The sensitivity of the transition temperature to changes in α2 F(ω)

The transition temperature of a superconductor depends on α² F(ω), the spectral function of the effective interaction due to phonon exchange. We discuss how strongly the transition temperature is influenced by different frequency parts of α² F(ω). For this purpose the functional derivative δT _c /δα² F(ω) is calculated. It is shown that all frequency regions of α² F(ω) yield a positive contribution toT _c and that the most effective range covers frequencies, slightly above 2πT _c . The functional derivative is calculated numerically for several superconductors from their measured α² F(ω)-spectra. Finally, we discuss the change in transition temperature due to the softening of α² F(ω) which has been observed in amorphous superconductors.     

KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

Phase transitions of sulfur at high pressure: Influence of temperature and pressure environment

Abstract

Phase transitions of orthorhombic sulfur were investigated above 10 GPa by Raman spectroscopy using red light excitation. Transitions into several phases that have been reported in previous studies using green light excitation, are confirmed. The phase behaviour is observed to depend strongly on the preparation method. In the presence of a pressure transmitting medium (methanol/ethanol, 4:1), a sequence of phases α-S₈ → [intermediate phase (“ip”) + S₆] → [S₆ + high pressure-low temperature phase (“hplt”)] is described and characterized. Without the use of a pressure transmitting medium, the phase sequence α-S₈ → [“ip” + “hplt”] + “hplt” is observed. In addition, contributions of amorphous sulfur are detected around 10 GPa, i.e. at pressures below the transformation of α-S₈ into the above-mentioned phases. Characteristic Raman spectra of the different phases are extracted and documented over a wide pressure range.     

The oscillator frequency in resonating-group-method calculations

For the example α-¹⁶O we present simple RGM calculations with equal (ω = ω′) and different (ω ≠ ω′) oscillator frequencies for the two nuclei. In the case ω ≠ ω′ and ω → ω′ the one-channel RGM space for angular momentum zero contains all ²⁰Ne states with four particles in the s-d shell and total spatial symmetry ($\text{[?] = [4]}$). These states form a basis for low-lying excited 0⁺ states of ²⁰Ne. The ω ≠ ω′ calculation (as well for ω → ω′ as for realistic ω, ω') exhibits, therefore, resonances corresponding to these states. We present also the calculation for ω = ω′ where these physically important resonances are missing.     

Direct measurement of the electron-phonon interaction in Pd,Mo and W by point-contact spectroscopy

The point-contact electron-phonon interaction function α²F has been obtained for the three transition metals Pd, Mo and W. The measured^Pα²F_p-spectra show clear structures which are in agreement with characteristic features in the phonon densities of states and calculated α²(ω)F(ω)-spectra.     

超导临界温度理论(Ⅰ)

本文求出了Eliashberg方程在T=T_c时的解,得到了下面的临界温度级数表示式:T_c=α₀(μ^*)(λ〈ω²〉)^1/2{1+1/λα₁(μ^*)〈ω⁴>/〈ω²>²+1/λ²(α₂₁(μ^*)〈ω⁶>/〈ω²>³+α₂₂(μ^*)〈ω⁴>²/〈ω²>⁴) +1/λ³(α₃₁(μ^*)〈ω⁸>/〈ω²>⁴+α₃₂(μ^*)(〈ω⁴>〈ω⁶>)/〈ω²>⁵)+α₃₃(μ^*)〈ω⁴>³/〈ω²>⁶+…},其中α₀(μ^*),α₁(μ^*)等仅是μ^*的函数。新的T_c公式表明了,T_c不仅依赖于λ、μ^*和〈ω²〉,而且依赖于有效声子谱α²F(ω)的各级矩〈ω²ⁿ〉。     

First-principles study of structural,elastic, electronic and optical properties of RDX under pressure

ABSTRACT

The influences of pressure on structural, elastic, electronic and optical properties of α-RDX under pressure from 0 to 40?GPa have been investigated by performing first-principles calculations. The obtained structural parameters based on the GGA-PBE+G calculations are consistent with previous experimental values. The results of B/G, C₁₂-C₄₄ and Poisson's ratio show that α-RDX has changed to ductility under pressure between 0 and 5?GPa. The obvious rotation of NO₂ group in the equatorial position appears, especially in the range of pressure from 10 to 15?GPa, which influences the elastic and mechanical properties of α-RDX. Moreover, we find that the electrons of α-RDX become more active under higher pressure by comparing the curves of DOS under different pressure. Furthermore, the anisotropy of optical properties under different pressures has been shown.     

