The anomaly of the specific heat of La2-xSrxCuO4+δ near Tc

The specific heat of three polycristalline samples of La_2-xSr_xCuO_4+δ (x = 0.15, 0.15, 0.16) near T_c was measured with a resolution better than 0.1%. The anomaly at T_c is analysed for fluctuations for the first time. It is well described by a superposition of a mean field step and a contribution due to gaussian fluctuations. By a fit of a Lawrence-Doniach type of model to the specific heat near T_c we estimate ΔC_MF and the anisotropic coherence lengths ξ and ξ⊥ of the superconductor.     

Effects of spin fluctuations in itinerant electron ferromagnets

Effects of spin fluctuations on the paramagnetic spin susceptibility, magnetization and specific heat are calculated in gaussian statistics as a power series of k_BT. The results are applied to nickel and iron. It is shown that in effect spin fluctuations reduce the molecular field coefficient above the Curie temperature.     

Fluctuations with a 1/f α spectrum in nonequilibrium phase transitions in a spatially distributed system

Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ～ f ^?α and S(k) ～ k ^?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ～ τ^?β) and size (P(s) ～ s^?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2).     

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.     

Random anisotropy in ising spin glass

The theory of Ghatak and Sherrington for the Ising spin glass with uniform uniaxial anisotropy has been extended for the random uniaxial anisotropy (RUA). The magnitude of the RUA is assumed to fluctuate randomly with gaussian probability distribution. The susceptibility and the specific heat have been calculated for a system of spin one and zero mean values of the anisotropy and the exchange interaction. It is found that the random fluctuations of the anisotropy produce a cusp in the susceptibility and a broad maximum in the specific heat.     

The mass enhancement and the specific heat of disordered and amorphous metals

The reduction of the mean free path in metals causes a change of the electronphonon interaction and the Eliashberg function α²(Ω)F(Ω). The values of α²(Ω)F(Ω) for pure, disordered and amorphous lead are used to calculate the enhancement of the density of states and the electronic specific heat in these materials. In pure lead the cyclotron mass (1+λ) has a maximum at 11 °K and the Sommerfeld constant (γ) has a maximum at 5 °K. In disordered lead with a mean free path of about 70 Å, both, 1+λ and γ are almost constant in this temperature range. For amorphous lead there is no temperature range where 1+λ and γ are sufficiently constant. A measurement of the specific heat in disordered non-superconducting metals could answer the question whether these metals are closer to the superconducting state when their mean free path is reduced, a fact which is true for all weak-coupling superconductors.     

Rotational levels from an α-nucleus folded potential

The Bohr-Sommerfeld quantisation rule is used to establish whether a given potential has levels whose energies increase or decrease with angular momentum. The α-¹⁶O model of ²⁰Ne is discussed in terms of a folded potential with a roughly gaussian shape.     

Test of 600 and 750 MeV NN matrix on elastic scattering Glauber model calculations

The 600 and 750 MeV proton nucleus elastic scattering cross section and polarization calculations have been performed in the framework of the Glauber model to test the pp and pn scattering amplitudes deduced from a phase shift analysis by Bystricky, Lechanoine and Lehar. It is well known that up to now we do not possess a non-phenomenological NN scattering matrix at intermediate energies. However proton-nucleus scattering analyses are used to extract information about short range correlations¹), Δ resonance²) or pion condensation presences)... etc. Most scattering calculations made at these energies have been done with phenomenological NN amplitudes having a gaussian q-dependence $$A(q) = \frac{{k\sigma }}{{4\pi }}(\alpha + i) e^{ - \beta ^2 q^2 /2} $$ and $$C(q) = \frac{{k\sigma }}{{4\pi }}iq(\alpha + i) D_e - \beta ^2 q^2 /2$$ K andσ being respectively the projectile momentum and the total pN total cross section. The parameters α, β and D are badly known and are adjusted by fitting some specific reactions as p+⁴He elastic scattering⁴). Even when these amplitudes provide good fits to the data, our understanding of the dynamics of the scattering remains obscure.     

Anomalous temperature dependence of the energy gap of AgGaS2

The lowest energy gap Eg of AgGaS₂ in the temperature range from 4.2 to 300° K was determined from the reflectivity, photoluminescence and absorption measurements. Below ～ 80° K the temperature coefficient of the energy gap is +6 × 10^-5eV/°K. Above ～80° K the sign of the coefficient reverses and the value is -1.8 × 10^-4eV/°K. The positive value is explained with the lattice dilation effect being the dominant mechanism for the energy gap variation at lower temperatures than ～80°K.     

