Global SO(3) × SO(3) × U(1) symmetry of the Hubbard model on bipartite lattices

In this paper the global symmetry of the Hubbard model on a bipartite lattice is found to be larger than SO(4). The model is one of the most studied many-particle quantum problems, yet except in one dimension it has no exact solution, so that there remain many open questions about its properties. Symmetry plays an important role in physics and often can be used to extract useful information on unsolved non-perturbative quantum problems. Specifically, here it is found that for on-site interaction U ≠ 0 the local SU(2) × SU(2) × U(1) gauge symmetry of the Hubbard model on a bipartite lattice with N_a^D sites and vanishing transfer integral t = 0 can be lifted to a global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry in the presence of the kinetic-energy hopping term of the Hamiltonian with t > 0. (Examples of a bipartite lattice are the D-dimensional cubic lattices of lattice constant a and edge length L = N_aa for which D = 1, 2, 3,... in the number N_a^D of sites.) The generator of the new found hidden independent charge global U(1) symmetry, which is not related to the ordinary U(1) gauge subgroup of electromagnetism, is one half the rotated-electron number of singly occupied sites operator. Although addition of chemical-potential and magnetic-field operator terms to the model Hamiltonian lowers its symmetry, such terms commute with it. Therefore, its 4^N_aD energy eigenstates refer to representations of the new found global [SU(2) × SU(2) × U(1)]/Z₂² = SO(3) × SO(3) × U(1) symmetry. Consistently, we find that for the Hubbard model on a bipartite lattice the number of independent representations of the group SO(3) × SO(3) × U(1) equals the Hilbert-space dimension 4^N_aD. It is confirmed elsewhere that the new found symmetry has important physical consequences.     

EPR studies of Gd3+-doped Ce2(SO4)3.8H2O and La2(SO4)3.9H2O single crystals

EPR spectra of Gd³⁺-doped Ce₂(SO₄)₃.8H₂O and La₂(SO₄)₃.9H₂O single crystals have been measured with an X-band spectrometer at room and low temperatures. The absolute signs of spin Hamiltonian parameters have been determined for the La₂(SO₄)₃.9H₂O host from intensities of lines at liquid helium temperature; for the Ce₂(SO₄).8H₂O host the lines broaden considerably below 60 K, not permitting the determination of absolute signs of spin Hamiltonian parameters. The data are analysed using a rigourous least-squares procedure, fitting simultaneously all lines obtained for several orientations of the external magnetic field. The zero-field splittings have been computed for both the hosts. The characteristics of EPR spectra of Gd³⁺ in these hosts are compared with those obtained in other rare-earth trisulphate octahydrate hosts.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Reaction of SO2 with Cu/TiO2(1 1 0): Effects of size and metal-oxide interactions in the chemical activation of Cu nanoparticles

The reaction of SO₂ with stoichiometric TiO₂(1 1 0), partially reduced TiO_2 − x(1 1 0) and Cu/TiO₂(1 1 0) was investigated using synchrotron based X-ray photoemission spectroscopy. SO₂ adsorbs on perfect TiO₂(1 1 0) forming SO₄ species at room temperature, while SO₂ dissociatively adsorbs on partially reduced TiO_2 − x(1 1 0) forming SO₄, SO₃ as well as two sulfide species. SO₂ exposure to Cu particles supported on perfect TiO₂(1 1 0) can lead to the formation of SO₄, SO₃ and sulfide species. When depositing Cu on SO₄/TiO₂(1 1 0) at room temperature, the dissociation efficiency of Cu atoms is much higher than that of Cu deposited on TiO₂(1 1 0) prior to SO₂ dosing. The post-deposited Cu atoms can efficiently contact and react with SO₄ species before they form Cu-Cu bonds and big clusters. Small Cu nanoparticles supported on TiO₂(1 1 0) are more reactive towards SO₂ than surfaces of bulk copper. The chemical reactivity of the Cu/TiO₂(1 1 0) system increases with Cu coverage until reaching a maximum at θ_Cu = 0.5-0.8 ML. After this point, an increase in Cu coverage leads to the formation of big Cu particles and the reactivity of the system decrease to that typical of bulk Cu. A comparison with results for SO₂/Cu/MgO(0 0 1) indicates that the effects of size and metal ↔ oxide interactions are important for the chemical activation of Cu nanoparticles on titania.     

