q-Breathers and the Fermi-Pasta-Ulam problem

The Fermi-Pasta-Ulam (FPU) paradox consists of the non-equipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.     

Low-lying Collective Modes of a 1D Dipolar Quantum Gas in an Anharmonic Trap

The low-lying collective modes of an anharmonically confined one-dimensional ultracold dipolar Bose gas are investigated by using time-dependent variational method. The frequencies of dipole mode and breathing mode are obtained analytically in the full crossover regime from a Tonks-Girardeau gas to a dipolar density wave state. We find that the frequency shifts caused by quartic distortion of the potential can be amplified by interparticle interaction and the collapse and revival of the collective excitations can be observed in the anharmonic trap.     

Solitons in a diatomic chain with competing nonlinearities

A one-dimensional diatomic chain whose energy contains cubic and quartic terms in the atomic displacements is considered. A modified asymptotic method is proposed for finding soliton solutions to equations describing systems with nonlinearities of various symmetry. It is shown that the dynamics of the model in question can be described in terms of equations that are similar to the dynamic equations for a diatomic chain with an even potential function. Soliton solutions of a new, unusual type are found in the specific case of a free diatomic chain with a purely cubic anharmonic potential.     

Energy features of an adiabatically loaded anharmonic oscillator

An excited anharmonic oscillator is considered under conditions of adiabatic (i.e., slow, as compared to the oscillation period) loading with an external force tending to a constant value at long times. The energy characteristics of the adiabatically loaded anharmonic oscillator, such as the instantaneous energy of the oscillator, the maximum kinetic (oscillation) energy, and the kinetic and potential energies averaged over the period, are analytically calculated as a function of the steady-state force. The analytical results are confirmed by the data of numerical calculations. It is established that the external force gives rise to a redistribution of the average kinetic and potential components of the initial energy of the anharmonic oscillator and that the transferred energy portions at a small external force considerably exceed the average work done by the external force.     

Nontrivial properties of heat flow: Analytical study of some anharmonic lattice microscopic models

We address the analytical investigation of nontrivial properties of heat flow, starting from microscopic models of matter. We present an integral representation for the expression of the heat flow, by taking as our crystal model a self-consistent chain of anharmonic oscillators, precisely, a chain of oscillators with harmonic interparticle interactions, anharmonic on-site potentials, thermal reservoirs at the boundaries, and still with some residual inner stochastic baths. We propose an approximative scheme to make the integral formalism analytically treatable: we test the approximations in harmonic models and analyze some anharmonic systems. For the case of graded anharmonic models with weak interparticle interactions, we derive an expression for the thermal conductivity, and show the existence of thermal rectification and also nonnegative differential thermal resistance. The details of our formalism allow us to note the ingredients behind these phenomena, and the generality of our results (i.e., the results will be valid for other interactions and regimes) shows that rectification in graded materials is a ubiquitous property.     

Anharmonic effects of periodic molecular systems in the vibron model approximation

The vibron model approximation to take into account anharmonic effects in periodic systems is discussed. This is achieved by considering a simple one-dimensional molecular crystal with four degrees of freedom. In this case the lattice dynamical treatment is separated into two sets of modes, the modes associated to the molecular degrees of freedom and those corresponding to the motions of the centre of mass of the molecules. The non-interacting molecular modes are studied in detail, and analytical expressions for the energies and wave functions for the two-phonon manifold are obtained. A local-normal mode transition as a function of the interaction parameters is identified, similar to that in isolated molecular systems.     

Anharmonic self energy shift of a librational mode

A sizable anharmonic self energy shift of the Raman active librational modes in KN₃ has been found and shown to be a linear function of temperature above the Debye characteristic temperature of the solid (ca. 351°K). The Grüneisen parameter for the librational mode is estimated from the data to be 1.40. The Raman active mode involving the translation of the K⁺ ion shows a negligibly small anharmonic shift.     

