Dispersive Estimates for Schrödinger Equations with Threshold Resonance and Eigenvalue

Let H=−Δ+V(x) be a three dimensional Schrödinger operator. We study the time decay in L^p spaces of scattering solutions e^−itHP_cu, where P_c is the orthogonal projection onto the continuous spectral subspace of L²(R³) for H. Under suitable decay assumptions on V(x) it is shown that they satisfy the so-called L^p-L^q estimates ||e^−itHP_cu||_p≤(4π|t|)^{−3(1/2−1/p)}||u||_q for all 1≤q≤2≤p≤∞ with 1/p+1/q=1 if H has no threshold resonance and eigenvalue; and for all 3/2<q≤2≤p<3 if otherwise.     

Electronic absorption spectrum of Ni2+ in lithium potassium sulphate single crystal

Single crystals of nickel-doped lithium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the bands could be made assumingO _h symmetry for the Ni²⁺ ion in the crystal. The bands have been assigned transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The crystal field parameters derived areDq=910cm^–1,B=890cm^–1 andC=3560cm^–1.The authors wish to express their thanks to Prof. K. Sreerama Murthy for his constant encouragement throughout this investigation. The authors are also thankful to Prof. Mihir Chowdhury, Indian Association for the cultivation of Science, Calcutta for giving permission to take the spectra.     

Optical absorption spectrum of Ni2+ ions doped in sodium potassium sulphate single crystal

Single crystals of nickel-doped sodium potassium sulphate were grown by slow evaporation method at room temperature. From the nature and position of the bands observed, a successful interpretation of all the observed bands could be made assuming the octahedral symmetry for the Ni^{2 +} ion in the crystal. The bands have been ascribed to transitions from the ground³A_2g(F) state to the excited³T_2g(F),¹E_g(D),³T_1g(F),¹T_2g(D) and³T_1g(P) states. The experimental and calculated energies are in good agreement. The crystal field parameters derived areDq= =880 cm^–1,B= 900cm^–1 andC=3600 cm^–1.One of the authors, Sujatha John expresses her thanks to the Secretary and the Principal, R. B. V. R. Reddy College, Hyderabad for according her permission to pursue the M. Phil. course.     

Raman-spectroscopy study of PbTiO3 thin films grown on Si substrates by metalorganic chemical vapor deposition

Raman spectra have been investigated in PbTiO₃ thin films grown on Si by metalorganic chemical vapor deposition. A large grazing-angle scattering technique was taken to measure the temperature dependence of Raman spectra below room temperature. All Raman modes in the thin films are assigned and compared with those in the bulk single crystal, a newA ₁(TO) soft mode at 104 cm^–1 was recorded which satisfies the Curie-Weiss relation ² =A(T _c –T). Intensities of theA ₁(1TO) andE(1TO) modes were anomalously strengthened with increasing temperature. Raman modes for the thin films exhibit remarkable frequency downshift and upshift which is related to the effect of internal stress.     

Annealing effect on the superconductivity of In2O3–ZnO thin films

We have investigated the relation among ρ–T characteristics, superconductivity, annealing conditions and the crystallinity of polycrystalline (In₂O₃)_1−x–(ZnO)_x films. We annealed as-grown amorphous films in air by changing annealing temperature and time. It is found that the films annealed at 200 °C or 300 °C for a time over 0.5 h shows the superconductivity. Transition temperature T_c and the carrier density n are T_c < 3.3 K and n ≈ 10²⁵–10²⁶ m⁻³, respectively. Investigations for films with x = 0.01 annealed at 200 °C have revealed that the T_c, n and crystallinity depend systematically on annealing time. Further, we consider that there is a suitable annealing time for sharp resistive transition because the transition width becomes wider with longer annealing times. We studied the upper critical magnetic field H_c2(T) for the film with different annealing time. From the slope of dH_c2/dT for all films, we have obtained the resistivity ρ dependence of the coherence length ξ(0) at T = 0 K.     

Temperature dependence of the critical current density in Y-Ba-Cu-O thin films

We present a study of the temperature dependence of the critical currentJ _c of several dc magnetron sputtered thin Y-Ba-Cu-O films on single crystalline SrTiO₃, ZrO₂ and Al₂O₃ substrates. Near the critical temperature T_c it is found thatJ _c(1–T/T_c)ⁿ withn=3 for the SrTiO₃ and ZrO₂ substrates, whilen=1·3 for the Al₂O₃ substrate. The temperature dependence in our samples approximately agrees with standard theories for weak links or with the Ambegaokar-Baratoff equation.     

