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.     

Adsorption of iso-butane on ZnO(0 0 0 1)-Zn

Presented are thermal desorption spectroscopy (TDS) and adsorption probability measurements of iso-butane on the Zn-terminated surface of ZnO. The initial adsorption probability, S₀, decreases linearly from 0.57 to 0.22 (±0.02) with impact energy, E_i = 0.74-1.92 eV, and is independent of adsorption temperature, T_s = 91-114 K (±5 K), indicating non-activated molecular adsorption. The coverage, Θ, dependent adsorption probabilities, S(Θ), show a cross-over from adsorbate-assisted adsorption (S increases with Θ) to Kisliuk-like dynamics at about the desorption temperature of iso-butane bi-layers (∼110 K). Thus, the adsorption dynamics are precursor-mediated. The enhanced (gas-surface) mass-match, caused by forming a second layer of the alkane, leads to adsorbate-assisted adsorption. A direct fitting procedure of the TDS data yields a pre-exponential factor of 2.5 × 10¹³/s and a coverage dependent heat of adsorption of E_d(Θ) = 39 − 6 ∗ Θ + 2.5 ∗ exp(−Θ/0.07) kJ/mol.     

Reduction of lower symmetry terms to cos 3τ′ and sin 3τ′ for vibration-internal rotation-overall rotation interactions in −XY3 molecules

In the calculation of the S_t, S_tS_t, dependence of the inertia tensor and the S_t, dependence of the Coriolis coupling for internal rotation in −XY3 molecules, terms of lower symmetry than cos 3τ and sin 3τ appear when curvilinear internal coordinates are used for the internal rotation and other vibrations. This paper shows how these lower symmetry terms are reduced to zero after transformation to symmetry coordinates for the internal rotation and other vibrations.     

CO2 adsorption on Cr(1 1 0) and Cr2O3(0 0 0 1)/Cr(1 1 0)

We attempt to correlate qualitatively the surface structure with the chemical activity for a metal surface, Cr(1 1 0), and one of its surface oxides, Cr₂O₃(0 0 0 1)/Cr(1 1 0). The kinetics and dynamics of CO₂ adsorption have been studied by low energy electron diffraction (LEED), Aug er electron spectroscopy (AES), and thermal desorption spectroscopy (TDS), as well as adsorption probability measurements conducted for impact energies of E_i = 0.1-1.1 eV and adsorption temperatures of T_s = 92-135 K. The Cr(1 1 0) surface is characterized by a square shaped LEED pattern, contamination free Cr AES, and a single dominant TDS peak (binding energy E_d = 33.3 kJ/mol, first order pre-exponential 1 × 10¹³ s⁻¹). The oxide exhibits a hexagonal shaped LEED pattern, Cr AES with an additional O-line, and two TDS peaks (E_d = 39.5 and 30.5 kJ/mol). The initial adsorption probability, S₀, is independent of T_s for both systems and decreases exponentially from 0.69 to 0.22 for Cr(1 1 0) with increasing E_i, with S₀ smaller by ∼0.15 for the surface oxide. The coverage dependence of the adsorption probability, S(Θ), at low E_i is approx. independent of coverage (Kisliuk-shape) and increases initially at large E_i with coverage (adsorbate-assisted adsorption). CO₂ physisorbs on both systems and the adsorption is non-activated and precursor mediated. Monte Carlo simulations (MCS) have been used to parameterize the beam scattering data. The coverage dependence of E_d has been obtained by means of a Redhead analysis of the TDS curves.     

One-dimensional models of internal rotation in CX3NO molecules (X = H, D, F)

Various non-empirical methods for estimating the parameters of one-dimensional internal rotation potentials and energies of torsional transitions were compared for the CX₃NO molecules (X = H, D, F) in the ground (S₀) and lowest excited singlet (S₁) electronic states. The potential energy surfaces were studied by the ab initio MR-AQCC/cc-pVTZ, MR-AQCC/cc-pVTZ(-f), MP2/6-311G(2d), and MP2/6-311G(d,p) methods. The one-dimensional internal rotation problem was solved using the following models: (1) geometry optimization at a given internal rotation coordinate; (2) intrinsic reaction path; (3) gradient extremal; and (4) use of only the data on potential energy surface stationary points. Special attention was paid to the problem of calculation of kinematic coefficient. In all cases, the calculated torsional energies for CX₃NO molecules (X = H, D, F) are in agreement with experiment. The results from different methods for constructing torsional cross-sections of the potential energy surface are virtually equivalent and differ insignificantly from the results of calculations within the framework of the simplest model, hence, estimates of the barrier to internal rotation are of most importance. It was found that a change in the zero-point energy could give a correction to the internal rotation potential as large as 15% of the potential barrier. However, in the case under consideration the calculations in the harmonic approximation taking into account this correction do not improve the agreement between the calculated torsional transitions and the experimental data.     

