On the formulation of D = 11 supergravity and the composite nature of its three-form gauge field

The underlying gauge group structure of the D = 11 Cremmer-Julia-Scherk supergravity becomes manifest when its three-form field A₃ is expressed through a set of one-form gauge fields, , , η_1α, and E^a, ψ^α. These are associated with the generators of the elements of a family of enlarged supersymmetry algebras parametrized by a real number s. We study in detail the composite structure of A₃ extending previous results by D’Auria and Fré, stress the equivalence of the above problem to the trivialization of a standard supersymmetry algebra E^(11|32) cohomology four-cocycle on the enlarged superalgebras, and discuss its possible dynamical consequences. To this aim we consider the properties of the first order supergravity action with a composite A₃ field and find the set of extra gauge symmetries that guarantee that the field theoretical degrees of freedom of the theory remain the same as with a fundamental A₃. The extra gauge symmetries are also present in the so-called rheonomic treatment of the first order D = 11 supergravity action when A₃ is composite. Our considerations on the composite structure of A₃ provide one more application of the idea that there exists an extended superspace coordinates/fields correspondence. They also suggest that there is a possible embedding of D = 11 supergravity into a theory defined on the enlarged superspace .     

Optical phonon modes and structure of ZnGa2Se4 and ZnGa2S4

We present the infrared and Raman study of the optical phonon modes of the defective compounds ZnGa₂Se₄ and ZnGa₂S₄. Most of the compounds have been found to crystallize in the thiogallate structure (defect chalcopyrite) with space group where all cations and vacancies are ordered. For some Zinc compounds a partially disordered cationic sublattice with various degrees of cation and vacancy statistical distribution, which lead to the higher symmetry (defect stannite), has been reported. For ZnGa₂Se₄ we have found three modes of A symmetry, showing Raman activity only. In addition, we have observed each five modes of B and E symmetry, showing infrared as well as Raman activity. The number of modes and their symmetry assignment, based on polarized measurements, clearly indicate space group for the investigated crystals of ZnGa₂Se₄.Regarding ZnGa₂S₄ we have found three modes exclusively showing Raman activity (2A⊕1B₁), and only eight modes showing infrared as well as Raman activity (3B₂⊕5E). The assignment of the modes has been derived by analyzing the spectral positions of the vibrational modes in comparison to a number of compounds. From the number and symmetry assignment of the optical phonon modes we confirm that ZnGa₂S₄ most likely crystallizes in space group .     

Quantum mechanics of Klein-Gordon-type fields and quantum cosmology

With a view to address some of the basic problems of quantum cosmology, we formulate the quantum mechanics of the solutions of a Klein-Gordon-type field equation: (∂_t²+D)ψ(t)=0, where and D is a positive-definite operator acting in a Hilbert space . In particular, we determine all the positive-definite inner products on the space of the solutions of such an equation and establish their physical equivalence. This specifies the Hilbert space structure of uniquely. We use a simple realization of the latter to construct the observables of the theory explicitly. The field equation does not fix the choice of a Hamiltonian operator unless it is supplemented by an underlying classical system and a quantization scheme supported by a correspondence principle. In general, there are infinitely many choices for the Hamiltonian each leading to a different notion of time-evolution in . Among these is a particular choice that generates t-translations in and identifies t with time whenever D is t-independent. For a t-dependent D, we show that regardless of the choice of the inner product the t-translations do not correspond to unitary evolutions in , and t cannot be identified with time. We apply these ideas to develop a formulation of quantum cosmology based on the Wheeler-DeWitt equation for a Friedman-Robertson-Walker model coupled to a real scalar field with an arbitrary positive confining potential. In particular, we offer a complete solution of the Hilbert space problem, construct the observables, use a position-like observable to introduce the wave functions of the universe (which differ from the Wheeler-DeWitt fields), reformulate the corresponding quantum theory in terms of the latter, reduce the problem of the identification of time to the determination of a Hamiltonian operator acting in , show that the factor-ordering problem is irrelevant for the kinematics of the quantum theory, and propose a formulation of the dynamics. Our method is based on the central postulates of nonrelativistic quantum mechanics, especially the quest for a genuine probabilistic interpretation and a unitary Schrödinger time-evolution. It generalizes to arbitrary minisuperspace (spatially homogeneous) models and provides a way of unifying the two main approaches to the canonical quantum cosmology based on these models, namely quantization before and after imposing the Hamiltonian constraint.     

Random walks and diameter of finite scale-free networks

Dynamical scalings for the end-to-end distance R_ee and the number of distinct visited nodes N_v of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈R_ee〉 shows the dynamical scaling behavior , where is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, in the limit t→∞ satisfies the relation , where d is the diameter of network with for γ≥3 or for γ<3. Based on the scaling relation 〈R_ee〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.     

