Boson peak in various random-matrix models

A so-called boson peak in the reduced density g(ω)ω² of vibrational states is one of the most universal properties of amorphous solids (glasses). It quantifies the excess density of states above the Debye value at low frequencies ω. Its nature is not fully understood and, at a first sight, is nonuniversal. It is shown in this work that, under rather general assumptions, the boson peak emerges in a natural way in very dissimilar models of stable random dynamic matrices possessing translational symmetry. This peak can be shifted toward both higher and lower frequencies (down to zero frequency) by varying the parameters of the distribution and the degree of disorder in the system. The frequency ω_b of the boson peak appears to be proportional to the elastic modulus E of the system in all cases under investigation.     

Phonons,Diffusons, and the Boson Peak in Two-Dimensional Lattices with Random Bonds

Within the model of stable random matrices possessing translational invariance, a two-dimensional (on a square lattice) disordered oscillatory system with random strongly fluctuating bonds is considered. By a numerical analysis of the dynamic structure factor S(q, ω), it is shown that vibrations with frequencies below the Ioffe-Regel frequency ω_IR are ordinary phonons with a linear dispersion law ω(q) ∝ q and a reciprocal lifetime б ~ q³. Vibrations with frequencies above ω_IR, although being delocalized, cannot be described by plane waves with a definite dispersion law ω(q). They are characterized by a diffusion structure factor with a reciprocal lifetime б ~ q², which is typical of a diffusion process. In the literature, they are often referred to as diffusons. It is shown that, as in the three-dimensional model, the boson peak at the frequency ωb in the reduced density of vibrational states g(ω)/ω is on the order of the frequency ω_IR. It is located in the transition region between phonons and diffusons and is proportional to the Young’s modulus of the lattice, ω _b ≃E.

     

The energy dependence of single particle spectra in e+e− annihilation

We present explicit predictions of the statistical bootstrap model for inclusive single particle spectra in e⁺e^? annihilation. The distribution (ω/σ_tot·E) (dσ/p² dp) is found to become, for E ? 3 GeV, a function only of the secondary energy ω, independent of the incident e⁺d^? energy E.     

High frequency cut-offs in superconductivity theory

The meaning of a high frequency cut-off for the Coulomb interaction at ±iω_max with ω_max ≈ E_f is investigated. It is not difficult to justify such a cut-off for nearly-free-electron metals. The real frequency Coulomb pseudopotential corresponding to the usual imaginary axis (μ¹, iω_c) pseudopotential is rigorously derived. It is markedly different from any assumed in previous work.     

On the relation between the Huang-Rhys number and properties of the host lattice

Experimentally observed Huang-Rhys numbers for Co²⁺ impurities in several zincblende type hosts correlate well with our theoretically predicted ω^-3_Da^-12 dependence (ω_D is the Debye frequency and a the lattice constant of the host).     

Double resonance interference in third-order light mixing

The first observation of interference effects between two sharp resonant contributions to the third-order nonlinear susceptibility χ₍₃₎ (ω₃=ω₀+ω₁?ω₂) is reported. Using two tunable near ir frequencies, ω₀=ω₁ and ω₂, the was seen in crystalline CuCl when 2ω₁ and ω₁?ω₂ were close to the sharp Z₃ exciton at 3.21 eV and the 210 cm^-1 Raman line, respectively. Three different tunable visible frequencies were used to observe similar interference effects in a benzene-cyclohexane mixture when ω₀?ω₂ and ω₁?ω₂ were close to the 992 cm^-1 Raman line of benzene and the 801 cm^-1 Raman line of cyclohexane, respectively.     

Nonlinear susceptibilities of vapors and solutions of organic dyes

Results of theoretical studies of laser and Kerr nonlinear susceptibilities of vapors and solutions of organic dyes using a series of polycyclic arenes as an example are presented. Nonlinear susceptibilities of the third χ⁽³⁾ (?3ω; ω, ω, ω) and the fifth χ⁽⁵⁾ (?3ω; ω, ω, ω, ω, ?ω) orders of a series of organic dyes responsible for third harmonic generation of Nd:YAG laser radiation are calculated within the context of the free electron model. Results of calculations of their Kerr third-order nonlinear susceptibilities χ⁽³⁾ (?ω; ω, ?ω, ω) and non-linear refractive indices n ₂ are presented. The calculation results are compared with experimental data on third harmonic generation in naphthalene vapors and with χ⁽³⁾ (?ω; ω, ?ω, ω) as well as n ₂ of paraterphenyl and naphthalene solutions.     

