On the roughening transition in abelian lattice gauge theories

We study the width of the confining string between static quarks in abelian lattice gauge theories using strong coupling expansions. We consider gauge groups Z_n and U(1) in 3 and 4 dimensions. This extends previous work with Lüscher, where SU(2) and Z₂ were studied. In ν = 3 dimensions we find evidence for a roughening transition. It is characterized by a divergence of the string width for an infinitely far separated quark-antiquark pair, while the string tension remains non-zero. In ν = 4 dimensions for the abelian groups we do not have evidence for a roughening transition away from a phase transition.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

Finite modular groups and lepton mixing

We study lepton mixing patterns which are derived from finite modular groups ΓN, requiring subgroups Gν and Ge to be preserved in the neutrino and charged lepton sectors, respectively. We show that only six groups ΓN with N=3, 4, 5, 7, 8, 16 are relevant. A comprehensive analysis is presented for Ge arbitrary and Gν=Z₂×Z₂, as demanded if neutrinos are Majorana particles. We discuss interesting patterns arising from both groups Ge and Gν being arbitrary. Several of the most promising patterns are specific deviations from tri-bimaximal mixing, all predicting θ₁₃ non-zero as favoured by the latest experimental data. We also comment on prospects to extend this idea to the quark sector.     

Bruhat Order in Full Symmetric Toda System

In this paper we discuss some geometrical and topological properties of the full symmetric Toda system. We show by a direct inspection that the phase transition diagram for the full symmetric Toda system in dimensions n = 3, 4 coincides with the Hasse diagram of the Bruhat order of symmetric groups S ₃ and S ₄. The method we use is based on the existence of a vast collection of invariant subvarieties of the Toda flow in orthogonal groups. We show how one can extend it to the case of general n. The resulting theorem identifies the set of singular points of dim = n Toda flow with the elements of the permutation group S _n , so that points will be connected by a trajectory, if and only if the corresponding elements are Bruhat comparable. We also show that the dimension of the submanifolds, spanned by the trajectories connecting two singular points, is equal to the length of the corresponding segment in the Hasse diagram. This is equivalent to the fact that the full symmetric Toda system is in fact a Morse–Smale system.     

CW laser action in acentric NdAl3(BO3)4 and KNdP4O12

We report low-threshold, room-temperature, cw lasing in two new high-Nd-concentration materials, NdAl₃(BO₃)₄ and KNdP₄O₁₂, the first ones with acentric space groups. For both materials, thresholds below 1 mW and slope power conversion efficiencies exceeding 20% have been measured. Fluorescence spectra and lifetimes have been measured in Nd_xGd_1?xAl₃(BO₃)₄ and Nd_xGd_1?xP₄O₁₂.     

Systematic study of horizontal gauge theories

We analyze all the possible continuous horizontal gauge groups G _H in relation with their possibility to explain m _b ? m _t. We assume that the only effective fermionic degrees of freedom correspond to the known fermions but allow the possibility of adding a right handed neutrino to each family. We assume that the Higgs fields which generate masses for these fermions, trough renormalizable Yukawa couplings, transform as an irreducible representation of SU(3)_c ? SU(2)_L ? U(1)_Y ? G_H. Under these assumptions we find two U(1)_H or U(1) _H1 ? U(1) _H2 models free of anomalies and able to guarantee that only the top has a renormalizable mass-generating Yukawa coupling.     

Forbidden rotational spectra of axially symmetric polar molecules

In this paper we consider the rotational transitions induced by centrifugal distortion in polar or quasipolar symmetric top molecules belonging to the point groups C_n and C_nv (n ≥ 3). It is shown that in this series only the molecules of point groups C₃, C_3v, C₄, and C_4v may possess rotational spectra induced by first-order centrifugal distortion. A general expression is given for the effective dipole moment operator and for its matrix elements. The peak absorption coefficients for some of the strongest ΔK = 3 transitions of the CH₃D molecule have been calculated and compared with the peak absorption coefficients of allowed transitions.     

Puzzle of low temperature phase of α-(ET)2 salts

α-(ET)₂ salts split into two groups: one superconducting and another with mysterious low temperature phase (LTP). The LTP does not exhibit X-ray signiture of conventional CDW or magnetic one for SDW. But the magnetic phase diagram suggests strongly a kind of CDW. We have analysed the threshold electric field of unconventional CDW (UCDW) both for H=0 and H≠0. The threshold electric field for UCDW with H=0 and for 3D weak-pinning limit describes reasonably well the one determined in α-(ET)₂KHg(SCH)₄. The result for H≠0 is also presented. We propose that the LTP in α-(ET)₂ salts is most likely UCDW.     

