Estimation of the influence of ionic dielectricity on the dynamic superconducting order parameter

We consider the influence of an ω-dependent ionic dielectric constant ?(ω) on the properties of a superconductor. Assuming that the pairing interaction is proportional to ?² we have solved the Eliashberg equations for this case, both for imaginary and real frequencies. The interaction potential depends on a coupling constant λ and on a longitudinal phonon frequency Ω. The dielectric constant is assumed to be independent of wavevector q, and to depend on frequency through the expression: ?(ω) = (ω² - ω²_long)/(ω² - ω²_trans), where ω_long, ω_trans are the frequencies of optical phonons of the dielectric. We find that along the imaginary frequency axis (but not for real frequencies) the weighted phonon propagator can be modeled by an appropriate choice of a cutoff frequency and an effective coupling constant. The influence of ?(ω) on T_c, the gap δ(ω), and the renormalization function Z(ω) are studied and it is found that these quantities increase significantly with the dielectric constant.     

Diffusion of vibrations in disordered systems

We consider diffusion of vibrations in random lattices with translational invariance. Above the frequency ω_IR corresponding to the Ioffe-Regel crossover (and depending on the strength of disorder), phonons cannot propagate through the lattice and transfer energy. At the same time, most of the vibrations in this range are not localized. We show that these delocalized excitations are similar to diffusons introduced by P. B. Allen, J. L. Feldman, J. Fabian, and F. Wooten (see, e.g., Phil. Mag. B 79, 1715 (1999)) to describe heat transport in glasses. In this range the energy in the lattice is transferred by means of diffusion of vibrational excitations. We have calculated the diffusivity of the modes D(ω) using both the direct numerical solution of Newton equations and the Edwards-Thouless formula. It is nearly constant above ω_IR and goes to zero at the localization threshold.     

On the low-temperature thermal conductivity of Ni-doped Al2O3

An attempt is made to explain the lower resonance anomaly in the thermal conductivity of Ni-doped Al₂O₃ by using τ_r ～ ω^-4s(ω² ? ω²_r)². An agreement between theory and experiment needs s = 0.71, and this is interpreted to mean that the frequency dependence of impurity-phonon coupling is approximately described by ω^0.71 for phonons having frequencies in close neighbourhood of ω_r.     

Study of complex refractive indices of gold and copper using emissivity measurements

We show from emissivity measurement that it is possible to determine the complex refractive index for smooth and opaque materials.⁽¹⁾ Moreover, for noble metals, Drudes's completed model can be used;⁽²⁾ thanks to the variations of the complex index as a function of the wavelength the; values of the plasma and relaxation frequency for conduction electrons (ω_p and ω_τ) respectively can be determined; First, we have shown how emissivity measurements can lead to values of (ω_p and ω_τ) (this study has been carried out on copper). Then we have computed deduced and determined a general dispersion formula as a function of temperature and frequency for, using gold for the experiments because of its chemical stability. Variation of zero frequency relaxation frequency with temperature due to interaction between conduction electrons and phonons matches Debye's model well,⁽³⁾ as has been verified. Relaxation frequency increases with the square of the radiation frequency, this behaviour due to interactions between conduction electrons had been described by Gurzhi,⁽⁴⁾ and verified. With the chosen model we are able to describe macroscopic properties of the emission radiation in the given range of temperature and wavelength with minimum requirement of parameters.⁽⁵⁾     

Singlet—triplet oscillations of spin-correlated radical pairs due to the Larmor precession in low magnetic fields

Singlet—triplet oscillations in spin-correlated radical pairs have been studied at magnetic field strengths low for one radical and high for the other. Oscillations with frequencies close to the Larmor frequency ω₀ of electron spin precession have been predicted under these conditions. Both numerical and exact analytical solutions in arbitrary magnetic fields are presented for three cases of hyperfine couplings in wide-spectrum radical. For the case of unresolved spectrum, singlet—triplet evolution was found to contain a single oscillating term with frequency ω₀. In the case of one spin-I magnetic nucleus, there are two low frequency oscillating terms with frequencies ω_? = ω₀ ? ω₀/(2I + 1) and ω₊ = ω₀ + ω₀/(2I + 1), the amplitude of the first term being larger than that of the second. The case of a number of equivalent protons also has been analysed as a superposition of one-nucleus oscillations. The predicted oscillations were observed in a time resolved magnetic field effect for several radical ion pairs produced by X-ray irradiation of alkane solutions with charge acceptors. For pairs (p-terphenyl-d ₁₄)^?./(isooctane)^+. and (p-terphenyl-d ₁₄)^?./(2,4-dimethylpentane)^+. the oscillation frequency in a field B ₀ of 0.5–4mT is about 20% lower than ω₀. Oscillations were observed also in pairs with equivalent nuclei: (p-terphenyl-d ₁₄)^+./(C₆F₆)^?. and (p-terphenyl-d ₁₄)^?./(hexamethylethane)^+.     