Study of S ion-assisted sulfurization of n-GaAs (1 0 0) surface

The chemical structure and site location of sulfur atoms on n-GaAs (1 0 0) surface treated by bombardment of S⁺ ions over their energy range from 10 to 100 eV have been studied by X-ray photoelectron spectroscopy and low energy electron diffraction. The formation of Ga-S and As-S species on the S⁺ ion bombarded n-GaAs surface is observed. An apparent donor doping effect is observed for the n-GaAs by the 100 eV S⁺ ion bombardment. It is found that the S⁺ ions with higher energy are more effective in the formation of Ga-S species, which assists the n-GaAs (1 0 0) surface in reconstruction into an ordered (1 × 1) structure upon subsequent annealing. The treatment is further extended to repair Ar⁺ ion damaged n-GaAs (1 0 0) surface. It is found that after a n-GaAs (1 0 0) sample is damaged by 150 eV Ar⁺ ion bombardment, and followed by 50 eV S⁺ ion treatment and subsequent annealing process, finally an (1 × 1) ordering GaAs (1 0 0) surface with low surface states is obtained.     

A DFT + U description of oxygen vacancies at the TiO2 rutile (1 1 0) surface

Experimental observations indicate that removing bridging oxygen atoms from the TiO₂ rutile (1 1 0) surface produces a localised state approximately 0.7 eV below the conduction band. The corresponding excess electron density is thought to localise on the pair of Ti atoms neighbouring the vacancy; formally giving two Ti³⁺ sites. We consider the electronic structure and geometry of the oxygen deficient TiO₂ rutile (1 1 0) surface using both gradient-corrected density functional theory (GGA DFT) and DFT corrected for on-site Coulomb interactions (GGA + U) to allow a direct comparison of the two methods. We show that GGA fails to predict the experimentally observed electronic structure, in agreement with previous uncorrected DFT calculations on this system. Introducing the +U term encourages localisation of the excess electronic charge, with the qualitative distribution depending on the value of U. For low values of U (?4.0 eV) the charge localises in the sub-surface layers occupied in the GGA solution at arbitrary Ti sites, whereas higher values of U (?4.2 eV) predict strong localisation with the excess electronic charge mainly on the two Ti atoms neighbouring the vacancy. The precise charge distribution for these larger U values is found to differ from that predicted by previous hybrid-DFT calculations.     

Analysis of the first triad of interacting states (0 2 0), (1 0 0), and (0 0 1) of D2O from hot emission spectra

The far-infrared and middle-infrared emission spectra of deuterated water vapour were measured at temperatures 1370, 1520, and 1940 K in the ranges 320-860 and 1750-3400 cm⁻¹. The measurements were performed in an alumina cell with an effective length of hot gas of about 50 cm. More than 3550 new measured lines for the D₂¹⁶O molecule corresponding to transitions from highly excited rotational levels of the (0 2 0), (1 0 0), and (0 0 1) vibrational states are reported. These new lines correspond to rotational states with higher values of the rotational quantum numbers compared to previously published determinations: J_max = 29 and K_a(max) = 22 for the (0 2 0) state, J_max = 29 and K_a(max) = 25 for the (1 0 0) state, and J_max = 30 and K_a(max) = 23 for the (0 0 1) state. The extended set of 1987 experimental rotational energy levels for the (0 2 0), (1 0 0), and (0 0 1) vibration states including all previously available data has been determined. For the data reduction we used the generating function model. The root mean square (RMS) deviation between observed and calculated values is 0.004 cm⁻¹ for 1952 rovibrational levels of all three vibration states. A comparison of the observed energy levels with the best available values from the literature and with the global predictions from molecular electronic potential energy surfaces of water isotopic species [H. Partridge, D.W. Schwenke, J. Chem. Phys. 106 (1997) 4618] is discussed. The latter confirms a good consistency of mass-dependent DBOC corrections in the PS potential function with new experimental rovibrational data.     