Scaling and memory effect in volatility return interval of the Chinese stock market

We investigate the probability distribution of the volatility return intervals τ for the Chinese stock market. We rescale both the probability distribution P_q(τ) and the volatility return intervals τ as to obtain a uniform scaling curve for different threshold value q. The scaling curve can be well fitted by the stretched exponential function , which suggests memory exists in τ. To demonstrate the memory effect, we investigate the conditional probability distribution P_q(τ|τ₀), the mean conditional interval 〈τ|τ₀〉 and the cumulative probability distribution of the cluster size of τ. The results show clear clustering effect. We further investigate the persistence probability distribution P_±(t) and find that P₋(t) decays by a power law with the exponent far different from the value 0.5 for the random walk, which further confirms long memory exists in τ. The scaling and long memory effect of τ for the Chinese stock market are similar to those obtained from the United States and the Japanese financial markets.     

Sub-coercive field dynamic hysteresis in morphotropic phase boundary composition of Pb(Zr1/2Ti1/2)O3-Pb(Zn1/3Nb2/3)O3 ceramic and its scaling behavior

Sub-coercive field dynamic ferroelectric hysteresis of a morphotropic phase boundary composition of the PZT-PZN ceramic was investigated under influence of the compressive stress. The scaling relation of hysteresis area 〈A〉 against frequency f, field amplitude E₀, and stress σ took a form of , which is not different significantly to that of other PZT-PZN compositions with pure tetragonal or rhombohedral structure, as well as to that of soft and hard PZT bulk ceramics. This study suggested that the domain structures, not ceramic compositions, played a key role in controlling dynamic hysteresis behavior of ferroelectric materials.     

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.     

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.     

Semi-ab initio calculations of superposition model and crystal field parameters for Co ions using the exchange charge model

This paper attempts for the first time to establish a reliable linkage between the two well-known and independent models of crystal field (CF), namely the exchange charge (ECM) and superposition models (SM). Our approach aims to show that the SM parameters can be reliably extracted from the distance dependence of the CF invariants for Co²⁺ as derived from the ECM through some semi-ab initio calculations which involved a single fitting parameter and a set of newly constructed procedures. Complete sets of the numerical values of SM parameters and t_k for Co²⁺ in its own host lattices of Li₂Co₃(SeO₃)₄, CoSO₄·H₂O, CoSeO₄·H₂O, and Co(OH)₂ are obtained and they are found to be around 13,000-16,000 cm⁻¹ for , 4100-5700 cm⁻¹ for , 4.1-5.0 for t₂ and 6.2-6.5 for t₄. The present results generally agree with but should be much better than those incomplete sets of results found by previous researchers using the conventional fitting approach. Plausible explanations for some noticeable discrepancies are also discussed together with the effects of different CF contributions on values of the SM parameters.     

Stock market and motion of a variable mass spring

We establish an analogy between the motion of spring whose mass increases linearly with time and volatile stock market dynamics within an economic model based on simple temporal demand and supply functions [E. Canessa, J. Phys. A 33 (2000) 3637]. The total system energy E_t is shown to be proportional to a decreasing time dependent spring constant k_t. This model allows to derive log-periodicity cos[log(t−t_c)] on commodity prices and oscillations (surplus and shortages) in the level of stocks. We also made an attempt to connect these results to the Tsallis statistics parameter q based on a possible force-entropy correlation [E. Canessa, Physica A 341(2004) 165] and find that the Tsallis second entropic term relates to the square of the demand (or supply) function.     

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.     

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.     

Ac magnetotransport in La0.7Sr0.3Mn0.95Fe0.05O3 at low dc magnetic fields

We report the ac electrical response of La_0.7Sr_0.3Mn_1−xFe_xO₃(x=0.05) as a function of temperature, magnetic field (H) and frequency of radio frequency (rf) current (). The ac impedance (Z) was measured while rf current directly passes through the sample as well as in a coil surrounding the sample. It is found that with increasing frequency of the rf current, Z(T) shows an abrupt increase accompanied by a peak at the ferromagnetic Curie temperature. The peak decreases in magnitude and shifts down with increasing value of H. We find a magnetoimpedance of for at around room temperature when the rf current flows directly through the sample and when the rf current flows through a coil surrounding the sample. It is suggested that the magnetoimpedance observed is a consequence of suppression of transverse permeability which enhances skin depth for current flow. Our results indicate that the magnetic field control of high frequency impedance of manganites is more useful than direct current magnetoresistance for low-field applications.     

New approach for analyzing time evolution of density operator in a dissipative channel by the entangled state representation

We analyze the time evolution of mixed state ρ₀ in a dissipative channel, characteristic of a decay constant κ, by virtue of the elegant properties of entangled state representation 〈η|. We find that the matrix element of the mixed state ρ(t) at time t in 〈η| representation is proportional to that of the initial ρ₀ in the decayed entangled state 〈ηe^-κt| representation, accompanying with a Gaussian damping factor . Thus we have a new insight about the nature of the dissipative process.     

Measurements of insulator band parameters using combination of single-electron and two-electron spectroscopy

We describe the application of low energy time-of-flight coincidence (e,2e) spectroscopy for measurements of the energy band parameters of a dielectric. The (e,2e) spectrometer can operate also in a single-electron mode by switching off coincidence conditions, and can be used for recording electron energy loss spectra (EELS). Thus, the combination of (e,2e) and EELS allows the measurement of energy gap E_g, valence bandwidth ΔE_val, electron affinity χ and excitonic levels position E_ex of a dielectric. The energy band parameters of LiF film deposited on Si(001) surface are measured: ΔE_val=