Partial diagonalization of Bethe-Salpeter type equations

We consider an equation of the Bethe-Salpeter type, with arbitrary potential and kernel, respectively, for space-like momentum transfer. The invariance group of the equation is then the Lorentz-group in three dimensions, the O(1, 2) group. The standard procedure for the diagonalization of such equations (valid for square integrable solutions only) is generalized to include the case of power bounded solutions, by means of a generalized O(1, 2) expansion formalism. The result is a two-dimensional integral equation for the O(1, 2) expansion coefficients. The right-most l-plane singularities of these determine the asymptotic behaviour of the amplitudes as in ordinary Regge theory. The formalism can be applied to other dynamical equations possessing O(1, 2) symmetry.     

Optimization in the extended variational approach: TheSU(2)-SO(3) phase structure on the lattice

We use the linear delta expansion with a trial action based on single links to explore the phase structure of the mixedSU(2)-SO(3) lattice gauge theory. The method can be regarded as a systematic expansion going beyond mean field theory or the variational method, to which it is closely related in first order. AtO(δ ²) the line of first-order phase transitions is shown to terminate, and atO(δ ³) the boundaries between the different phases are well reproduced.     

Phase transition in the three-dimensional chiral field

The essentially nonlinear chiral field in three dimensional space time non-renormalizable in the usual perturbation expansion is studied. We consider systematic $\text{1}\text{N}$ expansion for this model. In the framework of the latter a phase transition takes place: above the critical point the theory is in the O(N) symmetric phase, below it the O(N) symmetry breaks. The $\text{1}\text{N}$ renormalized expansion for both phases is described and the connection between the non-renormalizability of the conventional perturbation theory and the non-analytic dependence on the coupling constant is established.     

Spanning Forests on Random Planar Lattices

The generating function for spanning forests on a lattice is related to the q-state Potts model in a certain q→0 limit, and extends the analogous notion for spanning trees, or dense self-avoiding branched polymers. Recent works have found a combinatorial perturbative equivalence also with the (quadratic action) O(n) model in the limit n→?1, the expansion parameter t counting the number of components of the forest. We give a random-matrix formulation of this model on the ensemble of degree-k random planar lattices. For k=3, a correspondence is found with the Kostov solution of the loop-gas problem, which arise as a reformulation of the (logarithmic action) O(n) model, at n=?2. Then, we show how to perform an expansion around the t=0 theory. In the thermodynamic limit, at any order in t we have a finite sum of finite-dimensional Cauchy integrals. The leading contribution comes from a peculiar class of terms, for which a resummation can be performed exactly.     

On theO(1/N 2)β-function of the Nambu-Jona-Lasinio model with non-abelian chiral symmetry

We present the formalism for computing the critical exponent corresponding to the β-function of the Nambu-Jona-Lasinio model withSU(M)×SU(M) continuous chiral symmetry atO(1/N ²) in a largeN expansion, whereN is the number of fermions. We find that the equations can only be solved for the caseM=2 and subsequently an analytic expression is then derived. This contrasting behavior between theM=2 andM>2 cases, which appears first atO(1/N ²), is related to the fact that the anomalous dimensions of the bosonic fields are only equivalent forM=2.     

High resolution Raman spectroscopy of the fundamental vibrational band of 16O2

The vibrational Raman spectrum of ¹⁶O₂ has been recorded with high resolution (0.05 cm^?1 for the Q branch). The expansion of the Hamiltonian as a sum of irreducible tensors of the O(3) group allowed us to obtain easily the expressions for the energy levels, taking into account the off-diagonal matrix elements. From the analysis of the spectrum the excited state constants have been calculated; in particular the rotational constants obtained are: B₁ = 1.421884 ± 0.000013 cm^?1 and D₁ = (?4.864 ± 0.014)10^?6 cm^?1.     

