Boundary Lax pairs for the Toda field theories

Based on the recent formulation of a general scheme to construct boundary Lax pairs, we develop this systematic construction for the affine Toda field theories (ATFT). We work out explicitly the first two models of the hierarchy, i.e. the sine-Gordon () and the models. The Toda theory is the first non-trivial example of the hierarchy that exhibits two distinct types of boundary conditions. We provide here novel expressions of boundary Lax pairs associated to both types of boundary conditions.     

Synthesis and field-emission properties of the tungsten oxide nanowire arrays

High-density, uniformly distributed and quasi-aligned tungsten oxide nanowire arrays have been synthesized by a conventional thermal evaporation approach on indium tin oxide (ITO) coated glass substrates without any catalysts. The temperature of the substrate was . The tungsten oxide nanowires are single crystalline with growth direction of [0 1 0]. For commercial applications, field emission properties of tungsten oxide nanowires were studied under a poor vacuum at room temperature. The electron field-emission turn-on field (E_to), defined as the macroscopic field required to produce a current density of , is about . The performance reveals that the tungsten oxide nanowire arrays can be served as a good candidate for commercial application in field-emission displays.     

Structure of light hypernuclei

The structure of light hypernuclei with strangeness S=−1 and −2 is investigated with the microscopic cluster model and the Gaussian expansion method (GEM). We emphasize that the cluster picture as well as the mean-field picture is invaluable to understand the structure of Λ hypernuclei, Σ hypernuclei and double Λ hypernuclei. A variety of aspects of Λ hypernuclei is demonstrated through a systematic study of p-shell hypernuclei (,, , , , , ) and sd-shell ones (, ): for example, the appearance of genuine hypernuclear states with new spatial symmetry which cannot be seen in ordinary nuclei, the glue-like role of the Λ particle which shrinks the size of nuclear core and thus reduces the B(E2) value, and the halo and skin structures in and etc. The typical light hypernucleus is thoroughly investigated, including its production, structure and decay. Precise three-body and four-body calculations of , and using GEM provide important information on the spin structure of the underlying ΛN interaction, by comparing with recent experimental data from γ-ray hypernuclear spectroscopy. The Λ–Σ coupling effect is studied in and . The binding mechanism of is discussed together with the possible existence of , emphasizing the fact that the study of is useful for extracting information on the ΣN interaction differing from that from . A systematic study of double-Λ hypernuclei, constrained by the NAGARA data () within a four-body cluster model indicates that the recently observed Demachi–Yanagi event can be interpreted as the 2⁺ state of . The effect of hyperon mixing in and is investigated using one-boson-exchange potentials and quark-cluster-model interactions for the S=−2 sector. A close relation between nuclear deep hole states and hypernuclei is discussed, emphasizing the selection rule for fragmentation of the s-hole in light nuclei, which is promising for understanding the production mechanism of double-Λ and twin-Λ hypernuclei via Ξ-atomic capture.     

Theoretical structure and surface energy of the reconstructed {01.2} form of calcite (CaCO3) crystal

Two different reconstructions of the (01.2) face (Ca or CO₃ terminated) of calcite (CaCO₃) were studied: (i) R1 reconstruction: the outermost layer is based on the [0 1 0] × 1/3[2 1 1] rectangular mesh, which is symmetrical with respect to the c glide plane of the crystal, thus fulfilling the 2D symmetry of the face and (ii) R2 reconstruction: the outermost layer is based on a lozenge shaped mesh that does not respect the 2D symmetry of the face.The , , and slabs geometry optimizations of calcite (CaCO₃) were performed either at DFT level or by using empirical potentials; the results obtained with these two different calculation methodologies are in good agreement. With respect to their arrangement in the bulk, the CO₃ groups of the outermost layer are significantly rotated about the crystallographic a-axis and about the normal to the 01.2 plane; further, the thickness of the outermost layer is significantly lower than that of the underneath ones.The surfaces energies (γ) at 0 K, for relaxed and unrelaxed , , and faces, were determined either at DFT level or by using empirical potentials. Independently of the method of calculation employed, the stability order of the relaxed faces is < < < . Concerning the unrelaxed faces, whose energies were evaluated by using empirical potentials only, the stability order is instead < < < ; such different ordering shows the importance of geometry relaxation in the calculation of the surface energy. The values of the relaxed surface energies are , , and erg/cm².     

Algebraic Bethe ansatz for invariant integrable models: Compact and non-compact applications

We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U_q[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact model starting from systems with finite degrees of freedom.     

Double-quantum NMR spectroscopy of P species submitted to very large CSAs

We introduce an original pulse sequence, , which is a block super-cycled sequence employing as basic element a π pulse sandwiched by ‘window’ intervals. This homonuclear dipolar recoupling method allows the efficient excitation of double-quantum coherences between spin-1/2 nuclei submitted to very large chemical shift anisotropy. We demonstrate that this technique can be employed in double-quantum ↔ single-quantum ³¹P homonuclear correlation experiment at high magnetic field (B₀  14 T) and high MAS frequencies (ν_R  30 kHz). The performances of are compared to those of the double-quantum recoupling methods, such as BABA and bracketed fp-RFDR, which were already employed at fast MAS rates. The sequence displays a higher robustness to CSA and offset than the other existing techniques.     