CO adsorption on epitaxially grown Pt layers on Ru(0 0 0 1)

The adsorption of CO on epitaxially grown Pt films of variable thickness has been studied using infrared-absorption spectroscopy, scanning tunnelling microscopy and thermal desorption spectroscopy. Depending on the number of pseudomorphic Pt layers (N_Pt = 1-4) the internal and external CO stretching modes (ν_C-O and ν_Pt-CO, respectively) display characteristic frequency shifts due to the vanishing influence of the underlying Ru(0 0 0 1) substrate and Pt/Ru interface. For thicker layers (N_Pt ? 5) when this influence has become negligible, the compressive stress within the Pt film is gradually relieved, leading to a dislocation network. The structural heterogeneity during the ongoing relaxation process of the Pt film is reflected in the ν_C-O line shape; no line broadening is observed for either pseudomorphic or very thick films (N_Pt ? 15). For N_Pt ? 3 the adsorption of CO on Pt/Ru(0 0 0 1) films closely resembles CO on Pt(1 1 1), with residual deviations in line position and desorption temperatures gradually converging to zero.     

Four-fold magnetic anisotropy in a Co film on MgO(0 0 1)

The development of devices based on magnetic tunnel junctions has raised new interests on the structural and magnetic properties of the interface Co/MgO. In this context, we have grown ultrathin Co films (≤30 Å) by molecular-beam epitaxy on MgO(0 0 1) substrates kept at different temperatures (T_S). Their structural and magnetic properties were correlated and discussed in the context of distinct magnetic anisotropies for Co phases reported in the literature. The sample characterization has been done by reflection high energy electron diffraction, magneto-optical Kerr effect and ferromagnetic resonance. The main focus of the work is on a sample deposited at T_S=25 °C, as its particular way of growth has enabled a bct Co structure to settle on the substrate, where it is not normally obtained without specific seed layers. This sample presented the best crystallinity, softer magnetic properties and a four-fold in-plane magnetic anisotropy with Co〈1 1 0〉 easy directions. Concerning the samples prepared at T_S=200 and 500° C, they show fcc and polycrystalline structures, respectively and more intricate magnetic anisotropy patterns.     

XPS, electric and photoluminescence-based analysis of the GaAs (1 0 0) nitridation

In this paper, nitridation process of GaAs (1 0 0) substrates was studied in-situ using X-ray photoelectron spectroscopy (XPS) and ex-situ by means of electrical method I-V and photoluminescence surface state spectroscopy (PLS³) in order to determine chemical, electrical and electronic properties of the elaborated GaN/GaAs interfaces.The elaborated structures were characterised by I-V analysis. The saturation current I_S, the ideality factor n, the barrier height Φ_Bn and the serial resistance R_S are determined.The elaborated GaN/GaAs structures are also exhibited a high PL intensity at room temperature. From the computer-aided analysis of the power-dependent PL efficiency measurements (PLS³ technique), the value of the interface state density N_SS(E) close to the mid-gap was estimated to be in the range of 2-4 × 10¹¹ eV⁻¹ cm⁻², indicating a good electronic quality of the obtained interfaces.Correlation among chemical, electronic and electrical properties of the GaN/GaAs interface was discussed.     

Anisotropy of second-order nonlinear optical susceptibilities of arsenic triiodide-sulfur addition complex: AsI3 · 3S8