Experimental studies of optical surface excitations

Experimental methods for optical excitation of nonradiative surface waves, such as surface plasmons and surface phonons, are reviewed. Results for surface plasmons in InSb obtained by using samples with line gratings in the surface and by using the technique of attenuated total reflection (ATR) are compared. Best agreement between the theoretical and experimental surface plasmon dispersion curve ω(k) of InSb is found when using excitation by ATR, since the sample surface need not be disturbed in this case. Surface phonons have been excited optically by applying ATR to alkali halide crystals and to the polar semiconductor GaP. While agreement with the theoretical dispersion curve is extremely good for GaP and also for CaF₂, there are systematic deviations to lower frequencies for NaF and other alkali halides. In polar semiconductors the free carrier plasmon couples to the LO-phonon when ω_p ≈ ω_LO. This behaviour has been investigated theoretically and experimentally for the surface modes. For an interesting application of the ATR-technique, one can use the fact that dispersion and linewidth are a direct measure of the complex dielectric function ε(ω) in the frequency range of the optical surface waves.     

High frequency sound and the boson peak in amorphous silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, i.e. for frequencies ν > 0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J _l(q,ν) and J _t(q,ν), the longitudinal and transverse current correlation function, respectively. For wave-vectors q > 0.4 ?^-1 the spectra are sitting on top of a flat background. The dynamic structure factor S(q,ν) exhibits for q > 0.23 ?^-1 a boson peak which is located nearly independent of q around 1.7 THz and for which the intensity scales approximately linearly with temperature. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q = 1.7 ?^-1, the location of the first sharp diffraction peak in the static structure factor. By studying S(q,ν) for different system sizes we show that strong finite size effects are present in the low frequency part of the boson peak in that for small systems part of its intensity is missing. We discuss the consequences of these finite size effects for the structural relaxation. Received 27 June 2000 and Received in final form 9 January 2001     

Physical applications of inhomogeneous quantum groups

It is shown that the real formE _q (1, 1) is the kinematical symmetry of phonons. It is also indicated how a quantum symmetry works in the non-relativistic 1D lattice systemsPresented at the Colloquium on the Quantum Groups, Prague, 18–20 June 1992.     

Parametric Excitation of Plasma instabilities by two Monochromatic Pump waves

The dispersion characteristics of a plasma in a pump field ??(t) = ?? sub ω₀t + ??₁ sin ω₁t are considered. Firstly we assume, that the second wave is weak (|??₁| ? |??₀|) and the frequency ω₁ is near sω₀(ω₁ = sω₀ + Ω,Ω ? ω₀). We obtain the dispersion equation, describing the parametric coupling of the waves driven by the strong field ??₀ sin ω₀t under the resonance condition ω₀ ≈ ω_Le/P and derive the expressions for the growth rates (ω_Le is the electron LANGMUIR frequency; s, p are integers). In the second part it is shown, that a strong field ??₁ with a frequency ω₁ much larger than ω _Le(ω _Le ≈ pω₀) stabilizes the plasma; the growth rates are reduced and the frequency region of the parametric instability is contracted.     

Damping of optical phonons in metals and strongly doped semiconductors

The electron-phonon-induced damping of optical phonons arising in metals and strongly doped semiconductors under laser irradiation is investigated. The damping of both short-wave KV_F > ω₀ and long-wave KV_F < ω₀ optical phonons is calculated; K is the wavevector, ω₀ is the frequency of the optical phonon; V_F is the Fermi velocity. The electron- phonon-induced damping is important if the frequency of the optical phonon is larger than two frequencies of acoustic phonons of all branches in the range of the whole Brillouin zone. The damping of a soft transverse optical phonon in narrow-gap ferroelectric-semiconductors is also defined by the electron-phonon interaction. In other cases the main relaxation process for optical phonons in metals is the decay into two acoustic phonons due to lattice anharmonicity.     

