Phenomenological model of nonlinear dielectric losses related to the intrinsic conductivity of dielectrics

A phenomenological approach was applied to the dynamics of the intrinsic electric conductivity of dielectrics in an electric field in order to analyze its contribution to dielectric losses. The proposed differential equation contains only two parameters - the effective time of conductivity decay in an electric field, and , the time describing the recovery rate of the conductivity after switching off the field. The proposed approach predicts a linear dependence of specific conductivity of dielectrics on the sample thickness, as experimentally confirmed by Du Pont [1] for Teflon FEP. The field and time (or frequency) dependences of intrinsic conductivity and related dependences of dielectric losses were calculated, analyzed and illustrated with the published experimental data. The results show that the discussed contribution in dielectric losses is characterized by two hyperbolas (instead of one) while the distance between the branches depends on the intensity of applied electric field.Received: 3 November 2003, Published online: 29 June 2004PACS: 72.20.Ht High-field and nonlinear effects - 72.80.Sk Insulators - 77.22.Gm Dielectric loss and relaxation     

Renormalized parameters for impurity models

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level , an effective hybridization , and a quasiparticle interaction . The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.Received: 2 July 2004, Published online: 12 August 2004PACS: 75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions - 71.10.-w Theories and models of many-electron systems - 71.27. + a Strongly correlated electron systems; heavy fermions     

Sum-rule approaches to the elementary excitation spectrum of interacting gases of finite bosons in harmonic potentials

Based on the corrected sum rules and generalized virial identities, we derive an expression for all modes of excitation spectrum of interacting Bose gases at finite atom numbers in axially anisotropic potentials, in terms of the N-body ground state average. Using the variational Gaussian calculation for the ground-state wave function, its explicit analytic formulas are obtained. These results show clearly the dependence of excitation spectrum on the interaction strength parameter and trap geometry parameter for the system with N = 1 through . For and 1 the dependences have simple and intuitive physical interpretations. We compare the low-lying excitation spectra with the existing numerical results and make quantitative predications for future experiments and numerical simulation for higher-lying excitation modes.Received: 18 February 2004, Published online: 20 April 2004PACS: 67.40.Db Quantum statistical theory; ground state, elementary excitations - 67.90. + z Other topics in quantum fluids and solids; liquid and solid helium     

Thermal conductivity of doped $\mathsf{La_2CuO_4}$ as an example for heat transport by optical phonons in complex materials

We investigate the phonon thermal conductivity of doped based on out-of-plane thermal conductivity measurements. When room temperature is approached the temperature dependence of strongly deviates from the T^-1-decrease which is usually expected for heat transport by acoustic phonons. Instead, decreases much weaker or even increases with rising temperature. Simple arguments suggest that such unusual temperature dependencies of are caused by heat transport via dispersive optical phonons.Received: 20 October 2003, Published online: 20 April 2004PACS: 66.70. + f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves - 74.72.Dn La-based cuprates - 44.10. + i Heat conduction     

The stationary properties and the state transition of the tumor cell growth mode

We study the stationary properties and the state transition of the tumor cell growth model (the logistic model) in presence of correlated noises for the case of nonzero correlation time. We derived an approximative Fokker-Planck equation and the stationary probability distribution (SPD) of the model. Based the SPD, we investigated the effects of both correlation strength ( ) and correlation time ( ) of cross-correlated noises on the SPD, the mean of the tumor cell population and the normalized variance ( ) of the system, and calculated the state transition rate of the system between two stable states. Our results indicate that: (i) and play opposite roles in the stationary properties and the state transition of the system, i.e. increase of can produce a smaller mean value of the cell population and slow down the state transition, but increase of can produce a larger mean value of the cell population and enhance state transition; (ii) For large , there a peak structure on both - plot and - plot. For the small , increases with increasing , but increases with decreasing .Received: 26 June 2004, Published online: 30 September 2004PACS: 87.10. + e General theory and mathematical aspects - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.Ey Stochastic processes     

Thermal conductivity and competing orders in d-wave superconductors

We derive the expression for the thermal conductivity in the low-temperature limit in d-wave superconductors, taking into account the presence of competing orders such as spin-density wave, is-pairing, etc. The expression is used for analyzing recent experimental data in . Our analysis strongly suggests that competing orders can be responsible for anomalies in behavior of thermal conductivity observed in those experiments.Received: 9 December 2003, Published online: 2 April 2004PACS: 74.25.Fy Transport properties (electric and thermal conductivity, thermoelectric effects, etc.) - 74.72.Dn La-based cuprates - 74.72.-h Cuprate superconductors (high-Tc and insulating parent compounds)V.P. Gusynin: On leave from Bogolyubov Institute for Theoretical Physics, 03143 Kiev, UkraineV.A. Miransky: On leave from Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine     

Full-band extended states with random phases in one-dimensional disordered system with specific impurities