Electrochemical behavior of Li intercalation processes into a Li[NixLi(1/3−2x/3)Mn(2/3−x/3)]O2 cathode

Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂ (X=0.17, 0.25, 0.33, 0.5) compounds are prepared by a simple combustion method. The Rietvelt analysis shows that these compounds could be classified as having the α-NaFeO₂ structure. The initial charge-discharge and irreversible capacity increases with the decrease of x in Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂. Indeed, Li[Ni_0.50Mn_0.50]O₂ compound shows relatively low initial discharge capacity of 200 mAh/g and large capacity loss during cycling, with Li[Ni_0.17Li_0.22Mn_0.61]O₂ and Li[Ni_0.25Li_0.17Mn₀.₅₈]O₂ compounds exhibit high initial discharge capacity over 245 mAh/g and stable cycle performance in the voltage range of 4.8 -2.0 V. On the other hand, XANES analysis shows that the oxidation state of Ni ion reversibly changes between Ni²⁺ and about Ni³⁺, while the oxidation state of Mn ion sustains Mn⁴⁺ during charge-discharge process. This result does not agree with the previously reported ‘electrochemistry model’ of Li[Ni_xLi_(1/3−2x/3)Mn_(2/3−x/3)]O₂, in which Ni ion changes between Ni²⁺ and NI⁴⁺. Based on these results, we modified oxidation-state change of Mn and Ni ion during charge-discharge process.     

Integrable string models of WZNW model type with constant SU(2), SO(3), SP(2) and SU(3) torsion and hydrodynamic chains

The integrability of string model of WZNW model type with constant SU(2), SO(3), SP(2) torsion is investigated. The closed boson string model in the background gravity and antisymmetric B-field is considered as integrable system in terms of initial chiral currents. The model is considered under assumption that internal torsion related with metric of Riemann-Cartan space and external torsion related with antisymmetric B-field are (anti)coincide. New equation of motion and exact solution this equation was obtained for string model with constant SU(2), SO(3), SP(2) torsion. New equations of motion and new Poisson brackets (PB) for infinite dimensional hydrodynamic chains was obtained for string model with constant SU(n), SO(n), SP(n) torsion for n → ∞.     

Matrix elements for the representations of SO(n) and SO0(n, 1)

Matrix elements of the unitary irreducible representations of the group SO(n) of class higher then 1 (with respect to SO(n−1)) in Gel'fand-Zetlin basis are obtained in explicit form. They are represented as polynomials in cosθ and sinθ of the order equal to the first coordinate of the highest weight. Making use of them the representation matrix elements for the group SO₀(n, 1) in SO(n) basis are calculated.     

Di-urethanesil hybrid electrolytes doped with Mg(CF3SO3)2

Two siloxane-based di-urethanesil frameworks incorporating poly(oxyethylene) (POE) chains have been synthesized by the sol–gel process and doped with magnesium triflate (Mg(CF₃SO₃)₂) with the goal of developing electrolytes for the fabrication of solid-state rechargeable magnesium batteries. In these matrices, short POE chains are covalently bonded to the siloxane network via urethane linkages. The xerogels have been represented by the notation d-Ut(Y) _n Mg(CF₃SO₃)₂, where Y?=?300 and 600 represents the average molecular weight of the POE chains and n stands for salt composition (molar ratio of OCH₂CH₂ units per Mg²⁺). Xerogels with compositions ranging from 2?≤?n?<?∞ were prepared. A crystalline POE/Mg(CF₃SO₃)₂ complex of unknown stoichiometry is formed in the d-Ut(300) _n Mg(CF₃SO₃)₂ materials with n?≤?6 and in the d-Ut(600) _n Mg(CF₃SO₃)₂ materials with n?≤?5. The organically modified silicate electrolytes with the highest conductivity of the d-Ut(300) _n Mg(CF₃SO₃)₂ and d-Ut(600) _n Mg(CF₃SO₃)₂ series are the samples with n?=?6 (3.9?×?10^?8 S cm^?1 at 26 °C and 8.7?×?10^?5 S cm^?1 at 97 °C) and n?=?100 (2.63?×?10^?7 S cm^?1 at 20 °C and 1.4?×?10^?5 S cm^?1 at 85 °C), respectively. Since the electrolytes for Mg batteries that have been proposed up to now have many intrinsic problems and although the room temperature conductivity values exhibited by the systems developed in the present study are still low in view of practical application, this work opens new directions for the development of solid-state Mg ion electrolytes.     