The mean field perturbation theory of lattice gauge models with covariant gauge fixing

A mean field perturbative expansion with covariant gauge fixing is derived. It is proved that it reproduces the perturbative series at β→∞ in the case of the free energy density to the ordersO(β),O(lnβ),O(l) at least.     

Dynamical symmetry of the magnetic monopole

It is demonstrated that the interaction of a charged particle with a magnetic monopole possesses a large invariance; time can be arbitrarily re-parametrized. When the interaction occurs within conventional, non-relativistic dynamics, the entire theory admits an O(2, 1) conformal group of symmetry transformations, which seems to have escaped notice. Combining this invariance group with the O(3) group of spatial rotations shows that an O(2, 1) × O(3) group of invariances is present, in analogy with the Kepler/Coulomb system. Furthermore, at fixed angular momentum, the dynamics are characterized by a single, irreducible, unitary representation of the conformal O(2, 1) symmetry group, whose Casimir eigenvalue is determined by the monopole strength. Some similar properties of the isotropic harmonic oscillator are also mentioned.     

Crystal structure of Fe-doped lanthanum gallate for oxygen partial pressures studied by neutron powder diffraction

Neutron powder diffraction experiments were carried out to investigate a change in a crystal structure of La_0.8Sr_0.2Ga_0.65Fe_0.35O₃ for oxygen partial pressures, P_O2, at 800 °C. The crystal structure was refined on the basis of the R3?c symmetry for the P_O2 range from 10^? 1 to 10^? 20 atm, by the Rietveld analysis. It was found that lattice parameters, a and c, monotonically expand with decreasing P_O2, and then both expansions are rapidly suppressed below 10^? 4 atm. In the meantime, l_M–O and l_O–O(2) also discontinuously increased with decreasing P_O2, while l_O–O(1) did not change at all P_O2, where l_M–O, l_O–O(1) and l_O–O(2) are the bond lengths within a MO₆ octahedron (M = Ga_0.65Fe_0.35). This result indicates that the l_M–O and the l_O–O(2) are more important than the l_O–O(1) for such a complicated lattice expansion for P_O2.     

Discharged generator of singlet oxygen for oxygen-iodine laser. Transport kinetics of O2(a 1δg) and O2(b 1σ g + ) molecules and O(3 P) atoms in Ar:O2 and He:O2 flows excited by a 13.56-MHz discharge

To understand and reveal the basic physical factors providing the possibility of scaling of a discharged singlet oxygen generator (DSOG) in an oxygen-iodine laser, the production, and transport kinetics of metastable O₂(a ¹δ_g) and O₂(b ¹σ _g ⁺ ) molecules, as well as O(³ P) atoms, were investigated in Ar:O₂ and He:O₂ gas flows excited by a 13.56-MHz discharge in a wide range of pressures (4–40 Torr) and oxygen percentages. It is shown that the densities and transport kinetics of O₂(a ¹δ_g), O₂(b ¹σ _g ⁺ ), and O(³ P) appear similar for oxygen mixtures with argon and helium in the same conditions independent of discharge mode. Compared to pure O₂, the dilution of oxygen with an inert gas allows higher energy inputs per an oxygen molecule to achieved, especially under conditions of the homogeneous discharge mode (α-mode), which gives a higher efficiency of O₂(a ¹δ_g) excitation in Ar:O₂ and He:O₂ mixtures. But the maximum attainable yield of singlet oxygen in Ar:O₂ and He:O₂ at fixed partial O₂ pressure is found to be comparable with the O₂(a ¹δ_g) yield in pure oxygen at the same pressure. The reason for this is the increased three-body deactivation of O₂(a ¹δ_g) by atomic oxygen in the mixtures because of the greater total pressure. The estimation of the rate constant of O₂(a ¹δ_g) three-body quenching by O(³ P) in Ar:O₂ and He:O₂ mixtures as (1.5 ± 0.5) × 10^?32 cm⁶/s was carried out from the analysis of transport kinetics of singlet and atomic oxygen in the discharge afterglow at high pressures exceeding ～10 Torr. A similar analysis for the lower pressures has revealed that losses both of metastable O₂(a ¹δ_g) and O₂(b ¹σ _g ⁺ ) molecules, and of O(³ P) atoms on the surface of the discharge tube, are determined by the density of each of the components. The obtained loss probabilities of O₂(a ¹δ_g), O₂(b ¹σ _g ⁺ ), and O(³ P) on the silica surface show that the surface loss probabilities of all the species can increase noticeably under the discharge exposure. Thus, the key parameters determining the maximal O₂(a ¹δ_g) yield in the DSOG are a homogeneous volumetric mode of the discharge, energy input per oxygen molecule in this mode, and a low rate of O₂(a ¹δ_g) quenching. Just three-body quenching of O₂(a ¹δ_g) by O(³ P) limits the singlet oxygen yield with increasing pressure. The fast removal of atomic oxygen both in discharge and in the earlier afterglow could provide DSOG scaling with pressure.     