Specific heat of NaNO2 near its transition points

Using an a.c. technique, the specific heat of NaNO₂ was measured as a function of temperature near its antiferroelectric-to-paraelectric phase transition point (T_N). The transition was found to be of the second order. The critical exponents are; α = 0·38 for ? = 2 × 10^?4 ～ 1 × 10^?1, and α′ = 0·18 for ? = ?2 × 10^?4 ～ ?3 × 10^?3. The critical exponents deduced from the scaling-law relations are roughly close to the values obtained from a random phase approximation for a system with an isotropic interaction. However, a difference was recognized between the observed exponent for the specific heat and the values theoretically given for T > T_N by the random phase approximation for a system with a short-range interaction or for a system with a long-range dipolar interaction. A thermodynamical analysis was made by using the generalized Pippard relation, and the present result was found to be consistent with the pressure dependence of the antiferroelectric transition point.     

Gaussian fluctuations to U(N) and SU(N) lattice gauge theories in the mean field approximation

The mean field can be considered as a classical solution of an appropriately reformulated version of lattice gauge theories. Axial gauge fixing renders it stable. The quadratic forms for the fluctuations in the gaussian approximation are analyzed. The gaussian correction to the mean field free energy is expressed for all U(N) and SU(N) in terms of structure functions that are explicitly calculated for U(N), SU(∞, and SU(∞) numerical calculations are performed for the phase transition point, its latent heat, and some correlation lengths that are characteristic for this kind of mean field approach.     

The luminescence of Fe3+ and Cr3+ IN α-gallia

The photoluminescence of Fe³⁺ in octahedral oxygen co-ordination has been observed in Fe³⁺- doped α-gallia. The energy of the emission is in good agreement with that predicted from measured spectral data for Cr³⁺ in α-gallia and the literature data for Cr³⁺ and Fe³⁺ in α-alumina.     

Diffuse phase transition in a surface quartz layer with variations in temperature

The temperature dependence of the α-phase concentration in surface layers of a solution-grown quartz crystal has been studied in the range 290–820 K. This has been achieved by measuring the intensity of the 695.1, 785.0, and 1061.5 cm^?1 bands in the ?″(ν) IR damping spectra. It has been found that, in a surface layer ～0.15 μm thick, the concentration of the α-phase behaves with increasing temperature as expected for a first-order phase transition, namely, before 800 K, it remains constant, after which at T → 846 K, tends to zero. At a distance from ～1 to 20 μm from the surface, however, the concentration of the α-phase starts to decrease already at ～350 K, while at 812 K it decreases to one-fifth of the original value. This is paralleled by an increase in the intensity of the 804 cm^?1 band assigned to the β-phase. The diffusive pattern of the α-β phase transition is initiated by distortion of the quartz crystal lattice around growth dislocations. The internal stresses arising in these layers have been estimated from the shift of the band maxima. It has been established that at distances up to ～1 μm from the surface, tensile stresses reaching ～300–400 MPa appear at 400 K. These stresses drive in the surface layer of the macrocrystal microcracks culminating in total destruction of the sample. The appearance of tensile stresses is assigned to an increase in volume of the macrocrystal layer located at a distance from ～1 to 20 μm from the surface and the growth in it of the β-phase concentration. At the same time, compressive stresses develop in a layer ～1 to 20 μm thick at a temperature above 500 K, which reach a maximum at ～650 K, to fall off thereafter with increasing temperature. The compression is caused by vibrations of growth dislocation loops in the temperature range specified.     

对力对于锕系核性质的影响

本文用处理对力的粒子数守恒方法来分析对力对于锕系核性质的影响,其中包括奇A核和偶偶核的内部激发谱、β衰变、α衰变等。文中首先根据实验测得的寄A核的内部激发谱,计及对力的影响,定出了单粒子能级的Nilsson参数(见表3和5)。然后利用此单粒子能级进一步分析了偶偶核的内部激发谱和β衰变。由于现有数据的限制,只分析了Th²²⁸,Th²³⁰,U²³²,U²³⁴和Cm²⁴⁴等核。由能级位置和β衰变的分析,     

Formation of lithium-like boron and nitrogen ions in the <Superscript>4</Superscript><Emphasis Type="Italic">P</Emphasis><Subscript>5/2</Subscript> state in gaseous media