Supersymmetric non-linear σ model onE 8/SO(10)×SU(3)×U(1)

We calculate the Kähler potential of theE ₈/SO(10)×SU(3)×U(1) homogeneous space. Some quasi Nambu-Goldstone fermions living in the corresponding supersymmetric non-linear σ model are identified with the usual three families of quarks and leptons, and one mirror family. We also show that the dynamical breakdown of supersymmetry does not occur in this model.     

Reaction mechanism of elemental mercury oxidation to HgSO4 during SO2/SO3 conversion over V2O5/TiO2 catalyst

Experiments and density functional theory calculations were conducted to uncover the reaction chemistry of Hg⁰ oxidation during SO₂/SO₃ conversion over V₂O₅/TiO₂ catalyst. The results show that SO₂ promotes Hg⁰ oxidation over V₂O₅/TiO₂ catalyst with the assistance of oxygen. The promotional effect is dependent on the reaction temperature, and is associated with the bimolecular reaction between Hg⁰ and SO₃ over V₂O₅/TiO₂ catalyst. SO₂ can be oxidized to SO₃ which has high oxidation ability for Hg⁰ oxidation. SO₂/SO₃ conversion proceeds through a three-step reaction process in the sequence of SO₂ adsorption → SO₂ oxidation → SO₃ desorption. SO₂ oxidation presents an activation energy barrier of 223.84 kJ/mol. HgSO₄ species is formed from the bimolecular reaction between Hg⁰ and SO₃ over V₂O₅/TiO₂ catalyst. Hg⁰ oxidation by SO₃ over V₂O₅/TiO₂ catalyst occurs through three reaction pathways, which are energetically favorable for HgSO₄ formation. SO₂* → SO₃* is identified as the rate-determining step of HgSO₄ formation. During Hg⁰ oxidation by SO₃ over V₂O₅/TiO₂ catalyst, HgSO₄ desorption is a highly endothermic reaction process and requires a higher external energy. The proposed skeletal reaction network can be used to well understand the reaction mechanism of Hg⁰ oxidation during SO₂/SO₃ conversion over V₂O₅/TiO₂ catalyst.     

Structural, vibrational and dielectric properties of new potassium hydrogen sulfate arsenate: K4(SO4)(HSO4)2(H3AsO4)

A new compound, K₄(SO₄)(HSO₄)₂(H₃AsO₄) was synthesized from water solution of KHSO₄/K₃H(SO₄)₂/H₃AsO₄. This compound crystallizes in the triclinic system with space group P1¯ and cell parameters: a=8.9076(2) Å, b=10.1258(2) Å, c=10.6785(3) Å; α=72.5250(14)°, β=66.3990(13)°, γ=65.5159(13)°, V=792.74(3) Å³, Z=2 and ρ_cal=2.466 g cm⁻³. The refinement of 3760 observed reflections (I>2σ(I)) leads to R₁=0.0394 and wR₂=0.0755. The structure is characterized by SO₄²⁻, HSO₄⁻ and H₃AsO₄ tetrahedra connected by hydrogen bridge to form two types of dimer (H(16)S(3)O₄⁻?S(1)O₄²⁻ and H(12)S(2)O₄⁻?H₃AsO₄). These dimers are interconnected along the [1¯ 1 0] direction by the hydrogen bonds O(3)-H(3)?O(6). They are also linked by the hydrogen bridge assured by the hydrogen atoms H(2), H(3) and H(4) of the H₃AsO₄ group to build the chain S(1)O₄?H₃AsO₄ which are parallel to the “a” direction. The potassium cations are coordinated by eight oxygen atoms with K-O distance ranging from 2.678(2) to 3.354(2) Å.Crystals of K₄(SO₄)(HSO₄)₂(H₃AsO₄) undergo one endothermic peak at 436 K. This transition detected by differential scanning calorimetry (DSC) is also analyzed by dielectric and conductivity measurements using the impedance spectroscopy techniques. The obtained results show that this transition is protonic by nature.     