Theoretical study of the stereodynamics for the reaction F+HBr

The vector correlation between products and reagents for exothermic reaction F + HBr → HF + Br has been studied using a quasi-classical trajectory (QCT) method on the latest extended Lond–Eyring–Polanyi–Sato (LEPS) potential energy surface at three collision energies of 0.1 eV, 0.2 eV and 0.3 eV. Four polarization- dependent generalized differential cross-sections (2π/σ)(dσ₀₀/dω _t ), (2π/σ)(dσ₂₀/dω _t ), (2π/σ)(dσ₂₂₊/dω _t ), (2π/σ)(dσ_21?/dω _t ) have been presented in the centre of mass frame, respectively. The distribution of dihedral angle P(φ _r ), the distribution of angle between k and j ′ , P(θ _r ), are calculated. Both the influence of the collision energy and the influence of the reagent rotation on the product polarization have been studied in the present work, and the results indicate that the product rotational angular momentum j ′ is not only aligned, but also oriented along the direction perpendicular to the scattering plane. The orientation of the HF product rotational angular momentum vector j ′ depends very sensitively on the reagent rotation and also effected by the collision energy.     

Liquidity crisis, granularity of the order book and price fluctuations

We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity g) as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume ω and g. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function 〈φ(ω,g)〉_g～ω^δ with δ≈0.59. Instead the dependence on the granularity is φ(ω,g|ω)～g^α with α≈-1, showing a divergence of price fluctuations in the limit g→0. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.     

Electron-phonon coupling and phonon generation in normal-metal microbridges

The second derivative of current—voltage characteristic, $\text{d}{}^2\text{I}\text{d}\text{V}{}^2$, of a small orifice connecting two pieces of normal metals is shown to be proportional to the function $\text{G(ω) =}\text{α}\text{?}{}^2\text{(ω)F(ω)}$ at ω = eV, where F(ω) is the phonon density of states, and α̃² (ω) the square of the electron—phonon matrix element averaged over the Fermi surface and multiplied by the additional structure factor taking into account the geometry of the orifice. The constriction is shown to work, in a current-carrying state, as a source of non-equilibrium phonons emitted in the immediate vicinity of the orifice.     

超导临界温度理论(Ⅲ)

本文定出超导临界温度T_c级数公式(1)的前几项系数。对于形式为α²F(ω)=(λω)/2[a₁δ(ω-ω₁)+(1-a₁)δ(ω-ω₂)]的双δ型有效声子谱及若干具体材料的谱,将级数公式计算的T_c与Allen-Dynes公式(以下简称A-D公式)及Eliashberg方程的数值解作了比较。计算表明,当级数(1)收敛时,级数公式计算的结果较A-D公式更接近于数值解。此外,本文还给出了一个近似的T_c级数公式,得到了估计该T_c级数收敛半径的方法,并计算了若干材料的收敛半径值。因此,可估计级数公式(1)的适用范围。 关键词：     

Influence of pressure on electronic and optical properties of phosphorus-doped ZnO

In this work, the geometrical, electronic structure and optical properties of P-doped ZnO under high pressures have been investigated using first-principles methods. The pressure effects on the lattice parameters, electronic band structures, and partial density of states of crystalline P-doped ZnO are calculated up to 8 GPa. Moreover, the evolution of the dielectric function, absorption coefficient (αω)), reflectivity (R(ω)), and the real part of the refractive index (n(ω)) at high pressure are also presented.     

Enhancement of low energy phonon structure by high energy spectral weight

We have investigated the effect on the tunneling characteristics of adding weight to the electron phonon spectral density α²((ω)F(ω) at an energy ω_E well above its cut off ω_D. This not only adds structure in the current (I) as a function of voltage (V) at ω_E but more importantly enhances the structure below ω_D although no addition to the strength of the spectral density is made in that region.     

Electron-phonon relaxation time in mercury

Electron scattering times determined by Azbel'-Kaner cyclotron resonance in mercury are discussed in terms of the electron-phonon interaction. Anisotropy in the electron-phonon relaxation time is explained in terms of an orbital α _k ² (ω)F _k (ω) function which describes the electron-phonon interaction and the phonon spectrum. AT ⁵ temperature dependence of the electron-phonon relaxation frequency is also considered.     