Scaling function for energy-density correlations: Dispersion theory andε-expansion forT>T c

A dispersion representation for the static energy-density correlation function ² (q) ²(–q) _c =C(q,T)=A+Bt ^–h(z ²), wherez=q , t=(T—T)_c/T _c and is the correlation length, is discussed.h(z ²) is calculated to order ² in the zero-field critical region (T>T _c) for the standard isotropicn-component ⁴Ginzburg-Landau-Wilson model. Utilizing a procedure similar to that introduced by Bray for the two-point correlation function, the-expansion results are used in conjunction with an approximant for the spectral functionF(z/2) Imh(—z ²) based on the asymptotically exact short-distance expansion resulth ^–1(z ²)z ^/v[D ₀+D ₁ z ^{–(1 —)/v} +D ₂ z ^–1/v ] to predict quantitatively the full momentum dependence ofC(q,T) forT>T _c. In contrast to the two-point correlation function,C(q,T) is found to be a monotonic function as the critical temperature is approached at fixedq (forT>T _c).     

Interfacial Adsorption in Two-Dimensional Potts Models

The interfacial adsorption W at the first-order transition in two-dimensional q-state Potts models is studied. In particular, findings of Monte Carlo simulations and of density-matrix renormalization group calculations at q=16 are consistent with the analytic result, obtained in the Hamiltonian limit at large values of q, that Wt ^–1/3 on approach to the bulk critical temperature T _c, t=|T _c–T|/T _c. In addition, the numerical findings allow to estimate corrections to scaling. Our study supports and quantifies a previous conclusion by Bricmont and Lebowitz based on low temperature expansions.     

The ferroelectric phase transition in LiTaO3 studied by neutron scattering I. The Long-Range Order

Elastic neutron scattering from two reflections has been studied versus temperature, and the temperature dependence of the ferroelectric polarizationP(T) has been deduced. Neart _c =601°C the dependence is found to be classical: (T _c –T)^1/2. The study supports a model where the ferroelectric transition is accompanied by an order-disorder transition of the lithium ions.     

Structural properties and Raman spectroscopy of orthorhombic (Eu1−xPrx)0.6Sr0.4MnO3 (0≤x≤1.0)

The effect of Pr doping on structural properties and room temperature Raman spectroscopy measurements is investigated in manganites (Eu_1−xPr_x)_0.6Sr_0.4MnO₃ (0≤x≤1.0) with fixed carrier concentration. The result of the Rietveld refinement of x-ray powder diffraction shows that these compounds crystallize in an orthorhombic distorted structure with a space group Pnma. It is evident that, with increasing Pr substitution, three types of orthorhombic structures can be distinguished. The phonon frequencies of the three main peaks, in room temperature Raman-scattering measurements, have been discussed together with their structural characteristics, such as bond-length, bond-angles, and the change of orthorhombic structure type. With the increase of Pr content, the mode at 491  cm⁻¹ also shows a corresponding change. A step effect becomes evident, which seems to indicate the close dependence between the frequency shift of this mode and the change in crystal symmetry. This further supports the notion that the mode at 491  cm⁻¹ is closely correlated with the Jahn–Teller distortion. Moreover, we have found that the lowest frequency peak (assigned as an A_1g phonon mode) depends linearly on the tolerance factor t.     

Temperature dependence of the critical current in YBa2Cu3O7−δ and Bi2Sr2Ca1Cu2O8 Josephson junctions

We have studied the stationary Josephson effect on YBa₂Cu₃O_7−δ (T_c=90 K) and Bi₂Sr₂Ca₁Cu₂ O₈ (T_c=80 Kand 87 Kfortwosamplesofdifferentorigin) ceramic based junctions. The temperature dependence of the critical current near T_c has been found as I_c≈(T_c-T) for the Y-Ba-Cu-O samples indicating that they should be classified as S-N-I-N-S type junctions. The I-V curves of the Bi-Sr-Ca-Cu samples show the typical behaviour of S-I-S structures. Using Ambegaokar-Baratoff's theory for Bi₂Sr₂Ca₁Cu₂O₈, the temperature dependence of the superconducting state gap Δ(T) was calculated and it was evaluated that 1.452Δ(0)/k_BT_c3.5.     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Analytic Verification of the Droplet Picture in the Two-Dimensional Ising Model

It is widely accepted that the free energy F(H) of the two-dimensional Ising model in the ferromagnetic phase T<T _c has an essential branch cut singularity at the origin H=0. The phenomenological droplet theory predicts that near the cut drawn along the negative real axis H<0, the imaginary part of the free energy per lattice site has the form ImF[exp(±i)|H|]=±B|H|exp(–A/|H|) for small |H|. We verify this prediction in analytical perturbative transfer matrix calculations for the square lattice Ising model for all temperatures 0<T<T _c and arbitrary anisotropy ratio J ₁/J ₂. We obtain an expression for the constant A which coincides exactly with the prediction of the droplet theory. For the amplitude B we obtain B=M/18, where M is the equilibrium spontaneous magnetization. In addition we find discrete-lattice corrections to the above mentioned phenomenological formula for ImF, which oscillate in H ^–1.     