Crystal structure and thermal behavior of two new organic monosulfates NH3(CH2)5NH3SO4 1.5H2O and NH3(CH2)9NH3SO4 H2O

The chemical preparation, the calorimetric studies and the crystal structure are given for two new organic sulfates NH₃(CH₂)₅NH₃SO₄ 1.5H₂O (DAP-S) and NH₃(CH₂)₉NH₃SO₄·H₂O (DAN-S). DAP-S is monoclinic P2₁/n with unit cell dimensions: a=11.9330(2) Å; b=10.9290(2) Å; c=17.5260(2) Å; β=101.873(1)°; V=2236.77(6) Å³; and Z=8. Its atomic arrangement is described as inorganic layers of units and water molecules separated by organic chains. DAN-S is monoclinic P2₁/c with unit cell parameters: a=5.768(2) Å; b=25.890(10) Å; c=11.177(5) Å; β=115.70(4)°; V=1504.0(11) Å³ and Z=4. Its structure exhibits infinite chains, parallel to the [100] direction where the organic cations are interconnected. In both structures a network of strong and weak hydrogen bonds connects the different components in the building of the crystal.     

A Raman spectroscopic study of copiapites Fe2+Fe3+(SO4)6(OH)2 · 20H2O: environmental implications

Raman spectroscopy has been used to study selected mineral samples of the copiapite group. Copiapite (Fe²⁺Fe³⁺(SO₄)₆(OH)₂ · 20H₂O) is a secondary mineral formed through the oxidation of pyrite. Minerals of the copiapite group have the general formula AFe₄(SO₄)₆(OH)₂ · 20H₂O, where A has a + 2 charge and can be either magnesium, iron, copper, calcium and/or zinc. The formula can also be B_2/3Fe₄(SO₄)₆(OH)₂ · 20H₂O, where B has a + 3 charge and may be either aluminium or iron. For each mineral, two Raman bands are observed at around 992 and 1029 cm⁻¹, assigned to the (SO₄)²⁻ν₁ symmetric stretching mode. The observation of two bands provides evidence for the existence of two non‐equivalent sulfate anions in the mineral structure. Three Raman bands at 1112, 1142 and 1161 cm⁻¹ are observed in the Raman spectrum of copiapites, indicating a reduction of symmetry of the sulfate anion in the copiapite structure. This reduction in symmetry is supported by multiple bands in the ν₂ and ν₄(SO₄)²⁻ spectral regions. Copyright © 2010 John Wiley & Sons, Ltd.     

The analytical potential energy function of flue gas SO2（X1A1）

The equilibrium structure of flue gas SO2 is optimized using the density functional theory （DFT）/B3P86 method and CC-PV5Z basis. The result shows that it has a bent （C2v, X1A1） ground state structure with an angle of 119.1184°. The vibronic frequencies and the force constants are also calculated. Based on the principles of atomic and molecular reaction statics （AMIIS）, the possible electronic states and reasonable dissociation limits for the ground state of SO2 molecule are determined. The potential functions of SO and 02 are fitted by the modified Murrell-Sorbie＋c6 （M-S＋c6） potential function and the fitted parameters, the force constants and the spectroscopic constants are obtained, which are all close to the experimental values. The analytic potential energy function of the SO2 （X1A1） molecule is derived using the many-body expansion theory. The contour liues are constructed, which show the static properties of SO2 （XIA1）, such as the equilibrium structure, the lowest energies, the most possible reaction channel, etc.     

High-resolution study of the bΣ(b0)→XΣ(X10) transition of PI

Emission spectra of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of phosphorus iodide have been measured with a high-resolution Fourier-transform spectrometer. The PI radicals were generated and excited in a fast-flow system by reaction of phosphorus vapor (P_x) with iodine and microwave-discharged oxygen. Four sequences, Δv=0,+1,−1,−2, of the b¹Σ⁺(b0⁺)→X³Σ⁻(X₁0⁺) transition of PI comprising 28 bands were observed. Six bands were measured at high spectral resolution. Vibrational and rotational analyses have yielded accurate spectroscopic constants of the X₁0⁺ and b0⁺ states (in cm⁻¹): X₁0⁺: ω_e=371.296(4), ω_ex_e=1.3302(9), B_e=0.1194117(2), α_B=−0.0005676(7), D_e=4.56(2) ×10⁻⁸; b0⁺: T_e=11136.921(4), ω_e=400.165(6), ω_ex_e=1.345(2), B_e=0.1239237(2), α_B=−0.0005540(2), D_e=4.84(5) × 10⁻⁸, where the numbers in parentheses are the standard deviations of the parameters. No emissions of the b0⁺→X₂1 sub-system nor of the a¹Δ(a2)→X³Σ⁻(X₂1) transition have been observed leaving PI the only group Va halide for which the spin splitting in the X³Σ⁻ ground state is still unknown.     

