On short and semi-short representations for four-dimensional superconformal symmetry

Possible short and semi-short representations for and superconformal symmetry in four dimensions are discussed. For the well known short supermultiplets whose lowest dimension conformal primary operators correspond to -BPS or -BPS states and are scalar fields belonging to the SU(4) R-symmetry representations [0,p,0] and [q,p,q] and having scale dimension Δ=p and Δ=2q+p, respectively, are recovered. The representation content of semi-short multiplets, which arise at the unitarity threshold for long multiplets, is discussed. It is shown how, at the unitarity threshold, a long multiplet can be decomposed into four semi-short multiplets. If the conformal primary state is spinless one of these becomes a short multiplet. For a -BPS multiplet need not have a protected dimension unless the primary state belongs to a [1,p,1] representation.     

A generalized Kolmogorov-Sinai-like entropy under Markov shifts in symbolic dynamics

In this paper, a generalized Kolmogorov-Sinai-like entropy ( entropy) in the sense of Tsallis is proposed with a nonextensive parameter q under Markov shifts, which contains the classical Kolmogorov-Sinai (KS) entropy and the Rényi entropy as well as Bernoulli shifts as special cases. To verify the formula of this entropy, a one-dimensional iterative system is chosen as an example of Markov shifts, and its entropy is evaluated by a new refinement method of symbolic dynamics called symbolic refinement which differs from the conventional numerical method. The numerical results show that this entropy is monotonically decreasing as q increases.     

Crystal field effect and geometric frustration in Er2Ti2O7 —an XY antiferromagnetic pyrochlore

Magnetic susceptibility of powder Er₂Ti₂O₇ (ErT) is measured between 300 K and 80 K. shows a Curie-Weiss (CW) type behaviour with   ErTiO_3.5 and . A crystal field (CF) analysis of our experimental data, g-values (g_∥=0.27 and g_⊥=7.8) and the positions of two CF levels (reported earlier from an inelastic neutron scattering study) provide CF parameters and CF levels of the ground ⁴I_15/2 and excited multiplets of ErT. The theoretical follows a CW-type behaviour, with . Single-ion magnetic anisotropy (χ_⊥−χ_∥) is 9500×10⁻⁶ emu/mol ErTiO_3.5 at 300 K, which increases by ∼54 times at 10 K and ErT resembles an XY planar system. It can be inferred from CF analysis that the earlier observed change of from −13 K to −22 K below 50 K is not due to the CF effect. Nuclear hyperfine (HF) levels of ¹⁶⁷ErT and ¹⁶⁶ErT are calculated and the theoretical curve of vs. T (K) for T<T_N matches the observed results. Mössbauer lines expected for ¹⁶⁶ErT are also predicted.     

First-principles study of arsenic impurity clusters in molecular beam epitaxy (MBE) grown HgCdTe

The understanding of the microstructures of the arsenic tetramer , dimer , and singlet of HgCdTe is important to explain the high electrical compensation of molecular beam epitaxy (MBE) samples and the conversion to p-type behavior. The stable configurations were obtained from the first-principles calculations for the arsenic cluster defects [ (n=1, 2, and 4)] in as-grown HgCdTe. According to the defect formation energies calculated under Te-rich conditions, the most probable configurations of , , and have been established. For the optimized and the energy is favorable to combine in a nearest neighboring mercury vacancy , and the corresponding configurations can be used to explain the self-compensated n-type characteristics in as-grown materials. is likely to be more abundant than in as-grown materials, but arsenic atoms are more strongly bounded in than in , thus more substantial activation energy is needed for than that for . The atomic relaxations as well as the structural stability of the arsenic defects have also been investigated.     

MRCI studies on the electronic structure of AlN and AlN, and the electron affinity of AlN

Using multireference configuration-interaction methods and double to triple-zeta basis sets with semidiffuse and polarization functions, potential energies and spectroscopic constants for low-lying doublet, and quartet states of AlN⁻ were calculated. has R_e=3.280 bohr and . lies 0.17 eV above the ground state. Using an estimated electron affinity of 2.1 eV for AlN, four states of AlN⁻ are found to be stable, namely , , , and . Comparisons with the isovalent anions BN⁻ (three stable states) and AlP⁻ (seven stable states) are made. Photo-detachment of an electron from the state of AlN⁻ can lead to an accurate determination of the energy difference between the two close-lying lowest states of AlN, and , predicted here to be 0.09 eV apart.     

4-benzyl pyridinium dihydrogenmonophosphate C6H5CH2C5H4NHH2PO4 : Single-crystal structure and its conductivity in polycrystalline form

The salt 4-benzyl pyridinium dihydrogenmonophosphate is monoclinic P2₁/c with the following unit cell dimensions: ; ; ; and β=97.328(11). Also, , D_x=1.403, , F(000)=560; ; and R=0.0495 and R_w=0.0964 for 3733 independent reflections. The structure consists of infinite parallel two-dimensional planes built of H₂PO₄⁻ anions and C₆H₅CH₂C₅H₄NH⁺ cations mutually connected by strong O-H ?O and N-H ?O hydrogen bonding. There are no contacts other than the normal Van der Waals interactions between the layers. The conductivity relaxation parameters associated with some H⁺ conduction have been determined from an analysis of the spectrum measured in a wide temperature range.     

