Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Superconducting Correlations in Metallic Nanoparticles: Exact Solution of the BCS Model by the Algebraic Bethe Ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced Bardeen, Cooper, and Schrieffer model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors and correlation functions that describe superconducting pairing.

Optical properties of metallic films for vertical-cavity optoelectronic devices

We present models for the optical functions of 11 metals used as mirrors and contacts in optoelectronic and optical devices: noble metals (Ag, Au, Cu), aluminum, beryllium, and transition metals (Cr, Ni, Pd, Pt, Ti, W). We used two simple phenomenological models, the Lorentz-Drude (LD) and the Brendel-Bormann (BB), to interpret both the free-electron and the interband parts of the dielectric response of metals in a wide spectral range from 0.1 to 6 eV. Our results show that the BE model was needed to describe appropriately the interband absorption in noble metals, while for Al, Be, and the transition metals both models exhibit good agreement with the experimental data. A comparison with measurements on surface normal structures confirmed that the reflectance and the phase change on reflection from semiconductor-metal interfaces (including the case of metallic multilayers) can be accurately described by use of the proposed models for the optical functions of metallic films and the matrix method for multilayer calculations. (C) 1998 Optical Society of America.

Experimental study of phase equilibria in the systems Fe-Zn-O and Fe-Zn-Si-O at metallic iron saturation

The reported experimental work on the systems Fe-Zn-O and Fe-Zn-Si-O in equilibrium with metallic iron is part of a wider research program that combines experimental and thermodynamic computer modeling techniques to characterize zinc/lead industrial slags and sinters in the system PbO-ZnO-SiO2-CaO-FeO-Fe2O3. Extensive experimental,investigations using high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA) were carried out. Special experimental; procedures were developed to enable accurate measurements in these ZnO-containing systems to be performed in equilibrium with metallic iron; The systems Fe-Zn-O and FeZn-Si-O were experimentally investigated in equilibrium with metallic iron in the temperature ranges 900 degreesC to 1200 degreesC (1173 to 1473 K) and from 1000 degreesC to 1350 degreesC (1273 to 1623 K), respectively. The liquidus surface in the system Fe-Zn-Si-O in equilibrium with metallic iron was characterized in the composition ranges 0 to 33 wt pet ZnO and 0 to 40 wt pet SiO2. The wustite (Fe,Zn)O, zincite (Zn,Fe)O, willemite (Zn,Fe)(2)SiO4, arid fayalite: (Fe,Zn)(2)SiO4 solid solutions in equilibrium with metallic iron were measured.

Experimental study of phase equilibria in the "FeO"-ZnO-(CaO+SiO2) system with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron

The pseudoternary sections FeO-ZnO-(CaO + SiO2) with CaO/SiO2 weight ratios of 0.33, 0.93, and 1.2 in equilibrium with metallic iron have been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surfaces in these pseudoternary sections have been experimentally determined in the composition range from 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2). The sections contain primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (Fu(w)Zn(2-w)SiO(4)), melilite (Ca2ZnuFe1-uSi2O7), willemite (ZnvFe2-vSiO4), dicalcium silicate (Ca2SiO4), pseudowollastonite and wollastonite (CaSiO3), and tridymite (SiO2). The phase equilibria involving the liquid phase and the solid solutions-have also been measured.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Experimental study of phase equilibria in the "FeO"-ZNO-(CaO+SiO2) system with the CaO/SiO2 weight ratio of 0.71 at metallic iron saturation

The pseudoternary section FeO-ZnO-(CaO + SiO2) with a CaO/SiO2 weight ratio of 0.71 in equilibrium with metallic iron has been experimentally investigated in the temperature range from 1000 degreesC to 1300 degreesC (1273 to 1573 K). The liquidus surface in this pseudoternary. section has been determined in the composition range of 0 to 33 wt pct ZnO and 30 to 70 wt pct (CaO + SiO2)The system contains primary-phase fields of wustite (FexZn1-xO1+y), zincite (ZnzFe1-zO), fayalite (FewZn2-wSiO4), melilite (Ca2ZnuFe1-uSi2O7), and pseudowollastonite (CaSiO3). The phase equilibria involving the liquid phase and the solid solutions have also been measured.

Indications of coherence-incoherence crossover in layered metallic transport

For many strongly correlated metals with layered crystal structure the temperature dependence of the interlayer resistance is different to that of the intralayer resistance. We consider a small polaron model which exhibits this behavior, illustrating how the interlayer transport is related to the coherence of quasiparticles within the layers. Explicit results are also given for the electron spectral function, interlayer optical conductivity, and the interlayer magnetoresistance. All these quantities have two contributions: one coherent (dominant at low temperatures) and the other incoherent (dominant at high temperatures).