Studies of the quantum Hall to quantum Hall insulator transition in InSb-based 2DESs

The temperature dependence of ρ_xx is studied in the vicinity of the quantum Hall to quantum Hall insulator transition (ν=1→0) in InSb/InAlSb based 2DESs. ρ_xx displays a symmetric temperature dependence about the transition with on the QH side and on the insulating side. A plot of 1/T₀ for successive ν displays power-law divergence with 1/T₀∝|ν−ν_c|^−γ,² with γ=2.2±0.3. This critical behavior in addition to the behavior expected of the quantum transport regime confirms that the QH/QHI transition is indeed a good quantum phase transition.     

Nucleon Properties Below the Critical Point Temperature

In this paper, we extended our work (Abu-Shady, Int. J. Theory Phys. 49:2425, 2010) to include nucleon properties. The field equations have been solved in the mean-field approximation using the effective mesonic potential at finite temperature. We found that the nucleon first mass increases up to \frac45 T_c\frac{4}{5} T_{c} MeV (where T _c is the critical point temperature) then decreases at higher values of temperature which approach the critical temperature (T _c ). In addition, we found that the magnetic moments of the proton and neutron can be increased by increasing the temperature up to the critical temperature. Moreover, we examined the axial coupling constant g _A (0), and the pion-nucleon coupling constant g _πNN (0) as functions of temperature. The obtained results are compared with previous works. From the results, we conclude that finite temperature plays a significant role in the change of behavior of nucleon properties.     

LnP5O14铁弹相变的喇曼光谱研究

在200—300℃范围测量了单斜I镧系五磷酸盐LnP₅O₁₄(Ln=La,Ce,Pr、Nd,Sm,Eu,Gd,Tb)晶体的软光学模喇曼谱。不同LnP₅O₁₄的A_g-B_2g和A_g-A_g软模在铁弹相变点都软化到20cm^-1,另一个B_g-B_3g软模则软化到38cm^-1。软模频率对温度的依赖关系表明,这些晶体是很好的平均场理论系统。A_g-B_2g软模与e₅的耦合对铁弹相变起主要作用,此软模的强度变化可由双向线性模耦合模型来解释。这个系统T_c从La到Tb的增高是镧系收缩的结果。 关键词：     

Finite size effects at thermally-driven first order phase transitions: A phenomenological theory of the order parameter distribution

We consider the rounding and shifting of a firstorder transition in a finited-dimensional hypercubicL ^d geometry,L being the linear dimension of the system, and surface effects are avoided by periodic boundary conditions. We assume that upon lowering the temperature the system discontinuously goes to one ofq ordered states, such as it e.g. happens for the Potts model ind=3 forq3, with the correlation length of order parameter fluctuation staying finite at the transition. We then describe each of theseq ordered phases and the disordered phase forL by a properly weighted Gaussian. From this phenomenological ansatz for the total distribution of the order parameter, all moments of interest are calculated straight-forwardly. In particular, it is shown that forL exceeding a characteristic minimum sizeL _min the forthorder cumulantg _L (T) exhibits a minimum atT _min>T _c, withT _min–T _cL ^–d and the value of the cumulant and the minimum (g(T _min)) behaving asg(T _min)L ^–d. All cumulantsg _L (T) forL approximately intersect at a common crossing pointT _crossL ^–2d, with a universal valueg(T _cross)=1–n/2q, wheren is the order parameter dimensionality. By searching for such a behavior in numerical simulation data, the first order character of a phase transition can be asserted. The usefulness of this approach is shown using data for theq=3,d=3 Potts ferromagnet.     

Effect of annealing temperature on some physical properties of MgB2 by using the Hall probe ac-susceptibility method

A commercially available powder of MgB₂ is used as starting material for the examination of the influence of the annealing temperature on the properties of this intermediate-T_c superconductor. We performed scanning electron microscopy (SEM) and Hall ac-susceptibility measurements as a function of temperature and ac-field amplitude on samples annealed at 650, 750, 850 and 950 °C. The imaginary part of ac-susceptibility measurements is used to calculate both the inter-granular critical current density, J_c(T_p) and density of pinning force, α_j(0). It was observed that all T_c, J_c(T_p) and α_j(0) exhibit a non-monotonic behavior on the annealing temperature range studied in this work. T_c is measured to be 39.85±0.02 K and J_c(T_p) is estimated to be as high as 60 A/cm² at 39.2 K for the sample annealed at 850 °C. The peak temperature, T_p, in the imaginary part of the ac-susceptibility curves shifts to lower temperatures with both decreasing the annealing temperature and increasing the amplitude of the ac-magnetic fields. A comparison of the experimental ac-susceptibility data with theoretical critical-state models that are currently available is performed. SEM investigations showed that the grain size increases, and the grain connectivity improves when the annealing temperature increases up to 850 °C. The possible reasons for the observed changes in transport, microstructure and magnetic properties due to annealing temperature are discussed.