Electron in the field of flexural vibrations of a membrane: Quantum time,magnetic oscillations,and coherence breaking

We have studied the motion of an electron in a membrane under the influence of flexural vibrations with a correlator that decreases upon an increase in the distance in accordance with the law r–^2η. We have conducted a detailed consideration of the case with η < 1/2, in which the perturbation theory is inapplicable, even for an arbitrarily weak interaction. It is shown that, in this case, reciprocal quantum time 1/τ_q is proportional to g^1/(1–η)T^{(2–η)/(2–2η)}, where g is the electron–phonon interaction constant and T is the temperature. The method developed here is applied for calculating the electron density of states in a magnetic field perpendicular to the membrane. In particular, it is shown that the Landau levels in the regime with ω_cτ_q » 1 have a Gaussian shape with a width that depends on the magnetic field as B^η. In addition, we calculate the time τ_φ of dephasing of the electron wave function that emerges due to the interaction with flexural phonons for η < 1/2. It has been shown that, in several temperature intervals, quantity 1/τ_φ can be expressed by various power functions of the electron–phonon interaction constant, temperature, and electron energy.     

Density of states in random lattices with translational invariance

We propose a random matrix approach to describe vibrations in disordered systems. The dynamical matrix M is taken in the form M = AA ^T , where A is a real random matrix. It guaranties that M is a positive definite matrix. This is necessary for mechanical stability of the system. We built matrix A on a simple cubic lattice with translational invariance and interaction between nearest neighbors. It was found that for a certain type of disorder acoustical phonons cannot propagate through the lattice and the density of states g(ω) is not zero at ω = 0. The reason is a breakdown of affine assumptions and inapplicability of the macroscopic elasticity theory. Young modulus goes to zero in the thermodynamic limit. It reminds of some properties of a granular matter at the jamming transition point. Most of the vibrations are delocalized and similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999). We show how one can gradually return rigidity and phonons back to the system increasing the width of the so-called phonon gap (the region where g(ω) ∝ ω²). Above the gap the reduced density of states g(ω)/ω² shows a well-defined Boson peak which is a typical feature of glasses. Phonons cease to exist above the Boson peak and diffusons are dominating. It is in excellent agreement with recent theoretical and experimental data.     

Collective excitations of the polaron-gas

The dispersion of the collective excitations of a polaron-gas is calculated. It is found that the interaction between the L.O. phonons and the plasmons induces a relatively strong wave vector dependence in the ω⁺, ω^- modes. This dispersion is primarily a consequence of the interaction of the L.O. phonons with the resonant plasmon branch in the pair excitation spectrum.     

固态核磁共振半整数四极体系中心跃迁对梳状脉冲的响应

半整数四极核的中心跃迁对梳状脉冲序列的响应随四极常数ω_q而变化。在梳伏脉冲的平均射频汤强度ω_e(以弧度·秒^-1为单位)满足ω_q/ω_e<1/5时,测量中心线所得的谱,位于频率ω_e/2π处;而当ω_q/ω_e>2时,所得的谱线在2ω_e/2π处,理论计算与实验结果是一致的。本文得到的结论表明,梳状脉冲序列将可能成为研究这 关键词：     

Far-infrared reflection spectra,TO- and LO-phonon frequencies,coupled and decoupled plasmon-phonon modes,dielectric constants,and effective dynamical charges of manganese,iron, and platinum group pyrite type compounds

The far-infrared reflection spectra of hot-pressed samples of the pyrites MX₂ with M = Mn, Fe, Ru, and Os and X = S, Se, and Te and PtY₂ with Y = P, As, and Sb are presented in the range from 40 to 700 cm^?1. The spectra show five reststrahlen bands and more or less free carrier contributions due to deviation from stoichiometry. The oscillator parameters ω_j, ρ_j, γ_j, ω_p, and γ_o, the transverse optical phonon frequencies ω_TO, and the coupled plasmon-phonon frequencies Ω₊ and Ω_? were calculated. The uncoupled longitudinal optical phonon frequencies ω_LO were determined from ?Im $\text{(}\text{1}\text{}\text{?}\text{ge}\text{)}$ of the plasmon-free phonon spectra calculated from the oscillator parameters, neglecting the free carrier contributions. The obtained effective ionic charges (Szigeti charges) reveal an increasing covalency of the pyrites in the order pnictides > chalcides and Fe > Ru > Os > Mn compounds. The phonon frequencies reflect the increasing bond strengths on going from 3d to 4d and 5d metal compounds, discussed in a former work (Phys. Chem. Miner.9, 109 (1983)). The true intensities of the phonon modes for using them with respect to lattice dynamical calculations are discussed.     

What can we learn about critical magnetic phenomena from muon spin rotation experiments?