We experimentally determined the fraction of α_v of lithium-like boron B²⁺ and nitrogen N⁴⁺ ions in the ⁴ P _5/2 state having a velocity of 3.6 au that are formed upon capture of two (α₂) electrons by hydrogen-like B⁴⁺ and N⁶⁺ ions and upon capture of one (α₁) electron by helium-like (1s2s)^1,3 S metastable B³⁺ and N⁵⁺ ions in gaseous media (H₂, He, N₂, Ar), as well as upon passage through a celluloid film. In light-element media (H₂, He), α₂ increases proportional to the target thickness T _g and reaches a maximum at T _g ≈ 10¹⁶ atom/cm² (for B ions, α₂ ≈ 0.2 in H₂ and α₂ ≈ 0.4 in He). For boron and nitrogen ions passing through thin layers of heavier gases (N₂, Ne), α₂ depends considerably more weakly on T _g , and, in Ar, becomes practically constant. It is assumed that, since hydrogen and helium do not contain electrons with parallel spins, autoionizing lithium-like ions are formed as a result of successive (one by one) capture of electrons, whereas, in the heavier gases, simultaneous capture of two electrons predominates. At T _g ～ 10¹⁵ atom/cm², the fraction α₁ of boron ions is the highest in He, ～0.15, and the lowest in Ar, ～0.07, being in qualitative agreement with calculations.     

The specific heat of CeAl2 between 0.02 and 1 K

We report specific heat measurements on a CeAl₂ single crystal between 0.02 and 1 K. Above 0.08 K, we found C₀ = γT + βT³ with γ = (130±0.5) mJ/K²mole and β = (142±1) mJ/K⁴mole in good agreement with previous results above 0.3 K. Below 0.08 K, an excess specific heat C_N = αT^?2 with α = (6.4±1) mJK/mole was detected and interpreted in terms of hyperfine splitting of the Al²⁷ nuclear states. Our results suggest that in CeAl₂ (complex) antiferromagnetism coexists with the Kondo effect at least down to 20 mK.     

Propagation of Gaussian beams through parabolic index optical waveguides with random dielectric constant gradient

Abstract

The propagation of gaussian beams through parabolic index optical waveguides having random irregularities in the dielectric constant gradient has been studied. For fundamental mode propagation, the perturbation approach has been employed and an analytic expression for the loss of power from the fundamental mode has been obtained. For an incident gaussian beam with arbitrary width, geometrical optics approximation has been used and an exact analytical expression for the average value of the beamwidth has been derived for a particular random process, namely, the dichotomic Markov process. The fluctuations in the beamwidth have also been calculated.     

The sub-Coulomb 12C + 12C resonances in a microscopic 12C+12C,α+20Ne, 8Be+16O cluster basis

The low-J resonances in the Coulomb barrier region of the ¹² C+¹²C system are investigated in the framework of a microscopic cluster model basis including ¹²C+¹²C, α+ ²⁰Ne, and su8 Be+ ¹⁶O fragment decompositions. Calculations are carried out in an orthogonality condition model approximation in which Pauli-forbidden components are properly excluded from the basis but in which the interaction among cluster fragments is approximated by a local potential, obtained from a gaussian NN interaction by a folding procedure leading to both spherical and Q · Q terms. Only minor adjustments of overall strength and fall-off parameters are introduced to gain a consistent picture of the low-energy spectrum in the separate rearrangement channels. The basis includes cluster relative motion excitations with oscillator quanta from 12 to 20 and is not quite rich enough to give a detailed quantitative comparison between theory and experiment. Predicted excitation energies are too high by ~ 3 MeV and predicted ¹²C partial widths are too small to indicate a well-developed surface-peaked molecular character; but it does appear possible to identify a 5 MeV region as the potential seat of the 0⁺, 2⁺, 4⁺ resonances. The number and approximate spacing of the resonance fine structure components are in agreement with experiment.     

Exciton fission in excimer-forming crystal dynamics of excimer build-up

The optically induced fission of singlet excitons in both α- and β-perylene crystals is investigated at room temperature. In the monomeric β-perylene the fission thresold coincides with the energy of two triplet excitons whereas it is blueshifted by ～3500 cm^-1 in the excimer forming α-crystal. This indicates that the excimer is formed prior to the fission of the initially excited monomer state and it implies that the rate of excimer formation is exceeding 10¹² s^-1. Theoretical estimates led to k_exc ≈ 10¹²-10¹³ s^-1. Analysis of the experimental data shows also that two adjacent perylene molecules in the α-crystal, each of them in the T₁ electronic state, are bound with the binding energy B_2T1 ≈ 350 cm^-1.