Scaling and long-range dependence in option pricing I: Pricing European option with transaction costs under the fractional Black–Scholes model

This paper deals with the problem of discrete time option pricing by the fractional Black–Scholes model with transaction costs. By a mean self-financing delta-hedging argument in a discrete time setting, a European call option pricing formula is obtained. The minimal price of an option under transaction costs is obtained as timestep , which can be used as the actual price of an option. In fact, is an adjustment to the volatility in the Black–Scholes formula by using the modified volatility to replace the volatility σ, where is the Hurst exponent, and k is a proportional transaction cost parameter. In addition, we also show that timestep and long-range dependence have a significant impact on option pricing.     

Three equations of state for solids considering thermal effect

 The Einstein model to consider thermal effect in universal equations of state (UEOS) is modified. It is proposed that the zero-point vibration term should be deleted in a thermal UEOS, and the parameters cannot be directly taken as experimental data at a reference temperature, V_R, B_R, and , but their values at absolute zero temperature, V₀, B₀, and . An approach is proposed to solve V₀, B₀, and from V_R, B_R, and . The approaches are applied to three typical universal EOSs, including the Baonza, mGLJ and Morse EOSs. The numerical results show that the solved values of parameters are almost identical for different EOSs. And the thermo-physical properties predicted through different EOSs are almost identical at zero- and low-pressure conditions, once the same approach and input experimental data are used to solve the parameters. It is concluded that the prediction of thermo-physical properties at zero- and low-pressure conditions cannot be taken as the criteria to judge the applicability of a universal EOS.     

Theoretical study of optical recording with a solid immersion lens illuminated by focused double-ring-shaped radially-polarized beam

Based on the Richards–Wolf vector diffraction theory, the intensity distributions in the recording sample near a solid immersion lens are calculated for two different radially-polarized beams ( and modes). Numerical results show that a double-ring-shaped mode focusing has some excellent features in near-field optical storage, compared with a single-ring-shaped mode focusing. The recording density is markedly improved, the focal depth of the near-field recording system is substantially increased, and a subsurface recording is effectively obtained using the mode focusing.     

Absolute photoionization cross sections with ultra-high energy resolution for Ar, Kr, Xe and N2 in inner-shell ionization regions

The high-resolution absolute photoionization cross sections for Ar, Kr, Xe and N₂ in the inner-shell ionization region have been measured using a multi-electrode ion chamber and monochromatized synchrotron radiation. The energy ranges of the incident photons for the target gases were as follows: Ar: 242–252 eV (2p Rydberg excitation), Kr: 1650–1770 eV (near the 2p ionization thresholds), Xe: 665–720 eV (near the 3d ionization thresholds) and 880–1010 eV (near the 3p ionization thresholds), N₂: 400–425 eV (N 1s excitation and ionization). It is the first time to measure the absolute ionization cross sections of Ar, Kr, Xe and N₂ over the present energy ranges with the energy resolution of over 10,000. The natural lifetime widths of , , and resonances for Ar, resonance for Xe, and resonance for N₂ have been obtained based on the cross sections determined. The ionization energies into the Ar⁺ (), Ar⁺ () and Xe⁺ () ionic states are also determined using the Rydberg formula.     

Observation of the state of CH2 by optical–optical double resonance

We report the observation of levels in the state of CH₂ via optical–optical double resonance spectroscopy. Direct transitions between the lowest singlet state and the state are allowed by symmetry, but weak because they correspond to a two electron excitation in the single configuration approximation to the electronic wavefunction. The observed transitions involve sequential single photon absorptions at visible and near infrared wavelengths using state intermediate levels. Recent ab initio results (S.N. Yurchenko et al., J. Mol. Spectrosc. 208 (2001), 136) predicted the positions of some of the levels which are confirmed by the present results. The new spectra provide accurate energies for rotational levels in the , l = 0 level of the state.     

Existence of different intermediate Hamiltonians in type A -fold supersymmetry

Type A -fold supercharge admits a one-parameter family of factorizations into product of first-order linear differential operators due to an underlying symmetry. As a consequence, a type A -fold supersymmetric system can have different intermediate Hamiltonians corresponding to different factorizations. We derive the necessary and sufficient conditions for the latter system to possess intermediate Hamiltonians for the case. We then show that whenever it has (at least) one intermediate Hamiltonian, it can admit second-order parasupersymmetry and a generalized 2-fold superalgebra. As an illustration, we construct a set of generalized Pöschl–Teller potentials of this kind.     

Counting BPS operators in SYM

The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free super-Yang–Mills discussed, including a general result for large N. The partition function for quarter BPS operators in the chiral ring of super-Yang–Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free super-Yang–Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.     

