The resonance interaction of vibrational modes in one-dimensional nonlinear lattices

Resonances of vibrational modes were for the first time revealed for the example of the one-dimensional random Morse lattice. The observation of resonances was possible because of lattice deformation, when, at certain relative deformation values, vibrational modes satisfied the conditions of double (m _i ω _i + m _j ω _j = 0) or triple (m _i ω _i + m _j ω _j + m _k ω _k = 0) resonances. Of all the resonances observed, the resonance with the frequency ratio ω₂: ω₁ = 2: 1 was studied in detail. The dependences of mode lifetimes and the degree of energy exchange between them on such parameters as resonance frequency detuning, excitation energy level, etc. were determined. A model of two nonlinearly coupled harmonic oscillators was considered in detail on the assumption of a one-to-one correspondence between oscillators and vibrational modes. A consideration of the model problem of oscillators revealed analytic dependences of the dynamic behavior of vibrational modes on control parameters. Excellent agreement between the numerical results for the Morse lattice and analytic conclusions was obtained. It was shown that, for the Fermi-Pasta-Ulam lattice, the resonance interaction of vibrational modes was controlled by the same rules as with the Morse lattice.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

The harmonic oscillator energy level spacing for neutrons and protons in nuclei

Approximate expressions of?ω for neutrons and protons separately, as functions of the neutron numberN and the proton numberZ respectively, are derived. The dependence ?ω_n(?ω_p) on N(Z) is established using a rather recently proposed semi-phenomenological density distribution based on the separation energies of the last neutron or proton. The corresponding curves of?ω show “discontinuities in the slope” at the closed shells throughout the periodic table. The difference ?ω_n — {ie17-01} is also discussed.     

两耦合半无限超晶格中的局域界面声子-极化激元

采用转移矩阵方法，研究了含结构缺陷层的两耦合半无限超晶格(GaAs/AlAs)中的局域界面声子-极化激元模性质. 研究发现，含不同介电特性的缺陷超晶格结构中的局域界面声子-极化激元模在剩余射线区［ω_TO, ω_LO］的分布情况与数量存在不同，而且反对称模表现出不同的特征. 文中着重研究了缺陷层介电常数与角频率无关的缺陷超晶格，发现该结构中的局域界面声子-极化激元模对组分层的排列顺序与厚度、缺陷层的厚度以及横向波数有着不同程度的依赖.     

Zero-sound branches in asymmetric nuclear matter

A polarization operator constructed in the random phase approximation is used to obtain zero-sound excitations in isospin asymmetric nuclear matter (ANM). Two families of the complex solutions ω_sτ(k),τ= p,n are presented. The imaginary part of the solutions corresponds to the damping of the collective mode due to its overlapping with the particle-hole modes and the subsequent emission of a proton (ω_sp(k)) or a neutron (ω_sn(k)). The dependence of the solutions on the asymmetry parameter is studied.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Optic and acoustic plasmon modes of a semiconductor superlattice

The collective plasmon modes of s semiconductor superlattices consisting of alternating layers of electrons and holes or alternating layers of electrons with different densities are investigated. For wells widely separated in space, such that Bloch wavefunction overlap between wells is negligible, we find optical-like and acoustical-like plasmon modes propagating along the superlattice direction. Perpendicular to the superlattice direction, the acoustic mode (ω～q_″) recently observed by Olego and Pinczuk⁸ is found to be split into two acoustic branches.     

Theoretical calculations and Raman spectrum of intercalation modes in LixInSe

By using an extended linear-chain model which includes the interlayer forces, we have calculated the new vibrational modes, of Li intercalated InSe. The dispersion curves along thek _z wavevector perpendicular to the layers for the -polytype are determined in the first Brillouin zone. Assuming that the interlayer interaction is not modified upon intercalation and the interaction between lithium atom and adjacent layers in the van der Waals plane has the same value than the interlayer one, the new modes are determined with the force constant given by the rigid layer mode of the, -polytype at 18 cm^–1. This model gives the variation of the acoustic branches and the appearance of two optical intercalation modes at higher frequencies. The Brillouin zone boundary modes of the acoustic branches at 18 and 41 cm^–1 in the pure material are calculated to be 22 and 50 cm^–1 respectively forx=1/2. The dispersion of the new optical branches is flat along thez-direction and frequencies are obtained at 96 cm^–1 for the Li mode perpendicular tok _z and at 218 cm^–1 for the Li mode parallel tok _z. We compare also our results with the Li mode frequencies obtained in a total energy calculation. Raman scattering experiments have been performed in intercalated sample in order to verify the proposed model.     

Measurement of the surface density of states by field ionization

It is shown that recent measurements of field ion energy distributions from clean tungsten surfaces probe the density of metal states in the vicinity of the surface. We find j(ω) = (2π/kh)Σ_m| ∫ d³rψ_m(r)γ_z|²δ(ω??_m), where j(ω) is the ion current a ω, ψ_mand ?_m are electronic metal eigenfunctions and eigenvalues in the presence of the external electric field used in field ionization and γ(z) is a function which is large near the noble gas atom. An explicit expression for γ(z) is given in the text. It is estimated that tungsten metal states with values of k₆ at least as large as 0.5 Å^?1 make an appreciable contribution to j(ω) where k₆ is the electron momentum parallel to the surface.     