Raman spectroscopic study of the hydroxy‐arsenate‐sulfate mineral chalcophyllite Cu18Al2(AsO4)4(SO4)3(OH)24·36H2O

The mixed anion mineral chalcophyllite Cu₁₈Al₂(AsO₄)₄(SO₄)₃(OH)₂₄·36H₂O has been studied by using Raman and infrared spectroscopies. Characteristic bands associated with arsenate, sulfate and hydroxyl units are identified. Broad bands in the OH stretching region are observed and are resolved into component bands. Estimates of hydrogen bond distances were made using a Libowitzky function. Both short and long hydrogen bonds were identified. Two intense bands at 841 and ∼814 cm⁻¹ are assigned to the ν₁ (AsO₄)³⁻ symmetric stretching and ν₃ (AsO₄)³⁻ antisymmetric stretching modes. The comparatively sharp band at 980 cm⁻¹ is assigned to the ν₁ (SO₄)²⁻ symmetric stretching mode, and a broad spectral profile centred upon 1100 cm⁻¹ is attributed to the ν₃ (SO₄)²⁻ antisymmetric stretching mode. A comparison of the Raman spectra is made with other arsenate‐bearing minerals such as carminite, clinotyrolite, kankite, tilasite and pharmacosiderite. Copyright © 2010 John Wiley & Sons, Ltd.     

Lowering operators for the reduction U(n)↓SO(n)

A complete set of lowering operators is constructed for the reduction U(n)↓SO(n). In an irreducible representation of the unitary group U(n), every vector of maximal weight with respect to the subgroup SO(n) can be obtained using the lowering operators. The formula for the lowering operators is obtained using graphical techniques.     

The corrosion behavior of intermetallic compounds Ni3(Si,Ti) and Ni3(Si,Ti) + 2Mo in acidic solutions

The corrosion behavior of the intermetallic compounds homogenized, Ni₃(Si,Ti) (L1₂: single phase) and Ni₃(Si,Ti) + 2Mo (L1₂ and (L1₂ + Ni_ss) mixture region), has been investigated using an immersion test, electrochemical method and surface analytical method (SEM; scanning electron microscope and EPMA: electron probe microanalysis) in 0.5 kmol/m³ H₂SO₄ and 0.5 kmol/m³ HCl solutions at 303 K. In addition, the corrosion behavior of a solution annealed austenitic stainless steel type 304 was studied under the same experimental conditions as a reference. It was found that the intergranular attack was observed for Ni₃(Si,Ti) at an initial stage of the immersion test, but not Ni₃(Si,Ti) + 2Mo, while Ni₃(Si,Ti) + 2Mo had the preferential dissolution of L1₂ with a lower Mo concentration compared to (L1₂ + Ni_ss) mixture region. From the immersion test and polarization curves, Ni₃(Si,Ti) + 2Mo showed the lowest corrosion resistance in both solutions and Ni₃(Si,Ti) had the highest corrosion resistance in the HCl solution, but not in the H₂SO₄ solution. For instance, it was found that unlike type 304 stainless steel, these intermetallic compounds were difficult to form a stable passive film in the H₂SO₄ solution. The results obtained were explained in terms of boron segregation at grain boundaries, Mo enrichment and film stability (or strength).     

Tensor representation of the quantum groupSL q (2,C) and quantum Minkowski space

We investigate the structure of the tensor product representation of the quantum groupSL _q (2,C) by using the 2-dimensional quantum plane as a building block. Two types of 4-dimensional spaces are constructed applying the methods used in twistor theory. We show that the 4-dimensional real representation ofSL _q (2,C) generates a consistent non-commutative algebra, and thus it provides a quantum deformation of Minkowski space. The transformation of this 4-dimensional space gives the quantum Lorentz groupSO _q(3, 1).