We investigate transport properties of electrons in a one-dimensional (1D) disordered system consisting of a host chain attached with specific impurities. Every impurity, labelled by j and possessing site energy , is side-coupled to two adjacent sites of the host chain with hopping integral t _1j and changesthe original nearest-neighbor (NN) hopping to t _2j . We show that if and for all impurities, with t ₀ being the NN hopping of the host chain, the states in the whole band are extended, even though s and positions of impurities are random. The phases of these states, however, are spatially random, corresponding to finite free path and infinite localization length in such a 1D system.Received: 6 May 2004, Published online: 12 July 2004PACS: 72.15.Rn Localization effects (Anderson or weak localization) - 72.80.Ng Disordered solids - 73.20.Jc Delocalization processes     

Dependence of the average to-node distance on the node degree for random graphs and growing networks

In a connected graph, nodes can be characterised locally (with their degree k) or globally (e.g. with their average length path to other nodes). Here we investigate how depends on k. The numerical algorithm based on the construction of the distance matrix is applied to random graphs and the growing networks: the scale-free ones and the exponential ones. The results are relevant for search strategies in different networks.Received: 15 June 2004, Published online: 21 October 2004PACS: 02.10.Ox Combinatorics; graph theory - 05.10.-a Computational methods in statistical physics and nonlinear dynamics     

Splitting rules for the 2nd hierarchy structure of the electronic spectra of 2D FC(n) quasicrystals

On the basis of our former work and by means of the decomposition-decimation method, we study the splitting rules for the second hierarchy of the electronic energy spectra for two-dimensional Fibonacci-class quasicrystals with one kind of atom and two bond lengths. It is found that every line of the sub-spectra for n x n and (n + 1) x (n + 1) clusters of FC(n) splits according to the type Y_(n-1)-2-1 and type Y _n-2-1 respectively. The one for n x (n + 1) clusters of FC(n) consists of three sub-subbands when , and five sub-subbranches when . The general formulae of the number of energy levels for the spectra of the second hierarchy are obtained. The analytical results are confirmed by numerical simulations.Received: 18 March 2004, Published online: 23 July 2004PACS: 71.23.Ft Quasicrystals - 63.90. + t Other topics in lattice dynamics (restricted to new topics in section 63) - 33.70.Jg Line and band widths, shapes, and shifts     

Scaling of the spin stiffness in random spin- \frac{\mathsf 1}{\mathsf 2} chains

In this paper we study the localization transition induced by the disorder in random antiferromagnetic spin- chains. The results of numerical large scale computations are presented for the XX model using its free fermions representation. The scaling behavior of the spin stiffness is investigated for various disorder strengths. The disorder dependence of the localization length is studied and a comparison between numerical results and bosonization arguments is presented. A non trivial connection between localization effects and the crossover from the pure XX fixed point to the infinite randomness fixed point is pointed out.Received: 6 February 2004, Published online: 12 August 2004PACS: 75.10.Jm Quantized spin models - 75.40.Mg Numerical simulation studies - 05.70.Jk Critical point phenomena - 75.50.Lk Spin glasses and other random magnets     

Scaling the $\alpha $-relaxation time of supercooled fragile organic liquids

It was shown recently [1] that the structural -relaxation time of supercooled o-terphenyl depends on a single control parameter , which is the product of a function of density , by the inverse temperature T ^-1. We extend this finding to other fragile glassforming liquids using light scattering data. Available experimental results do not allow to discriminate between several analytical forms of the function , the scaling arising from the separation of density and temperature in . We also propose a simple form for , which depends only on three material-dependent parameters, reproducing relaxation times over 12 orders of magnitude.Received: 16 July 2004, Published online: 23 December 2004PACS: 66.20. + d Viscosity of liquids; diffusive momentum transport - 78.35. + c Brillouin and Rayleigh scattering; other light scattering - 64.70.Pf Glass transitions     

Packet transport along the shortest pathways in scale-free networks

We investigate a problem of data packet transport between a pair of vertices on scale-free networks without loops or with a small number of loops. By introducing load of a vertex as accumulated sum of a fraction of data packets traveling along the shortest pathways between every pair of vertices, it is found that the load distribution follows a power law with an exponent . It is found for the Barabási-Albert-type model that the exponent changes abruptly from for tree structure to as the number of loops increases. The load exponent seems to be insensitive to different values of the degree exponent as long as .Received: 4 February 2004, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 05.65. + b Self-organized systems - 02.10.Ox Combinatorics; graph theory     

Design of omnidirectional asymmetrical high reflectors for optical telecommunication wavelengths