57Fe hyperfine interaction parameters and selected magnetic properties of high purity MFe12O19 (M=Sr,Ba)

Much of the confusion regarding the ⁵⁷Fe Mössbauer spectroscopic hyperfine parameters of SrFe₁₂O₁₉ and BaFe₁₂O₁₉ at 300 K has been removed by means of an interlaboratory investigation of well-characterized samples prepared from high purity starting materials. In contrast to previous investigations, the contributions of each of the five Fe sublattices to the Mössbauer spectrum are discernible at 300 K and five components are necessary for an adequate fit of the data. The relative magnitudes of the hyperfine fields, H_n, and isomer shifts, δ, are as follows: for SrFe₁₂O₁₉ and BaFe₁₂O₁₉: H_n(2b)< H_n(12k)<H_n(4f₁) <H_n(2a)<H_n(4f₂), for SrFe₁₂O₁₉ δ(4f₁≤δ(2b)<δ(12k)δ(2a)<δ(4f₂), and for BaFe₁₂O₁₉ δ4f₂), and for BaFe₁₂O₁₉ δ(4f₁<δ(4f₁)<(12k) < δ(4f₂)<δ(2a). The above assignment is based on considerations of both magnetic and crystal/chemical structures.The high purity starting materials seem to have appreciable influences on both hyperfine interaction parameters and bulk magnetic properties as observed by others for spinel and garnet ferrites.     

Generalized O(1, 2) expansions of multiparticle amplitudes. II. The O(1, 2) laplace transform

We extend a previous work [1] on generalized O(1, 2) expansions for power-bounded multiparticle amplitudes. This extension allows one to shift the contour-integral in the O(1, 2) integral representation an arbitrary but finite distance into the left half of the l-plane. The discrete terms in the representation get absorbed into the integral in this case, but instead new discrete terms appear which are of the order of magnitude O(s^?1) for large values of s. These new discrete terms disappear if the Mandelstam symmetry holds.     

Generalized O(2, 1) expansions for asymptotically growing amplitudes,II: Space-time region

We extend a previous treatment [1] of O(2, 1) expansions for nonsquare-integrable many particle amplitudes to the case where one “incoming” and one “outgoing” cluster have space-like O(2, 1) momenta.     

Dimensional regularisation and instantons

Dimensional regularisation is applied to the calculation of the quantum corrections to the instanton tunnelling amplitude in an SU(2) gauge theory. The principal feature is the introduction of an n-dimensional field configuration (a “quasi-instanton”), which generalises the O(5) invariance of the instanton and allows a coordinatisation of the function space of fields in its neighbourhood. This enables the functional integral measure to be factorised, with integrations over the translation and dilatation degrees of freedom being extracted. It is shown that a conformally invariant definition of orthogonality must be used in relation to the zero-mode eigenfunctions of the small oscillations expansion, irrespective of regularisation. An O(n + 1) covariant formalism is employed. An unconventional choice of gauge fixing term, which is not a perfect square, is made and is shown to allow the important freedom of calculating in a gauge specified by an arbitrary parameter α.     