Measurements of the spin precession frequencies ω_μ and transvers relaxation rates Γ₂ of positive muons (μ⁺) magnetic phase of several iron-cobalt alloys and coabalt, and in amorphous Fe_o.91Zr_0.09 alloys are discussed with particular reference to the influence of critical phenomena on ω_μ and Γ₂. Although the temperature dependence ω_μ(T) is well described by scaling law ω_μ ∝ (T_c?T)^β′ where α′ varies strongly with the co concentration in the FeCo alloys, it is shown that the exponent α′ is not identical to the static scalling parameter β describing the critical behaviour of the spontaneous magnetization M. In paramagnetic iron we find Γ₂∝(T-T_c)^0.72, which is attributed to the effect of dynamical spin fluctuations on the μ⁺. Due to the apparent difference between the temperature dependence of ω_μ and that of M below T_c the frequency shifts observed in the paramagnetic regime are probably not directly proportional to the magnetic susceptibility. In amorphous Fe_0.91Zr_0.09 allosy frequency shifts and transverse relaxation rates are found up to nearly 2 T_c. Due to the shape of the Fe_0.91Zr_0.09 sample, demagnetization inhomogeneities certainly play an important rôle.     

Molecular motion in supercooled glycerol

Quasi-elastic Rayleigh scattering of 14·4 keV photons has been measured on supercooled liquid glycerol at -30°C and 0°C by employing the Mössbauer effect. Total scattered intensity, quasi-elastically scattered intensity I _q and energy width of I _q(k, ω) have been determined for k=0·6 to 4·2 Å^-1. The molecular motion is modelled as: random-walk diffusional motions for the centre-of-mass translation and for the orientation of independent rigid molecules, plus fast-bounded translational jitter (vibration). The model parameters are evaluated. The temperature dependence of the translational diffusion constant corresponds to an activation energy of 12 kcal/mol. Comparison is made especially with N.M.R. results for rotational motion. The effect of orientational jitter (libration) is considered and its possible influence on nuclear magnetic relaxation is pointed out.     

INFLUENCES OF NONLINEAR INTERACTIONS ON POLARITONS

In this paper, we have analysed theoretically the polarization and dielectric constant generated by the nonlinear interactions between ions in ionic crystals. The spectrum of polaritons (coupling modes of photons and optical phonons) under nonlinear interactions has been developed. A new branch of dispersion relations has emerged in the original frequency gap between ω_TO and ω_LO.     

Spatial-temporal dispersion of the kinetic coefficients near the Anderson transition

A generalization of the Vollhardt-Wölfle localization theory is proposed to make it possible to study the spatial-temporal dispersion of the kinetic coefficients of a d-dimensional disordered system in the low-frequency, long-wavelength range (ω?_F and q?k _F ). It is shown that the critical behavior of the generalized diffusion coefficient D(q,ω) near the Anderson transition agrees with the general Berezinskii-Gor’kov localization criterion. More precisely, on the metallic side of the transition the static diffusion coefficient D(q,0) vanishes at a mobility threshold λ _c common for all q: D(q, 0)∝t=(λ _c ?λ)/λ _c →0, where λ=1/(2π?_F τ) is a dimensionless coupling constant. On the insulator side, q≠0 D(q,ω)∝?iω as ω→0 for all finite q. Within these limits, the scale of the spatial dispersion of D(q,ω) decreases in proportion to t in the metallic phase and in proportion to ωξ ², where ξ is the localization length, in the insulator phase until it reaches its lower limit ～λ _F. The suppression of the spatial dispersion of D(q,ω) near the Anderson transition up to the atomic scale confirms the asymptotic validity of the Vollhardt-Wölfle approximation: D(q,ω)?D(ω) as |t|→0 and ω→0. By contrast, the scale of the spatial dispersion of the electrical conductivity in the insulator phase is of order of the localization length and diverges in proportion to |t|^?v as |t|→0.     

Phonon dispersion in AgBr and exchange of the transverse mode Eigenvectors at L

Using inelastic neutron scattering, phonon dispersion curves for AgBr at 85 K are measured along the 〈100〉, 〈110〉 and 〈111〉 directions in reciprocal lattice. Special attention is payed to the anomalous behaviour of the TA and TO branches at the L-point (0.5; 0.5; 0.5). With high resolution (Δv = 0.24 THz) their frequencies are determined to be 1.54 and 1.93 THz, respectively. The ratio of their integrated intensities is found to be 2.15 ± 0.4. This value is in good agreement with the ratio of 2.38 calculated under the assumption that at L the heavier (Ag⁺) ions is vibrating with the higher and the lighter (Br^-) ion with the lower frequency, as suggested by recent lattice dynamical calculations. Comparison of our phonon frequencies with corresponding optical data prove that the momentum-conserving phonons associated with the lowest indirect exciton transition belong to the TO and LA phonon branches at L. Since the lowest conduction band minimum at Γ is well established experimentally, our results in turn imply that the uppermost valence band maximum is right at the L-point.