Comparison of |Q|=1 and |Q|=2 gauge-field configurations on the lattice four-torus

It is known that exactly self-dual gauge-field configurations with topological charge |Q|=1 cannot exist on the untwisted continuum four-torus. We explore the manifestation of this remarkable fact on the lattice four-torus for SU(3) using advanced techniques for controlling lattice discretization errors, extending earlier work of De Forcrand et al. for SU(2). We identify three distinct signals for the instability of |Q|=1 configurations, and show that these signals manifest themselves early in the cooling process, long before the would-be instanton has shrunk to a size comparable to the lattice discretization threshold. These signals do not appear for the individual instantons which make up our |Q|=2 configurations. This indicates that these signals reflect the truly global nature of the instability, rather than the local discretization effects which cause the eventual disappearance of the would-be single instanton. Monte-Carlo generated SU(3) gauge-field configurations are cooled to the self-dual limit using an -improved gauge action chosen to have small but positive errors. This choice prevents lattice discretization errors from destroying instantons provided their size exceeds the dislocation threshold of the cooling algorithm. Lattice discretization errors are evaluated by comparing the -improved gauge-field action with an -improved action constructed from the square of an -improved lattice field-strength tensor, thus having different discretization errors. The number of action-density peaks, the instanton size, and the topological charge of configurations is monitored. We observe a fluctuation in the total topological charge of |Q|=1 configurations, and demonstrate that the onset of this unusual behavior corresponds with the disappearance of multiple-peaks in the action density. At the same time discretization errors are minimal.     

Hydrogen bonds mediated magnetism in Cu(bmen)2Pd(CN)4

Results of synthesis, X-ray structure analysis, electron spin resonance, susceptibility, magnetization and specific heat measurements of powdered Cu(bmen)₂Pd(CN)₄ (,N^′-dimethyl-1,2-diaminoethane) are reported. Its structure is formed of quasi-linear chains of the [-Cu(bmen)₂-NC-Ni(CN)₂-CN-]_n composition; these are interlinked by hydrogen bonds (HBs) leading to two-dimensional patterns. Upon magnetic, spectral and thermodynamic measurements the compound was identified as an S=1/2 Heisenberg antiferromagnet on a square lattice with due to the dominant role of HBs in creating a square network. The long-range ordering observed at 0.24 K is proposed to be of a Néel type. The possibility of tuning the exchange interactions in various directions is considered.     

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.     

On complex singularities of the 2D Euler equation at short times

We present a study of complex singularities of a two-parameter family of solutions for the two-dimensional Euler equation with periodic boundary conditions and initial conditions in the short-time asymptotic régime. As has been shown numerically in Pauls et al. [W. Pauls, T. Matsumoto, U. Frisch, J. Bec, Nature of complex singularities for the 2D Euler equation, Physica D 219 (2006) 40-59], the type of the singularities depends on the angle ? between the modes p and q. Thus, the Fourier coefficients of the solutions decrease as with the exponent α depending on ?. Here we show for the two particular cases of ? going to zero and to π that the type of the singularities can be determined very accurately, being characterised by α=5/2 and α=3 respectively. In these two cases we are also able to determine the subdominant corrections. Furthermore, we find that the geometry of the singularities in these two cases is completely different, the singular manifold being located “over” different points in the real domain.     

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.     

The quark model and b baryons

The recent observation at the Tevatron of (uub and ddb) baryons within 2 MeV of the predicted Σ_b-Λ_b splitting and of baryons at the Tevatron within a few mega electron volts (MeV) of predictions has provided strong confirmation for a theoretical approach based on modeling the color hyperfine interaction. The prediction of  = 5790-5800 MeV is reviewed and similar methods used to predict the masses of the excited states and . The main source of uncertainty is the method used to estimate the mass difference m_b-m_c from known hadrons. We verify that corrections due to the details of the interquark potential and to Ξ_b- mixing are small. For S-wave qqb states we predict , and . For states with one unit of orbital angular momentum between the b quark and the two light quarks we predict , and . Results are compared with those of other recent approaches.     

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.     