On the theory of Boson peak in glasses

A universal mechanism of the Boson peak formation in glasses is proposed. The mechanism is based on the concept of interacting quasilocal oscillators. Even in the case of weak interaction, the low-frequency spectrum becomes unstable. Due to anharmonicity, the system undergoes a transition into a new stable configuration. As a result, below some characteristic frequency ω_c, proportional to the typical strength of interaction, the renormalized density of states becomes a universal function of ω with a Boson peak feature; i.e., the reduced density of states g(ω)/ω² has a maximum at a frequency ω_b?ω_c. We derive an analytic form of this function.     

Feldgleichungen der TREDERschen Gravitationstheorie,die aus einem Variationsprinzip ableitbar sind. I

In the frame work of TREDER 's gravitational theory we consider two classes of field equations which are derivable from two classes of LAGRANGE ian densities Ω⁽¹⁾(ω₁, ω₂), Ω⁽²⁾(s?₁, s?₂). ω₁, ω₂; s?₁, s?₂ are parameters. Ω⁽²⁾(ω₁, ω₂) gives us field equations which are up to the post-NEWTON ian approximation in the sense of NORDTVEDT , THORNE and WILL equivalent to the field equations given by BRANS and DICKE . For ω₂ = ?1 ?2ω₁ field equations follow from Ω⁽¹⁾(ω₁, ?1 ?2ω₁) which are in the above mentioned sense of post-NEWTON ian approximation equivalent to EINSTEIN 's equations. The field equations following from Ω⁽¹⁾(ω₁, ω₂) have a cosmological model with the well known cosmological singularities for T → ± ∞ in case that ω₁/(1 +3ω₁ +ω₂) ? γ > 0. For ω₁/(1 +3ω₁ +ω₂) ≤ 0 cosmological models with no cosmological singularities exist. From Ω⁽²⁾(s?₁, s?₂) we obtain field equations which at the best give us perihelion rotation 7% above EINSTEIN 's value and light deflection 7% below the corresponding EINSTEIN 's value. But in that case we are able to show the existence of a cosmological model without any cosmological singularity.     

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.     

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.     

Optical mixing in InSb

Abstract

In this paper, the authors have derived the expression for the combination frequency components ω₃ = 2ω₁-ω₂ in the current density by solving the appropriate Boltzmann transfer equation for electrons, when two laser beams of frequencies of ω₁ and ω₂ are incident on a degenerate nonparabolic semiconductor viz. InSb; the nonlinearity due to collision mechanism as well as the nonparabolicity of conduction band has been taken into account. The ionized impurity scattering has been considered to be the sole mechanism of electron scattering. The expression for the current density is further substituted in the wave equation to obtain the expression for the amplitude of combination frequency wave in the transmitted component. The calculated value of output power of frequency ω₂ is found to be 1/10th of the experimental value (Patel, Slusher and Fleury, 1966), ⁽⁷⁾ and thus is in better agreement as compared to earlier investigators (Wolff and Pearson, 1966; Kaw, 1968). ^{(5, 10)}     

Plasmons in semiconductors and insulators: A simple formula

Based on the dielectric function of an excitonic system, a simple model dielectric function is constructed. The high energy zero of this function yields the plasma frequency, and is given by: (hω_x)² = (hω_f)² + E_x² where ω_f is the free electron plasma frequency and E_x the lowest exciton energy. It is argued that this formula is valid for both, Frenkel and Wannier excitons, and comparison is made with experiments on a variety of crystals, ranging from InSb to Ar. In all cases, surprisingly good agreement is found.     