Vibrational spectra of M3PCr4O16 (M = K,NH4)

The infrared and Raman spectra of the two phosphochromates M₃PCr₄O₁₆ (M = K, NH₄) have been recorded and analysed. The spectra could be interpreted on the basis of the vibrations of Cr-O-P, O-P-O and CrO₃ groups. A large number of vibrational bands have been observed for each mode due to the existence of different Cr-O bond lengths. The anion is more distorted in potassium phosphochromate. The three ammonium groups are distinct.     

Strong coupling expansions for the mass gap in lattice gauge theories

We derive strong coupling expansions for the mass gap in euclidean lattice gauge theories in any space-time dimension. For gauge groups SU(2), SU(3), Z₂ and Z₃ the series are calculated up to order g^?16. They are used to get rough estimates for the lowest glueball mass in continuum SU(2) and SU(3) gauge theories, assuming a sudden crossover from strong to weak coupling behaviour in the lattice theory.     

Comparative analysis of the influence of bulky β-alkyl substituents on fluorescent properties of some series of spatially distorted meso-phenyl substituted porphyrins

We present results of our systematic investigation and comparative analysis of the spectral-kinetic properties of absorption and fluorescence of two series of related planar porphyrins in liquid media at 293 K, in which deviations from the planarity are caused by contact steric interactions of eight peripheral β-pyrrole methyl (?CH₃) or ethyl (?C₂H₅) groups with a successively increasing number (from one to four) and varying position of meso-phenyl (Ph) substituents in the porphyrin macrocycle. It is substantiated that considerable differences between the spectral-kinetic properties of absorption and fluorescence of the octaethyl- and octamethylporphyrin molecules, which have the same number of meso-phenyl substituents, are caused by fundamentally different roles played by β-ethyl and β-methyl groups, which differ in volume and which determine differences in the character of steric interactions and the efficiency of the dynamic relaxation of the tetrapyrrole macrocycle. It is revealed that there is a difference between calculated f _theor and experimentally determined f _exp values of the fluorescence probability, which is caused by conformational rearrangements of spatially distorted porphyrin macrocycles in the S ₁ excited state, which reduce the oscillator strength and lower the energy of the long-wavelength transition S ₀ → S ₁. It is found that the chemical nature, the size, and the number of bulky -CH₃ or -C₂H₅ β-pyrrole groups affect weakly rate constants of fluorescence quenching by molecular oxygen and do not create noticeable steric hindrances for contact interactions of the oxygen molecule with the π-conjugated system of the tetrapyrrole macrocycle.     

The application of extended permutation-inversion groups to internal rotation of a symmetric rotor top in a symmetric or asymmetric rotor molecule

By applying the concept of extended groups to the internal rotation problem in molecules with unequal halves, it has proved possible to construct a consistent formalism involving groups which correspond to very high, but finite multiples of the original Longuet-Higgins permutation-inversion group of the molecule. This formalism thus bridges the gap between the infinite extended groups used for linear molecules and the double groups used for molecules with two identical coaxial rotors. For the example of CF₃NO considered explicitly in this paper, with permutation-inversion group isomorphic to C_3v, the extended group is found to be isomorphic to C_3m,v, where m is an integer obtained from the rational number $\text{p}\text{m}$ which equals within experimental error the ratio ρ of top and molecule moments-of-inertia frequently introduced in discussions of the internal rotation problem. The extended group formalism can be used to rederive in an interesting fashion many results already well known from theoretical discussions in the earlier infrared and microwave literature, and shows promise for the treatment of as yet unsolved problems in molecules exhibiting internal rotation.     

Photoluminescence properties of Eu in Y(PO3)3 under VUV excitation

The photoluminescence properties of Y_1−x(PO₃)₃:xEu³⁺ (0<x≤0.2) are investigated. The excitation spectrum of Y_0.85(PO₃)₃:0.15Eu₃⁺ shows that both the (PO₃)₃³⁻ groups and the CT bands of O²⁻-Y³⁺ can efficiently absorb the excitation energy in the region of 120-250 nm. Under 147 nm excitation, the optimal emissive intensity of Y_1−x(PO₃)₃:xEu³⁺ (0<x≤0.2) is about 36% of the commercial phosphor (Y,Gd)BO₃:Eu³⁺, which hints that the absorbed energy by the host matrix could be efficiently transferred to Eu³⁺. We try to study the concentration quenching mechanism of Y_1−x(PO₃)₃:xEu³⁺ (0<x≤0.2) under 147 and 172 nm excitation.     