Near-infrared diode laser spectroscopy of the HCSi radical

The , , and band spectra of HCSi radical were investigated by means of near-infrared diode laser spectroscopy to determine precise molecular constants for the and states. The detailed analysis of the rotationally resolved band spectra, studied for the first time in the present investigation, leads to the precise determination of molecular constants for the state associated with the Renner-Teller interaction. We obtained −0.15126663(53) and 495.00698(30) cm⁻¹ as the Renner-Teller parameter ε and the bending vibrational frequency ω₂, respectively. Based on the molecular constants for the and states, the rotational levels of the state were analyzed to obtain molecular constants and information on upper state perturbations. Using the available spectroscopic data, valence force fields for both the and states were estimated to aid in understanding the vibrational energy levels of the HCSi radical.     

Time-resolved spectroscopy of Al, Ti, and Mo X pinch radiation using an X-ray streak camera

Time-resolved spectroscopic measurements of the radiation emitted from Al, Ti, and Mo X pinches have been made with time resolution. The radiation is emitted from micropinch plasmas with sizes of order in times in the 10- range. Spectra implied that dense, plasmas were produced, such as a lifetime, 1.5- electron temperature and near solid-density Ti plasma. The experimental systems and analysis methods are described in detail, including line ratio calculations for μm-scale Ti and Al plasmas with ion densities of 10¹⁹-10²⁴ cm⁻³ and electron temperatures.     

Theoretical study of local lattice structure of Mn in perovskite fluorides A2MF4 (A=K, Rb; M=Mg, Zn, Cd) series

A theoretical method for investigating the inter-relation between the molecular structure and electronic structure has been established on the basis of the 252×252 complete energy matrices for a 3d⁵ configuration ion in a tetragonal ligand field. By means of this method, which is independent of the X-ray diffraction, the local structure of the paramagnetic Mn²⁺ ion in perovskite fluorides A₂MF₄ (A=K, Rb; M=Zn, Mg, Cd) are determined directly by analyzing the EPR spectrum of octahedral Mn²⁺ center in A₂MF₄ crystals and the optical absorption spectrum of the (MnF₆)⁴⁻ cluster. It is shown that, comparing with the octahedral cubic structure, the local micro-structure in the vicinity of Mn²⁺ displays an elongated distortion when and a compressed distortion when , and ΔR vs. as well as ΔR vs. in the distortion region is, respectively, approximately linear. Simultaneously, the theoretical zero-field-splitting parameters , and are in good agreement with the experimental values.     

Anomalous thermostat and intraband discrete breathers

We investigate the dynamics of a macroscopic system which consists of an anharmonic subsystem embedded in an arbitrary harmonic lattice, including quenched disorder. The coupling between both parts is bilinear. Elimination of the harmonic degrees of freedom leads to a nonlinear Langevin equation with memory kernels and noise term for the anharmonic coordinates . For zero temperature, i.e. for , we prove that the support of the Fourier transform of and of the time averaged velocity-velocity correlation functions of the anharmonic system cannot overlap. As a consequence, the asymptotic solutions can be constant, periodic, quasiperiodic or almost periodic, and possibly weakly chaotic. For a sinusoidal trajectory with frequency we find that the energy E_T transferred to the harmonic system up to time T is proportional to T^α. If equals one of the phonon frequencies ω_ν, it is α=2. We prove that there is a zero measure set L such that for in its full measure complement R?L, it is α=0, i.e. there is no energy dissipation. Under certain conditions L contains a subset L^′ such that for the dissipation rate is nonzero and may be subdissipative (0≤α<1) or superdissipative (1<α≤2), compared to ordinary dissipation (α=1). Consequently, the harmonic bath does act as an anomalous thermostat, in variance with the common belief that elimination of a macroscopically large number of degrees of freedom always generates dissipation, forcing convergence to equilibrium. Intraband discrete breathers are such solutions which do not relax. We prove for arbitrary anharmonicity and small but finite coupling that intraband discrete breathers with frequency exist for all in a Cantor set C(k) of finite Lebesgue measure. This is achieved by estimating the contribution of small denominators appearing for , related to . For the small denominators do not lead to divergencies such that is a smooth and bounded function in t.     

Non-isospectral integrable couplings of Ablowitz-Ladik hierarchy with self-consistent sources

A kind of new non-isospectral integrable couplings of discrete soliton equations hierarchy with self-consistent sources associated with is presented. As an application example, the integrable coupling hierarchy of non-isospectral Ablowitz-Ladik with self-consistent sources is derived by using of the loop algebra .     

Relaxor behavior of K0.5La0.5Bi2Ta2O9 ceramics

Potassium lanthanum bismuth tantalate (K_0.5La_0.5Bi₂Ta₂O₉), a new relaxor ferroelectric was synthesized via the solid-state reaction route. X-ray structural studies along with Rietveld refinement confirmed it to be an n=2 member of the Aurivillius family of oxides and the refined lattice parameters are , and . The appearance of 1/2{h00} and 1/2{hk0} type superlattice reflections in the electron diffraction patterns reflected the presence of ordered polar regions. A broad dielectric peak associated with frequency dependent dielectric maximum temperature was observed. The value of the diffuseness parameter γ=1.93, obtained from the fit of a modified Curie-Weiss law established the relaxor nature of the title compound. The dielectric relaxation obeyed the Vogel-Fulcher relation wherein and . The relaxor behavior was attributed to the local polar ordering on A-sites.