On the large order expansion for the anharmonic oscillators

Using functional approaches, we investigate the large-K behaviour of theK ^th coefficientE _k in the perturbation expansion for the ground-state energyE(g) of the generalized anharmonic oscillatorX ^2N with internalO(_n)-symmetry. We establish the equivalence between the pure functional approach and the method of Collins-Soper at any order in 1 /K. For that purpose, we first develop an algebraic treatment of perturbation series and prove a theorem on Borelsummable functions. Finally, we compute analytically the 1 /K and 1 /K ² corrections to the leading term forN=2.     

Independence of local algebras in Quantum Field Theory

It is shown that localC*-algebras \(\mathfrak{A}\) (O ₁) and \(\mathfrak{A}\) (O ₂) associated with spacelike separated regionsO ₁ andO ₂ in the Minkowski space are independent. The proof is accomplished by a theorem concerning the structure of theC*-algebra generated by \(\mathfrak{A}\) (O ₁) and \(\mathfrak{A}\) (O ₂).     

Crystal growth and refinement of K1.88Ga1.88Sn8.12O16 hollandite-type compound

We grew single crystals of K_1.88Ga_1.88Sn_6.12O₁₆ hollandite-type compound and precisely determined their crystal structure by X-ray diffraction. K_1.88Ga_1.88Sn_6.12O₁₆ fibrous crystals measuring an average of about 2 mm in length and 60 μm in diameter were obtained by slow-cooling (from 1623 K to 1273 K) of a flux melt consisting of a 40 mol% crystal composition of (K₂O)₁(Ga₂O₃)₁(SnO₂)₁ and a 60 mol% flux composition of (K₂O)₂(MoO₃)₁(B₂O₃). The unit cell of K_1.88Ga_1.88Sn_6.12O₁₆ (a = 1.0389(2) nm, c = 0.3132(2) nm, V =  0.3381(2) nm³) was larger than that of K_1.52Ga_1.52Ti_6.48O₁₆. The ionic size difference with the replacement of Ti by Sn, 10%, was relaxed by an anisotropic expansion of the octahedra by 2.6% in the (001) plane and 5.8% along the c-axis.     

Interaction of Li<Subscript>1+<Emphasis Type="Italic">x</Emphasis></Subscript>(Ni,Mn,Co)O<Subscript>2</Subscript> cathode materials with single and complex oxides at 900 °C

In order to find efficient barrier materials and inert dopants for the high temperature processing of Li-ion battery cathode materials, a chemical stability of Li_1+x (Ni,Mn)O₂ at 900 °C in air in contact with Al₂O₃, Nb₂O₅, SnO₂, TiO₂, and CeO₂ is studied. The interaction of Li_1+x (Ni,Mn)O₂ with Al₂O₃, Nb₂O₅, and SnO₂ results in the formation of the corresponding complex oxides—LiAlO₂, Li₃NbO₄, and Li₂SnO₃. A first stage of the chemical degradation of Li_1+x (Ni,Mn)O₂ is usually accompanied by the transformation of its hexagonal crystal structure into the cubic one. The reaction of Li_1+x (Ni,Mn)O₂ with titania is accompanied by the disappearance of TiO₂ and the formation of the Li_1+x (Ni,Mn)O₂-based solid solution. XRD analysis confirmed the absence of chemical interaction of Li_1+x (Ni,Mn)O₂ with CeO₂ while SEM data demonstrated the absence of eutectic melting at 900 °C. The similar absence of traces of the high temperature chemical interaction with Li_1+x (Ni,Mn)O₂ is found also for LiAlO₂, Li₃NbO₄, and Li₂SnO₃. Galvanostatic and cyclic voltammetry studies of Li_1+x (Ni,Mn,Co)O₂–CeO₂ composites demonstrated the increase in the initial discharge capacity of the composite cathodes compared to the native Li_1+x (Ni_,Mn_,Co)O₂.