Stability of higher-dimensional Einstein-Yang-Mills theories on symmetric spaces

We study (4 + d)-dimensional Einstein-Yang-Mills theories with arbitrary gauge groups, G_YM. The theory is compactified on a d-dimensional symmetric coset space $\text{G}\text{H}$ with a symmetric, topologically non-trivial classical gauge field, embedded in an H-subgroup of the Yang-Mills group. These theories are known to be classically stabilized by gravity if G_YM = H, $\text{G}\text{H}$ is a sphere and d ≠ 3. We study classical instabilities caused by embedding H in a larger gauge group. The small fluctuation spectrum is completely calculable, and leads to a stability condition. For two-dimensional spheres this condition is precisely the Brandt-Neri stability condition for non-abelian monopole fields. For four-spheres we find stability for SU(2) instantons embedded in arbitrary gauge groups and we reproduce the fluctuation spectrum around instantons. For higher-dimensional spheres the stable solutions of this type are completely classified, and occur only for d = 5, 6, 8, 9, 10, 12 and 16. The results show a remarkable agreement with expected topological stability. We also give a few examples with other symmetric spaces, such as CP_n, where the stability criterion appears less restrictive.     

Quasi-1 structure on q-Poincaré algebras

We use braided groups to introduce a theory of 1-structures on general inhomogeneous quantum groups, which we formulate as quasi-1 Hopf algebras. This allows the construction of the tensor product of unitary representations up to a quantum cocycle isomorphism, which is a novel feature of the inhomogeneous case. Examples include q-Poincaré quantum group enveloping algebras in R-matrix from appropriate to the previous q-Euclidean and q-Minkowski space-time algebras R₂₁x₁x₂ = x₂x₁R and R₂₁u₁Ru₂ = u₂R₂₁u₁R. We obtain unitarity of the fundamental differential representations. We further show that the Euclidean and Minkowski-Poincaré quantum groups are twisting equivalent by another quantum cocycle.     

On a general analytic formula for U q(su(3)) Clebsch-Gordan coefficients

We present the projection operator method in combination with the Wigner-Racah calculus of the subalgebra U _q(su(2)) for calculation of Clebsch-Gordan coefficients (CGCs) of the quantum algebra U _q(su(3)). The key formulas of the method are couplings of the tensor and projection operators and also a tensor form for the projection operator of U _q(su(3)). We obtain a very compact general analytic formula for the U _q(su(3)) CGCs in terms of the U _q(su(2)) Wigner 3nj symbols.     

Interactions between tri-methylaluminum molecules and their effect on the reaction of tri-methylaluminum with an OH-terminated Si (0 0 1) surface

We studied the interaction between tri-methylaluminum (Al(CH₃)₃, TMA) molecules and their effect on TMA reactions with a fully OH-terminated Si (0 0 1) surface for initial aluminum oxide thin-film growth using density functional theory. The reaction between an adsorbed TMA and the surface produced a di-methylaluminum (-Al(CH₃)₂, DMA) group, and further reaction to a uni-methylaluminum (-AlCH₃, UMA) group with energy barriers of 0.50 and 0.21 eV, respectively. A second TMA adsorbed near the already adsorbed TMA, DMA, or UMA group showed higher energy barriers (0.68-1.01 eV) for its reaction to produce a DMA group due to the interaction between them. Therefore, the fully OH-terminated Si (0 0 1) surface would be covered by the mixture of the adsorbed TMA and UMA groups at an intermediate surface temperature.     

Spectrum and intensity of light scattered from SF6 along the coexistence curve

Our two groups have measured independently the “Rayleigh linewidth” (Γ), the reduced compressibility (??/?μ)_T, and the pressure (P) of SF₆ along the liquid and vapor sides of the coexistence curve. We find that (??/?μ)_T = 1.67 × 10^-10 (1 - T/T_c)^{-1.22 ± 0.015}g²erg^-1cm^-3 and (?P/?T)lχ = (7094 ± 0.1) × 10⁵ dyne/cm² ° We analyze our linewidth measurements in terms of the Kadanoff-Swift-Kawasaki mode-mode coupling theory using estimates for the viscosity and correlation range.     

All possible Cayley-Klein contractions of quantum orthogonal groups

Spaces of constant curvature and their motion groups are described most naturally in the Cartesian basis. All these motion groups, also known as CK groups, are obtained from an orthogonal group by contractions and analytical continuations. On the other hand, quantum deformation of orthogonal group SO(N) is most easily performed in the so-called symplectic basis. We reformulate its standard quantum deformation to the Cartesian basis and obtain all possible contractions of quantum orthogonal group SO _q (N) for both untouched and transformed deformation parameters. It turned out that, similar to the undeformed case, all CK contractions of SO _q (N) are realized. An algorithm for obtaining nonequivalent (as Hopf algebra) contracted quantum groups is suggested. Contractions of SO _q (N), N = 3, 4, 5, are regarded as examples.     

Rigid lattice NMR spectra of proton conductors H(H2O)nSbO3

The “rigid lattice” ¹H NMR spectra of H(H₂O)_nSbO₃ have been interpreted for n=0.20, 0.92 and 1. For n?0.92 the compounds contain deformed H₃O⁺ ions and OH groups. For n=1 the real formula is (H₃O)_0.7H_0.3SbO₃,0.3 H₂O. The results are discussed in relation to the level of proton conductivity.