Superplasticity and superplastic forming ability of a Zr-Ti-Ni-Cu-Be bulk metallic glass in the supercooled liquid recgion

The superplastic deformation behavior and superplastic forming ability of the Zr41.25Ti13.75Ni10Cu12.5Be22.5 (at.%) bulk metallic glass (BMG) in the supercooled liquid region were investigated. The isothermal tensile results indicate (hat the BMG exhibits a Newtonian behavior at low strain rates but a non-Newtonian behavior at hiqh-strain rates in the initial deformation stage. The maximum elongation reaches as high as 1624% at 656 K. and nanocrystallization was found to occur during the deformation process. Based cm the analysis on tensile deformation. a gear-like micropart is successfully die-forged via a superplastic forgings process. demonstrating that the BMG has excellent workability in the supercooled liquid region. (C) 2004 Elsevier B.V. All rights reserved.

Phase equilibria in the system Fe-Zn-O at intermediate conditions between metallic-iron saturation and air

The phase equilibria in the FeO-Fe2O3-ZnO system have been experimentally investigated at oxygen partial pressures between metallic iron saturation and air using a specially developed quenching technique, followed by electron probe X-ray microanalysis (EPMA) and then wet chemistry for determination of ferrous and ferric iron concentrations. Gas mixtures of H-2, N-2, and CO2 or CO and CO2 controlled the atmosphere in the furnace. The determined metal cation ratios in phases at equilibrium were used for the construction of the 1200 degrees C isothermal section of the Fe-Zn-O system. The univariant equilibria between the gas phase, spinel, wustite, and zincite was found to be close to pO(2) = 1 center dot 10(-8) atm at 1200 degrees C. The ferric and ferrous iron concentrations in zincite and spinel at equilibrium were also determined at temperatures from 1200 degrees C to 1400 degrees C at pO(2) = 1 center dot 10(-6) atm and at 1200 degrees C at pO(2) values ranging from 1 center dot 10(-4) to 1 center dot 10(-8) atm. Implications of the phase equilibria in the Fe-Zn-O system for the formation of the platelike zincite, especially important for the Imperial Smelting Process (ISP), are discussed.

Crystallization behavior of (Cu60Zr30Ti10)(99)Sn-1 bulk metallic glass

The crystallization behavior and crystallization kinetics Of (CU60Zr30Ti10)(99)Sn-1 bulk metallic glass was studied by X-ray diffractometry and differential scanning calorimetry. It was found that a two-stage crystallization took place during continuous heating of the bulk metallic glass. Both the glass transition temperature T-g and the crystallization peak temperatures T-p displayed a strong dependence on the heating rate. The activation energy was determined by the Kissinger analysis method. In the first-stage of the crystallization, the transformation of the bulk metallic glass to the phase one occurred with an activation energy of 386 kJ/mol; in the second-stage, the formation of the phase two took place at an activation energy of 381 kJ/mol.

Synthesis and mechanical properties of Cu-based bulk metallic glass composites containing in-situ TiC particles

Cu-based bulk metallic glass matrix composites (BMGMCs) containing in-situ TiC particles were fabricated successfully. The yield and fracture strength increased from 1930 MPa, 2250 MPa to 2210 MPa, 2500 MPa, respectively. The ductility was improved and the hardness was also enhanced by 25%. The fracture mechanism was investigated in detail. (C) 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effects of Al2O3 on phase equilibria in the olivine primary phase field of the MgO-"FeO"-SiO2-Al2O3 system in equilibrium with metallic iron

Liquidus temperatures and phase equilibria have been determined in the olivine primary phase field of the MgO-FeO-SiO2-Al2O3 system. Liquidus isotherms have been determined in the temperature range from 1748 to 1873K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO2 with 2 and 3wt% Al2O3 in the liquid. The study enables the liquidus to be described for a range of SiO2/MgO ratios. It was found that liquidus temperatures in the olivine primary phase field decrease with the addition of Al2O3.

Effect of Al2O3 and Cr2O3 on loquidus temperatures in the cristobalite and tridymite primary phase fields of the MgO-"FeO"-SiO2 ststem in equilibrium with metallic iron

The effects of alumina and chromite impurities on the liquidus temperatures in the cristobalite/tridymite (SiO2) primary phase fields in the MgO-FeO-SiO, system in equilibrium with metallic iron have been investigated experimentally. Using high temperature equilibration and quenching followed by electron probe X-ray microanalysis (EPMA), liquiclus isotherms have been determined in the temperatures range 1 673 to 1 898 K. The results are presented in the form of pseudo-ternary sections of the MgO-FeO-SiO, system at 2, 3 and 5 wt% Al2O3, 2 wt% Cr2O3, and 2 wt% Cr2O3+2 wt% Al2O3. The study enables the liquidus to be described for a range of SiO2/MgO and MgO/FeO ratios. It was found that liquiclus temperatures in the cristobalite and tridymite primary phase fields, decrease significantly with the addition of Al2O3 and Cr2O3.