We report the anisotropic linear and second-order nonlinear optical (NLO) properties of arsenic triiodide-octa-sulfur (1:3) adduct, AsI₃ · 3S₈, which spontaneously crystallizes in the trigonal rhombohedral non-centrosymmetric space group R3m. The trigonal symmetry of the AsI₃ · 3S₈ molecule coincides with the crystal symmetry. The crystals are optically uniaxial with n_o/n_e of about 1.2 and show dichroism at the UV-visible wavelengths. Second harmonic generation (SHG) tensor elements were determined from Maker fringes measured with an Nd:YAG laser (∼10 ns pulse, 1064 nm). The coefficient d_222,eff = 32.0 pm/V for the light polarized parallel to the layers of iodine and sulfur atoms in the AsI₃ · 3S₈ crystal ab plane is markedly larger than d₃₃₃ = 11.6 pm/V for the polarization of light parallel to the crystal c axis. The anisotropy parameter, defined as the d_222,eff/d₃₃₃ ratio, is about 2.7 for the AsI₃ · 3S₈ crystal, smaller than that for the isomorphous CHI₃ · 3S₈ crystal (7.3) but larger than for the SbI₃ · 3S₈ crystal (0.7). Highly anisotropic components of the first hyperpolarizability tensor of an AsI₃ · 3S₈ molecule, β, were derived from the quadratic nonlinear susceptibility tensor of the crystal.     

Absorption spectra of CO2 and CO2 near 1.05 μm

The absolute line intensities of the Fermi triad 2003i-00001 (i = 1, 2, 3) of ¹²C¹⁶O₂ and ¹³C¹⁶O₂ isotopic species of carbon dioxide were retrieved from Fourier-transform spectra recorded at Doppler limited resolution in the region 9200-9700 cm⁻¹. The accuracy of the line intensity determination is estimated to be better than 15% for most lines. The vibrational transition dipole moments squared and Herman-Wallis coefficients have been determined. The global fittings of the observed line intensities within the framework of the effective operators method have been performed. The fitting results reproduce the data within experimental uncertainty.     

A Study on Entanglement Sudden Death in the Open Bipartite Systems

Examining the relation between concurrence and energy in the open bipartite systems, we give an enlightening discussion about reason which causes the entanglement sudden death. We consider two two-level atoms A and B initially entangled to some extent and coupled individually to two cavities which are initially in their vacuum states. We analyze the dynamics of entanglement and energy for two atoms after tracing over the cavity degrees of freedom. By comparing with concurrence and energy, we obtain a conclusion, i.e., there is a critical value U _C =0, when the energy U<U _C =0, or, U′≤0, the concurrence must be zero and the ESD will occur for a period of time. Then, we discuss how non-Markovian effects and detunings influence the critical value. Finally, we point out the impact of initial degree of entanglement on the critical value of the energy.     

Adsorption dynamics of CO2 on Cu(1 1 0): A molecular beam study

Molecular beam scattering measurements have been conducted to examine the adsorption dynamics of CO₂ on Cu(1 1 0). The initial adsorption probability, S₀, decreases exponentially from 0.43 ± 0.03 to a value close to the detection limit (∼0.03) within the impact energy range of E_i = (0.12-1.30) eV. S₀ is independent of the adsorption temperature, T_s, and the impact angle, α_i, i.e., the adsorption is non-activated and total energy scaling is obeyed. The coverage, Θ, dependent adsorption probability, S(Θ), agrees with precursor-assisted adsorption dynamics (Kisliuk type) above T_s ∼ 91 K. However, below that temperature adsorbate-assisted adsorption (S increases with Θ) has been observed. That effect is most distinct at large E_i and low T_s. The S(Θ) data have been modeled by Monte Carlo simulations. No indications of CO₂ dissociation were obtained from Auger Electron Spectroscopy or the molecular beam scattering data.     

Theoretical studies of electronic states and phonon modes on the TiC(0 0 1)(1 × 1) surface

We present a comprehensive picture of structural and electronic properties of the TiC(0 0 1)(1 × 1) surface. Our investigations are based on first-principles calculations within the local-density approximation of the density-functional theory. Good agreement has been observed between our calculation and experimental data for the atomic geometry of the surface. In particular, the calculated bond lengths between the first-layer C and the second-layer Ti (d_1C-2Ti = 2.188 Å) and between the first-layer Ti and the second-layer C (d_1Ti-2C = 2.031 Å) are in good agreement with the corresponding experimental values of 2.25 Å and 2.14 Å, respectively. We have also identified surface electronic states and provided clear support for previously available photoemission measurements. We have further calculated surface phonon modes at the zone centre and at the zone-edge point X using a linear response scheme based on the ab initio pseudopotential method. Our calculated surface phonon results are in excellent agreement with electron energy loss spectroscopy results.     