Semiconducting properties of refractory oxides systems

Abstract

The electrical conductivity and thermoelectric power of pure and doped oxides system La₂O₃-Cr₂O₃-Al₂O₃ were investigated. Only single phase was observed in the compositions studied (20 atom fraction of aluminium).

The conductivity increases with increasing chromium content in the range of compositions studied, the values ranging from 10^?4 (ω-cm)^?1 to 1. 2 × 10^?1(ω-cm)^?1. In the case of samples doped with calcium (0. 01) the corresponding values range from 2 × 10^?1 (ω-cm)^?1 to 1. 67(ω-cm)^?1. The significance of the results has been discussed.     

Omega phase of zirconium: Formation under shock wave compressin and stability at atmospheric pressure

Abstract

The structure of Zr after shock compression in the 8–32 GPa range at initial tempertures 290 K and 90 K has been investigated by X-ray diffraction and transmission electron microscopy. ω-phase fraction vs. peak pressure and crystallographic relationship between α- and ω-phases have been obtained. A dilatometric study of Zr samples containing ω-phase has been performed.     

The optical properties of expanded liquid cesium

Abstract

The density dependence of the optical properties of expanded cesium has been investigated by means of reflectivity measurements in the range 0.5 – 4.0 eV. The dielectric functions ?₁ (ω) and ?₂(ω) have been derived by means of a modified Kramers-Kronig analysis. The data give useful information about the variation of the electronic structure of liquid cesium with large changes in density, large enough to reveal the existence of precursors of the metal-nonmental transition.     

Surface-Enhanced Hyper-Raman Spectroscopy

Abstract

Hyper-Raman scattering (HRS), first theoretically predicted by Decius and Rauch in 1959 [l] and experimentally demonstrated by Terhune et al. in 1965 [2], is a nonlinear optical process involving two incident photons (ω₀) and one emitted photon (ω). The emitted hyper- Raman photon frequencies are Raman-shifted relative to the second harmonic frequency (2ω₀) of the incident laser radiation [3–6]. The energy difference (2ω₀ – w) corresponds to one of the characteristicvibrational frequencies of the scattering medium or molecule. In Fig. 1 is given a schematic illustration of resonant and nonresonant HRS. The primary advantage of this nonlinear optical technique lies in its more relaxed selection rules compared with IR and Raman [7,8]. AlllR-active vibrational modes are hyper-Raman allowed, and those modes inactive in both IR and Raman (i.e., the “silent” modes) may be active in hyper-Raman scattering.     

“Negative” gap in the spectrum of localized states of (In<Subscript>2</Subscript>O<Subscript>3</Subscript>)<Subscript>0.9</Subscript>(SrO)<Subscript>0.1</Subscript>

The reflection R(?ω), transmission t(?ω), absorption α(?ω), and refraction n(?ω) spectra of polycrystalline In₂O₃–SrO samples with low optical transparency, which contain In₂O₃ and In₂SrO₄ crystallites with In₄SrO_{6 + δ} interlayers, are examined. In the region of small ?ω values, the reflection coefficient decreases as the resistance of samples saturated with oxygen increases. Spectral dependences n(?ω) and α(?ω) are calculated using the classical electrodynamics relations. The results are compared to the data based on the t(?ω) spectra. The calculated absorption spectra are interpreted within the model with an overlap of tails of the density of states in the valence band and in the conduction band. A “negative” gap E _gn in the density of states with a width from–0.12 to–0.47 eV is formed in highly disordered samples in this model. It is demonstrated that the high density of defects and the band of deep acceptor states of strontium in the major matrix In₂O₃ phase are crucial to tailing of the absorption edge and its shift toward lower energies. The direct gap E _gd = 1.3 eV corresponding to the In₂SrO₄ phase is determined. The energy band diagram and the contribution of tunneling, which reduces the threshold energy for interband optical transitions, are discussed.     

The upper critical field of quenched condensed Sn,Tl, In and Hg with extremely short mean free path

Quenched condensed films of Sn, Tl, In and Hg are fine crystalline and have very short mean free path. The upper critical field of these disordered superconductors is measured. The initial slope,dB _c 2/dT is compared with a strong coupling calculation. We use α² F(ω) which is measured for these superconductors in the pure state and for Sn in the quenched state. The strong coupling behavior enhances the upper critical field by 15–20%. We find a fair (about 10%) agreement between the experimental and theoretical values ofdB _c 2/dT except for Hg. In Hg one has either to consider band structure effects or the α² F(ω) of quenched condensed Hg is quite different from that of pure Hg.