The effect of the Bi source on optical properties of Bi2Te3 nanostructures

nanostructures were synthesized by using different Bi sources via a simple solvothermal process, in which and BiCl₃ were used as the Bi sources. Optical properties of nanostructures prepared with and BiCl₃ as the Bi sources were investigated by micro-Raman spectroscopy. The Raman scattering spectrum of hexagonal nanoplates prepared by using as the Bi source shows that the infrared (IR) active mode A_1u, which must be odd parity and is Raman forbidden for bulk crystal due to its inversion symmetry, is greatly activated and shows up clearly in the Raman scattering spectrum. We attribute the appearance of the infrared active A_1u mode in the Raman spectrum to crystal symmetry breaking of hexagonal nanoplates. However, the Raman scattering spectrum of nanostructures with irregular shape prepared by using as the Bi source only exhibits the two characteristic Raman modes of crystals. Micro-Raman measurements on nanostructures with different morphologies offer us a potential way to tailor optical properties of nanostructures by controlling the morphologies of the nanostructures, which is very important for practical applications of nanostructures in thermoelectric devices.     

Quantum critical behaviour in doped Y bB12 studied by ab initio calculations

The Kondo insulator Y bB₁₂ is known to undergo a transition to the metallic state with doping or under an external magnetic field. Within the virtual crystal approximation (VCA), we calculated the occupation of the Yb 4f and 5d shells, and , as a function of doping of Y bB₁₂ with the rare earths Tm and Lu. We found that exhibits an anomalous change at the critical concentration of the dopant, in agreement with experiment ( for Y b_1−xLu_xB₁₂ and for Y b_1−xTm_xB₁₂). We suggest that the critical behaviour seems to be strictly connected with the change of and in consequence the change of the Yb valency.     

Model calculations of the energy band structures of double stranded DNA in the presence of water and Na ions

Using the ab initio Hartree-Fock crystal orbital method in its linear combination of atomic orbitals form we have calculated the band structures of poly(-) and poly(-). Here, besides the nucleotide bases, the sugar and phosphate parts of the nucleotide were also taken into account together with their first water shell and Na⁺ ions. We use the notation with a tilde above the abbreviation of a base for the whole nucleotide; for instance poly() means a guanine base with the deoxyribose and PO₄⁻ groups to which it is bound. The obtained band structures were compared with previous single chain calculations as well as with the earlier poly(-) and poly(-) calculation without water but in the presence of counterions. One finds that all the bands of poly(-) and poly(-) are shifted considerably upwards as compared to the previous single chain results (poly(), poly(), poly() and poly()). This effect is explained by the ∼0.2e charge transfer from the sugars of both chains to the nucleotide bases. The fundamental gaps between the nucleotide base-type highest filled and lowest unfilled bands are decreased in both cases by 1-3 eV, because the valence bands are purine-type and the conduction bands pyrimidine-type, respectively, while in the case of single homopolynucleotides they belong to the same base. We also pointed out that the LUMO is mainly Na⁺-like in both investigated cases and several unoccupied bands (belonging to the Na⁺ ions, the phosphate group and the water molecules) can be found between this and the first unoccupied pyrimidine-like empty band.     

Effect of exchange-coupling interaction on anisotropy of grain in nanoscaled magnets

The effect of inter-grain exchange-coupling interaction on the anisotropy of grain in nanoscaled magnets has been investigated by putting forward an expression of anisotropy at grain boundary, , which is suitable for different coupling conditions, and expresses well the coherency between soft and hard grains. The average anisotropy of grain 〈K^ij〉 has been calculated based on and the theory of partial exchange-coupling interaction. It has been found that the average anisotropy of hard or soft grain, 〈K^hh〉 or 〈K^ss〉, increases with increasing grain size D monotonously when hard-hard or soft-soft grains couple. When soft-hard grains touch each other, with increasing D, the variation of average anisotropy of soft-hard grain 〈K〉 depends on the anisotropy at grain interface , which denotes the affection degree of hard grain on the anisotropy of soft grain. Compared with other results, it is more reasonable that ranges from to . The variations of anisotropy with D we calculated are consistent with those of coercivities given by other authors when is fixed in a certain range.     

Entanglement perturbation theory for the elementary excitation in one dimension

The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin- antiferromagnetic Heisenberg model, it reproduces the des Cloiseaux-Pearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at k=π.     

Computation of energy exchanges by combining information theory and a key thermodynamic relation: Physical applications

By considering a simple thermodynamic system, in thermal equilibrium at a temperature T and in the presence of an external parameter A, we focus our attention on the particular thermodynamic (macroscopic) relation . Using standard axioms from information theory and the fact that the microscopic energy levels depend upon the external parameter A, we show that all usual results of statistical mechanics for reversible processes follow straightforwardly, without invoking the Maximum Entropy principle. For the simple system considered herein, two distinct forms of heat contributions appear naturally in the Clausius definition of entropy, . We give a special attention to the amount of heat , associated with an infinitesimal variation at fixed temperature, for which a “generalized heat capacity”, , may be defined. The usefulness of these results is illustrated by considering some simple thermodynamic cycles.