Wall effects on sound propagation in tubes

Numerical solutions have been obtained for the exact equations describing the propagation of periodic axisymmetric waves in a rigid cylindrical tube. Results were obtained for air over a range of conditions corresponding to shear wave numbers (s = R √?ω/μ) from 0·2 to 5000 and reduced frequencies (k = ωR/a) from 0·01 to 6. For conciseness and convenient application, the results for the attenuation and phase shift coefficients are given in the form of simple polynomials for the ranges 5 ? s ? 5000 and 0·01 ? k ? 6. This range covers virtually all values of tube diameter and sound frequency likely to be met in practical situations that are consistent with a continuum gas model.     

Propagation and conversion of non-axisymmetric modes in non-uniform helicon-sustained plasma

An effect of the radial plasma density gradient on the oblique wave propagation in the helicon-frequency range is investigated. It is shown that the dispersion features of electrostatic and electromagnetic modes are essentially changed in strongly non-uniform helicon plasma. In particular, the transition between helicon eigenmode frequency scales ω ～ k _z and ω ～ k _z ² is demonstrated. The process of total conversion of long-wavelength helicon mode into short-wavelength electrostatic wave in near-axis region of a plasma column is analysed. Due to modification of the wave dispersion relations, the densities at which the mode conversion occurs are considerably reduced if the density gradient is steep enough. The estimation of collisionless axial damping rate of helicon mode connected with linear mode conversion is presented. This damping is compared with the usual collision damping.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

Two-photon echo method to determine the transverse relaxation time of excitonic molecules

A nonlinear optical method to determine the transverse relaxation time of excitonic molecules by means of two-photon echo is proposed. In the case of two-photon transition such as excitonic molecule one needs three pulses to obtain an echo signal. When the wave-vector and frequency of the three successive pulses are denoted by k₁,ω₁, k₂,ω₂ and k₃,ω₃, the two-photon echo can be observed in the direction of 4k₂-2k₁-k₃ with frequency 4ω₂-2ω₁-ω₃. Tuning both ω₁ and ω₂ to be two-photon resonant with excitonic molecule, we can satisfy the phase-matching condition rather easily for appropriate values of ω₃ due to the large dispersion of excitonic polaritons. From the correlation trace of the two-photon echo we can determine directly the transverse relaxation time of excitonic molecules.     

Quantum theory of nonresonant electromagnetic and ultrasonic absorption in glasses

We develop quantum theory of nonresonant ultrasonic and electromagnetic absorption in glasses at low temperatures. In the quantum region where ?ω?kT the nonresonant absorption coefficients are proportional to ω³ which seems to be in agreement with the existing experimental data.The existence of characteristic temperature T_c (or characteristic energy E_c = kT_c) of the order of 10 + 20 K is established. At higher interlevel spacing E the concept of two-level systems in their conventional form is not applicable because of their strong coupling to the phonons. Neither the perturbation theory is applicable for calculation of absorption in the frequency interval ?ω?_c or at temperature interval T?T_c = E_c/k.     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

Low-frequency behavior of optical spatial dispersion effects

A theoretical explanation is given for the frequency independence of the nonreciprocal birefringence of light, which was recently observed in the semiconductors Cd_1?x Mn_xTe, Zn_1?x Mn_xTe, and GaAs in the frequency range below the frequency corresponding to the interband absorption edge. It is shown that the symmetry of the effect becomes higher at such frequencies if the light-induced excitation energy ?ω_n(k) only slightly depends on the photon momentum k. In this case, the nonreciprocal birefringence is completely determined by the second-rank magnetoelectric tensor. It is shown that the nonreciprocal birefringence of light can be observed in magnetic media with a tensor order parameter.     

非晶态超导体的2△0/(kBTc)和声子谱参量

提出了能够很好地描述非过渡金属无序和非晶态超导体的2Δ₀/(k_BT_c)与声子谱参量之间关系的一个公式:2Δ₀(k_BT_c=4.95[1-(T₀<ω>^1/2)/A(1/(λω₀)+1/(20λ<ω>)+1/(20<ω>))]。计算了大量已知声子谱的非晶和无序超导体的能隙2Δ₀对T_c的比,结果表明在百分之几的范围内与实验值符合。指出了非过渡金属和合金的非晶态超导体,既可以是一个2Δ₀/(k_BT_c)值远大于BCS理论值(3.53)的强耦合超导体,也可以是一个2Δ₀/(k_BT_c)值比BCS理论值还要小得多的弱耦合超导体。 关键词：     

The ferroelectric mode in orthorhombic KNbO3

Both Raman scattering and infrared reflectivity measurements have been performed to determine the complete optic mode spectrum of orthorhombic KNbO₃ and characterize the ferroelectric modes. The low frequency, k ～ 0 mode is quasitransverse and possesses a spacial anisotropy similar to the TA branch at finite k. Of the original cubic ferroelectric mode, the component along the remaining soft direction is found at 56 cm^-1 and not overdamped (Γ/ω = 1), while the other two components have stiffened equally so that the mode is essentially isotropic in the orthogonal polarizations.