Coefficient of restitution for one-dimensional harmonic solids

Using a numerical algorithm based on the time evolution of normal modes, we calculate the coefficient of restitution eta for various one-dimensional harmonic solids colliding with a hard wall. We find that, for a homogeneous chain, eta=1 in the thermodynamic limit. However, for a chain in which weaker springs are introduced in the colliding front half, eta remains significantly less than one even in the thermodynamic limit, and the "lost" energy goes mostly into low frequency normal modes. An understanding of these results is given in terms of how the energy is redistributed among the normal modes as the chain collides with the wall. We then contrast these results with those for collisions of one-dimensional harmonic solids with a soft wall. Using perturbation theory, we find that eta=1 for all harmonic chains in the extremely soft wall limit, but that inelasticity grows with increasing chain size in contrast to hard wall collisions.     

钛酸铅及掺杂体系纳米晶A_1对称性横光学声子模的特征

本文讨论了ＰｂＴｉＯ３、Ｐｂ１－ｘＬａｘＴｉ１－ｘ／４Ｏ３和Ｐｂ１－ｘＣａｘＴｉＯ３纳米晶拉曼散射中Ａ１（ＴＯ）声子峰的不规则线型和多峰劈裂现象。认为以简正振动坐标构成的非谐性双势阱势能函数和Ｍｏｒｓｅ势能函数的Ｓｃｈｒｄｉｎｇｅｒ方程的解与实验观测到的Ａ１（１ＴＯ）模式在高温下的劈裂峰特征比较一致。从能量角度解释了随ｃ／ａ下降,ωＡ１（ＴＯ）快速向低频移动的原因。     

Statistical energy analysis, energy distribution models and system modes

Expressions for the energy influence coefficients of a built-up structure are found in terms of the modes of the whole structure. These coefficients relate the time and frequency average energies of the subsystems to the subsystem input powers. Rain-on-the-roof excitation over a frequency band Ω is assumed. It is then seen that the system can be described by an SEA model only if a particular condition involving the mode shapes of the system is satisfied. Broadly, the condition holds if the mode shapes of the modes in the frequency band of excitation are, on average, typical enough of all the modes of the system in terms of the distribution of energy throughout the system. If this condition is satisfied then the system can be modelled using an “quasi-SEA” approach, irrespective of the level of damping or of the strength of coupling. However, the resulting model need not be of a proper SEA form, and in particular the indirect coupling loss factors may not be negligible.     

Exact solutions for extended waves in 1d anharmonic lattices

A cyclic chain of n equal classic particles coupled by anharmonic forces has a set of extended vibrational modes, for which exact solutions are given. This requires for the power law of the forces certain conditions to be fulfilled. Each mode is characterized by a wave number and the undulations of the particles depend on the total energy and on a new constant of motion that formally expresses a kind of angular momentum. Exact solutions for n = 7 with a twelfth power potential are discussed.     

A neutron scattering study of the vibrational modes of hydrogen in the β-phases of Pd-H,Pd-10Ag-H and Pd-20Ag-H

The localised modes associated with interstitial hydrogen in the β-phases of Pd and Pd-Ag alloys have been studied by neutron energy loss at 295K, 80K and for Pd at 30K. Their energies vary little but their widths increase significantly with temperature and silver content, an effect which is ascribed to local disorder and anharmonic contributions.     

Coulomb excitations of a nuclear slab in relativistic mean-field theory

Time-dependent relativistic mean-field theory is used to describe the dynamic behaviour of a nuclear slab excited at time zero by a rapid Coulomb push. At small incident energies of the projectile, we observe oscillations of small amplitude with isovector character. With increasing excitation energy, the motion becomes increasingly anharmonic, and parts of the nuclear material are ejected. At the highest energies, we find a rapid dissociation between the proton and neutron part of the slab. It turns out that the character of the oscillations is strongly influenced by the strength of the ρ-meson coupling. For vanishing coupling, we observe two modes corresponding in nature to the Goldhaber-Teller mode and the Steinwedel-Jensen mode of the giant dipole resonance in realistic nuclei. At larger ρ-meson coupling, the Goldhaber-Teller mode is more and more suppressed, and one is left with one strongly damped mode of the Steinwedel-Jensen type.     

