with nearest-neighbour coupling containing quartic soft or hardnonlinearity. This study is focused on two-dimensional breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of existence of two-dimensional gap breathers by using the numerical method, the local anharmonicity approximation and the rotating wave approximation. We obtain six types of two-dimensional gap breathers, i.e., symmetric, mirror-symmetric and asymmetric, no matter whether the centre of the breather is on a light or a heavy atom.     

A model for vibrational properties of the atomic interface in A/B fcc metals

The motivation of this theoretical work is to introduce a model calculation for the elastic waves scattering and coherent phonon transport at an atomic nanojunction between face-centered cubic (fcc) leads. The model system A/B consists of two perfect semi-infinite fcc leads A and B, oriented in the same direction and joined by an atomic interface. It is applied to the system Cu/Ni and its inverse Ni/Cu. A theoretical approach based on the matching method is used to study the dynamics of the system A/B.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.     

Two-dimensional discrete gap breathers in a two-dimensional discrete diatomic Klein-Gordon lattice

We study the existence and stability of two-dimensional discrete breathers in a two-dimensionai discrete diatomic Klein-Gordon lattice consisting of alternating light and heavy atoms, with nearest-neighbor harmonic coupling. Localized solutions to the corresponding nonlinear differential equations with frequencies inside the gap of the linear wave spectrum, i.e. two-dimensional gap breathers, are investigated numerically. The numerical results of the corresponding algebraic equations demonstrate the possibility of the existence of two-dimensional gap breathers with three types of symmetries, i.e., symmetric, twin-antisymmetric and single-antisymmetric. Their stability depends on the nonlinear on-site potential （soft or hard）, the interaction potential （attractive or repulsive） and the center of the two-dimensional gap breathers （on a light or a heavy atom）.     

Multi-site Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains

Multi-site compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. We obtain that the two-site compact-like discrete breathers with codes σ = （0,..., 0, 1, 1, 0,..., 0）and codes σ= （0,..., 0, 1, -1, 0, ..., 0） can exist in discrete one-dimensional monatomic chain with quartic on-site and inter-site potentials. However, the former can only exist in hard quartic on-site potential and cannot exist in soft quartic on-site potential, whereas the latter is just reversed. A11 of the two-site Compact-like discrete breathers with codes σ = （0,..., 0, 1, 1, 0,..., 0） and σ （0,... ,0, 1, -1,0,... ,0} cannot exist in a pure K4 chain.