High power diode-pumped passively Q-switched and mode-locking Nd:GdVO4 laser at 912 nm

A high power diode-end-pumped passively Q-switched and mode-locking (QML) Nd:GdVO₄ laser at 912 nm was demonstrated for the first time, to the best of our knowledge. A Z-type laser cavity with Cr⁴⁺:YAG crystals as the intracavity saturable absorber were employed in the experiments. Influence of the initial transmission (T_U) of the saturable absorber on the QML laser performance was investigated. Using the T_U = 95% Cr⁴⁺:YAG, as much as an average output power of 2.0 W pulsed 912 nm laser was produced at an absorbed pump power of 25.0 W, then the repetition rates of the Q-switched envelope and the mode-locking pulse were ~ 224 kHz and ~ 160 MHz, respectively. Whereas the maximum output power was reduced to 1.3 W using the T_U = 90% Cr⁴⁺:YAG, we obtained a 100% modulation depth for the mode-locking pulses inside the Q-switched envelope.     

Determination of the rate of H + O2 + M → HO2 + M (M = N2, Ar, H2O) from ignition of syngas at practical conditions

In H₂ and H₂/CO oxidation, the H + O₂ + M termination step is one of the most important reactions at elevated pressures. With the recent, increased interest in synthetic fuels, an accurate assessment of its rate coefficient becomes increasingly important, especially for real fuel/air mixtures. Ignition delay times in shock-tube experiments at the conditions selected in this study are only sensitive to the rates of the title reaction and the branching reaction H + O₂ = OH + O, the rate of which is known to a high level of accuracy. The rate coefficient of the title reaction for M = N₂, Ar, and H₂O was determined by adjusting its value in a detailed chemical kinetics model to match ignition delay times for H₂/CO/O₂/N₂, H₂/CO/O₂/Ar, and H₂/CO/O₂/N₂/H₂O mixtures with fuel/air equivalence ratios of ? = 0.5, 0.9, and 1.0. The rate of H + O₂ + N₂ = HO₂ + N₂ was measured to be 2.7 (−0.7/+0.8) × 10¹⁵ cm⁶/mol² s for T = 916-1265 K and P = 1-17 atm. The present determination agrees well with the recent study of Bates et al. [R.W. Bates, D.M. Golden, R.K. Hanson, C.T. Bowman, Phys. Chem. Chem. Phys. 3 (2001) 2337-2342], whose rate expressions are suggested herein for modeling the falloff regime. The rate of H + O₂ + Ar = HO₂ + Ar was measured to be 1.9 × 10¹⁵ cm⁶/mol² s for T = 932-965 K and P = 1.4 atm. The rate of H + O₂ + H₂O = HO₂ + H₂O was measured to be 3.3 × 10¹⁶ cm⁶/mol² s for T = 1071-1161 K and P = 1.3 atm. These are the first experimental measurements of the rates of the title reactions in practical combustion fuel/air mixtures.     

Kinetic stabilization of Fe film on GaAs(1 0 0): An in situ X-ray reflectivity study

We study the growth of Fe films on GaAs(1 0 0) at a low temperature, 140 K, by in situ X-ray reflectivity (XRR) using synchrotron radiation. The XRR curves are well modeled by a single Fe layer on GaAs both at the growth temperature and after annealed at the room temperature. We found that the surface became progressively rougher during the growth with the growth exponent, β_S = 0.43 ± 0.14. The observed β_S is attributed to the restricted interlayer diffusion at the low growth temperature. The change of the interface width during growth was minimal. When the Fe film was annealed to room temperature, the surface smoothed, keeping the interface width almost unchanged. The confinement of the interface derives from that the diffusion of Ga and As proceeds via the inefficient bulk diffusion, and the overlying Fe film is kinetically stabilized.     

Theoretical line list of D2 O up to 16,000 cm with an accuracy close to experimental

A line list for D₂ ¹⁶O isotopologue of water molecule was calculated in the region 0-16,000 cm⁻¹ with energy levels up to J=30. Variational calculations are based on the semi-theoretical potential energy surface obtained by morphing ab initio potential using the experimental energy levels of D₂ ¹⁶O. For energy levels with J=0, 2, 5 and 10, the standard deviation of the fit is 0.023 cm⁻¹. This line list should make an excellent starting point for spectroscopic modeling and analysis of D₂O rovibrational spectra.