Oscillating Propagation of Kink in Nondissipative Frenkel-Kontorova Chain Due to External DC Force

We report the oscillating propagation of kink in a nondissipative Frenkel-Kontorova （FK） chain driven by external DC force, which is different from the usual propagation of localized modes with equal speed. When the kink moves in the opposite direction of the external DC force, the kink will be accelerated and the potential of the FK chain in the external force field is transformed to be the kinetic energy of the kink. If the kink reaches the boundary of the FK chain, the kink will be bounced back and moves in the opposite direction, then the kink will be decelerated gradually and the kinetic energy of the kink ＆ transformed to be the potential of the FK chain in the external force field. If the speed of the kink reaches zero, the kink will move in the opposite direction again driven by the external DC force, and a new oscillating cycle begins. Simulation result demonstrates exactly the transformation between the kinetic energy of the kink and the potential of the FK chain in the external force field. The interesting energy exchange is induced by the special topology of kinks, and other localized modes, such as breathers and envelope solitons, have no the interesting phenomenon.     

Self-energy of phonons in anharmonic one-dimensional crystals

Using the expression obtained by Green's function methods the self-energy of phonons, interacting through anharmonic terms of third and fourth order in the expansion of the potential energy, is calculated for a linear chain without further approximations. The phonon energy shift and width show strong dependence on the frequency and the wave-vector.     

Doping dependence of bilayer resonant spin excitations in (Y, Ca)Ba2Cu3O6+x

Resonant magnetic modes with odd and even symmetries were studied by inelastic neutron scattering experiments in the bilayer high-Tc superconductor Y1-xCa+Ba2Cu3O6+y over a wide doping range. The threshold of the spin excitation continuum in the superconducting state, deduced from the energies and spectral weights of both modes, is compared with the superconducting d-wave gap, deduced from electronic Raman scattering in the B1g symmetry on the same samples. Above a critical doping level of delta approximately =0.19, both mode energies and the continuum threshold coincide. We find a simple scaling relationship between the characteristic energies and spectral weights of both modes, which indicates that the resonant modes are bound states in the superconducting energy gap, as predicted by the spin-exciton model of the resonant mode.     

Multiplication of high-energy electrons in irradiated materials studied using the Boltzmann kinetic equation

Processes involved in the formation of electron collision cascades created by nonrelativistic high-energy electrons, which can develop in materials exposed to electron and gamma radiation fluxes, have been considered. The problem is solved using the Boltzmann kinetic equation for high-energy electrons moving in a medium. A model scattering indicatrix is constructed for this equation with an arbitrary potential of interaction between colliding particles. Using this scattering indicatrix, the distribution of the particle energies is obtained. Based on this energy distribution (with an arbitrary interparticle interaction potential), a cascade function is found that describes the multiplication of knock-out electrons (electron cascade) generated when a high-energy electron with a certain energy is scattered on the electron subsystem of the irradiated material. The cascade function has been calculated for the Coulomb potential of the interaction between a high-energy electron and atomic-shell electrons.     

Selective optical generation of coherent acoustic nanocavity modes

Femtosecond pump-probe experiments on a Ga0.85In0.15As nanocavity enclosed by two Ga(0.85)In(0.15)As/AlAs phonon Bragg mirrors reveal selective generation of terahertz confined acoustic modes and regular folded phonons. Selective generation of the confined modes alone is achievable for laser excitation at certain energies below the mirror absorption edges, corresponding to electronic transitions within the cavity layer only. Calculations based on the photoelastic effect explain the experimental results. Decay times of cavity and regular modes evidence longer decay times and anharmonic effects for the cavity mode.     

Conjecture on the effect of small anharmonicity on vibrational modes of glass

We conjecture here that, unlike for crystal lattice modes, some nearly harmonic vibrational modes of a glass lattice may have their (thermally populated) energy levels shifted (from equal spacing) more than they are broadened, both the shifting and broadening arising from small anharmonic terms in the lattice potential. This conjecture could be verified by observing either (a) saturating infrared absorption, (b) an infrared photon echo, or (c) altered infrared absorption (possibly even gain) of a probe beam in the presence of a second pump beam.