Step formation on hydrogen-etched 6H-SiC{0 0 0 1} surfaces

The formation of step bunches and/or facets on hydrogen-etched 6H-SiC(0 0 0 1) and () surfaces has been studied, using both nominally on-axis and intentionally miscut (i.e. vicinal) substrates. It is found that small miscuts on the (0 0 0 1) surface produce full unit-cell high steps, while half unit-cell high steps are observed on the () surface. The observed step normal direction is found to be for both surfaces. Hence, for intentionally miscut material, a miscut oriented towards this direction produces much better order in the step array compared to a miscut oriented towards a direction. For (0 0 0 1) vicinal surfaces that are miscut towards the direction, the formation of surface ripples is observed for 3° miscut and the development of small facets (nanofacets) is found for higher miscut angles. Much less faceting is observed on miscut () surfaces. Additionally, the (0 0 01) surface is found to have a much larger spatial anisotropy in step energies than the () surface.     

Elliptic quantum group , Hopf algebroid structure and elliptic hypergeometric series

We propose a new realization of the elliptic quantum group equipped with the H-Hopf algebroid structure on the basis of the elliptic algebra . The algebra has a constructive definition in terms of the Drinfeld generators of the quantum affine algebra and a Heisenberg algebra. This yields a systematic construction of both finite- and infinite-dimensional dynamical representations and their parallel structures to . In particular we give a classification theorem of the finite-dimensional irreducible pseudo-highest weight representations stated in terms of an elliptic analogue of the Drinfeld polynomials. We also investigate a structure of the tensor product of two evaluation representations and derive an elliptic analogue of the Clebsch–Gordan coefficients. We show that it is expressed by using the very-well-poised balanced elliptic hypergeometric series .     

Quantum-dot size dependence of exciton fine-structure splitting

A systematic variation of the exciton fine-structure splitting with quantum dot size in single MOCVD-grown self-organized InAs/GaAs quantum dots is observed, ranging from several tens to as much as , thus covering more than one order of magnitude. Piezoelectricity is identified to be the dominant factor governing the observed trend. A change in sign of the fine-structure splitting is reported for the first time, originating from quantum dots with confinement potentials elongated in the and crystal direction, respectively.     

Critical Casimir amplitudes for n-component models with -symmetry breaking quadratic boundary terms

Euclidean n-component ⁴ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry . The boundary terms imply the Robin boundary conditions at the boundary planes at z=0 and at z=L. Particular attention is paid to the cases in which m_j of the n variables associated with plane take the special value corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane has a multicritical surface–bulk point, called m_j-special, at which an O(m_j) symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as Δ_C/L^d−1 as L→∞ at the bulk critical point. The Casimir amplitudes Δ_C are determined for small =4−d in the general case where m_c,c components _α are critically enhanced at both boundary planes, m_c,D+m_D,c components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining m_D,D components satisfy asymptotic Dirichlet boundary conditions at both . Whenever m_c,c>0, the corresponding small- expansions involve, besides integer powers of , also fractional powers ^k/2 with k3 modulo powers of logarithms. Results to order ^3/2 are given for general values of m_c,c, m_c,D+m_D,c, and m_D,D. These are used to estimate the Casimir amplitudes Δ_C of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with (m_c,c,m_c,D+m_D,c)=(1,0), (0,1), and (1,1).     

Relaxation time of a CFT plasma at finite coupling

Following the recent formulation of second order relativistic viscous hydrodynamics for conformal fluids, we compute finite coupling corrections to the relaxation time of supersymmetric Yang–Mills plasma. The result is expected to be universal for any strongly coupled conformal gauge theory plasma in four dimensions.     

Anomalous dimension with wrapping at four loops in SYM

In this paper we give all the details of the calculation that we presented in our previous paper [F. Fiamberti, A. Santambrogio, C. Sieg, D. Zanon, Wrapping at four loops in SYM, arXiv: 0712.3522], concerning the four-loop anomalous dimension of the Konishi descendant tr(ZZ−ZZ) in the SU(2) sector of the planar SYM theory. We explicitly consider all the wrapping diagrams that we compute using an superspace approach and Gegenbauer polynomial x-space techniques.     

Observation of the quantum Hall effect in cleaved InAs surfaces

We have performed the in-plane magnetotransport measurements on the two-dimensional electron gas at the cleaved p-InAs (1 1 0) surface by deposition of Ag. The surface electron density N_s is determined from the Hall coefficient at . The coverage dependence of N_s is well explained by the assumption that each adsorbed Ag atom denotes one electron into InAs until the surface Fermi level reaches the adsorbate-induced donor level. The electron mobility μ is about and does not show a clear dependence on the coverage over . In the high-magnetic field regime of B>1/μ, Shubnikov–de Hass oscillations were observed. A beating pattern due to the strong spin–orbit interaction appears for high N_s. For lower N_s of , an apparent quantum Hall plateau for ν=4 and vanishing of the longitudinal resistivity were observed around .