Low-frequency dispersion of the effective transverse conductivity in inhomogeneous media in strong magnetic field

On crystalline silicon specimens with a nonuniform carrier concentration distribution produced by an optical method, a dispersion of the effective transverse conductivity σ _⊥ ^eff (ω) is observed near the frequency ω≈ω_c=τ _⊥ ^?1 ≡ε/4πσ _⊥ ^eff . At ω<ω_c, an anomalous transverse effective conductivity is observed: σ _⊥ ^eff (ω) is greater than the transverse conductivity of a homogeneous specimen σ _⊥ ^h (ω) (in the frequency range studied in the experiment σ _⊥ ^h (ω) = const). Near ω≈ω_c, the conductivity σ _⊥ ^eff decreases, and, at ω>ω_c it coincides with σ _⊥ ^h .     

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：     

强近共振激光脉冲驱动下二能级系统中试探脉冲的瞬态反应

我们用缀饰模型研究强近共振激光脉冲驱动下二能级系统与弱试探脉冲的相互作用。当试探脉冲的频率ω₂调到共振频率ω₂=ω₁±<Ω₂₁^D>时,试探脉冲呈现吸收或放大效应。还得到非线性混频效应的瞬态过程。共振增强存在于此非线性混频过程中。 关键词：     

高频引力波对环形波导中电磁波的调制作用

讨论了垂直入射的、频率为ω_g的平面高频引力波对环形波导管中频率为ω_e的电磁波的调制作用．一般情况下，在波导管中与引力波传播方向垂直的对称平面附近，电磁波的能流密度会出现三种新的频率成分（2ω_e±ω_g）和ω_g．在ω_g》ω_e时，能流密度振幅的相对调制量与引力波的无量纲振幅h₀数量级相同．特别是当ω_g，ω_e和电磁波绕波导传播的绕行频率ω₀满足关系ω_g＝2ω_e》ω₀时，由于类似于共振的机制，能流密度会出现比h₀大几个数量级的振幅相对调制量．这个结果不会由于参数的微小改变而消失，这对于探测极微弱的引力辐射信号将是十分重要的 关键词：     

Photoinduced infrared activity in trans(CH)x: Inter[retation in terms of a lattice dynamical model

A lattice dynamical calculation for the photoinduced infrared vibrational modes is reported. By using the perturbed Green function method we have been able to compute the new frequencies and the integrated intensities of the photoinduced infrared modes at ω_1H⋍500 cm⁻¹, ω_2H⋍1260 cm⁻¹ and ω_3H⋍1370 cm⁻¹ in trans(CH)_x and at ω_1D⋍400 cm⁻¹ and ω_2D⋍1045 cm⁻¹ in trans(CD)_x. Most of the features of the photoinduced infrared spectra can be explained in terms of long conjugation length segment properties. Only the higher frequency tail of the band shape peaked at ω_1H and ω_1D can be related to the pertubbation determined by a photogenerated charge trapped in short segments. The calculated frequencies and integrated intensities are in good agreement with the experimental results.     

无序层状系统电导率的自洽研究

本文运用无序层状系统模型模拟无序超晶格的性质,根据β-S方程,在弱局域限,给出了动力学密度响应函数x(q,ω),并由x(q,ω)求得了平行和垂直于平面的电导率和局域化长度的表达式,导出了依赖于频率ω的扩散系数D_k(ω)的自洽方程,并进行了讨论。 关键词：     

Spin susceptibility of cuprates in the model of a 2D frustrated antiferromagnet: Role of renormalization of spin fluctuations in describing neutron experiments

Experimental data on the spin susceptibility of HTSC cuprates are reproduced on the basis of a spherically symmetric approach in the frustrated Heisenberg model. The inclusion of real and imaginary renormalizations in spin Green’s functions makes it possible to explain the evolution of spin excitation spectrum ω(q) and susceptibility spectrum χ(q, ω) in the range from insulator to optimal doping. In the low-frustration limit corresponding to the weakly doped mode, the saddle singularity of ω(q) and scaling of χ_2D(ω) =∫d q Im χ(q, ω) are reproduced and an analytic expression is derived for the scaling function. In the strong frustration (optimal doping) mode, the stripe scenario is demonstrated; this leads to a peak of χ_2D (ω) in the region of ω～60 meV.