A design for omnidirectional asymmetrical high reflectors for optical telecommunication wavelengths is described. Asymmetry was introduced by applying a power law, so that the coordinates y of the transformed object were determined through the coordinates x of the quarter-wave stack air/H(LH)¹⁵/air in accordance with the following rule y = x ^{1 + k} . Here k is the coefficient defining the asymmetry degree. It is shown that a high-reflection band at any incident angle for both polarizations, i.e., an omnidirectional high reflection band of 0.74 m for optical telecommunication wavelengths 0.85 and 1.3 m is found for the transformed system: air/Te(SiO₂/Te)¹⁵/air corresponding to the optimized k value 0.24.Received: 20 May 2004, Published online: 14 December 2004PACS: 42.70.Qs Photonic bandgap materials - 78.20.Bh Theory, models, and numerical simulation - 77.55. + f Dielectric thin films     

A new analysis of $\pi K$ scattering from Roy and Steiner type equations

With the aim of generating new constraints on the OZI suppressed couplings of chiral perturbation theory a set of six equations of the Roy and Steiner type for the S- and P-waves of the scattering amplitudes is derived. The range of validity and the multiplicity of the solutions are discussed. Precise numerical solutions are obtained in the range GeV which make use as input, for the first time, of the most accurate experimental data available at GeV for both and amplitudes. Our main result is the determination of a narrow allowed region for the two S-wave scattering lengths. Present experimental data below 1 GeV are found to be in generally poor agreement with our results. A set of threshold expansion parameters, as well as sub-threshold parameters are computed. For the latter, a matching with the SU(3) chiral expansion at NLO is performed.Received: 28 October 2003, Revised: 12 December 2003, Published online: 13 February 2004Work supported in part by the EU RTN contract HPRN-CT-2002-00311 (EURIDICE) and by IFCPAR contract 2504-1.     

Optical evidence for the proximity to a spin-density-wave metallic state in $\mathsf{Na_{0.7}CoO_2}$

We present the optical properties of Na_0.7CoO₂ single crystals, measured over a broad spectral range as a function of temperature (T). The capability to cover the energy range from the far-infrared up to the ultraviolet allows us to perform reliable Kramers-Kronig transformation, in order to obtain the absorption spectrum (i.e., the complex optical conductivity). To the complex optical conductivity we apply the generalized Drude model, extracting the frequency dependence of the scattering rate ( ) and effective mass (m ^*) of the itinerant charge carriers. We find that at low temperatures and for . This suggests that Na_0.7CoO₂ is at the verge of a spin-density-wave metallic phase.Received: 6 August 2004, Published online: 9 September 2004PACS: 78.20.-e Optical properties of bulk materials and thin films - 74.70.Dd Ternary, quaternary and multinary compounds (including Chevrel phases, borocarbides, etc.) - 75.30.Fv Spin-density waves     

Measurement of the strange spectral function in hadronic \tau decays

Tau lepton decays with open strangeness in the final state are measured with the OPAL detector at LEP to determine the strange hadronic spectral function of the lepton. The decays , and with final states consisting of neutral and charged kaons and pions have been studied. The invariant mass distributions of of these final states have been experimentally determined. Monte Carlo simulations have been used for the remaining and for the strange final states including mesons. The reconstructed strange final states, corrected for resolution effects and detection efficiencies, yield the strange spectral function of the lepton. The moments of the spectral function and the ratio of strange to non-strange moments, which are important input parameters for theoretical analyses, are determined. Furthermore, the branching fractions and have been measured.Received: 18 February 2004, Revised: 30 April 2004, Published online: 15 June 2004     

The effect of mixture lengths of vehicles on the traffic flow behaviour in one-dimensional cellular automaton

The effect of mixture lengths of vehicles on the asymmetric exclusion model is studied using numerical simulations for both open and periodic boundaries in deterministic parallel dynamics. The vehicles are filed according to their length, the small cars type 1 occupy one cell whereas the big ones type 2 takes two. In the case of open boundaries two cases are presented. The first case corresponds to a chain with two entries where densities are calculated as a function of the injecting rates and of vehicles type 1 and type 2 respectively, and the phase diagram ( ) is presented for a fixed value of the extracting rate . In this situation the first order transition from low to high density phases occurs at and disappears for . The second case corresponds to a chain with one entry, where is the injecting rate of vehicles independent of their nature. Type 2 are injected with the conditional probability , where and n is the concentration of type 2. Densities are calculated as a function of the injecting rates , and the phase diagrams ( , ) are established for different values of n. In this situation the gap which is a characteristic of the first order transition vanishes with increasing for . However, the first order transition between high and low densities exhibit an end point above which the global density undergoes a continuous passage. The end point coordinate depends strongly on the value of n. In the periodic boundaries case, the presence of vehicles type 2 in the chain leads to a modification in the fundamental diagram (current, density). Indeed, the maximal current value decreases with increasing the concentration of vehicles type 2, and occurs at higher values of the global density.Received: 13 May 2004, Published online: 3 August 2004PACS: 05.50. + q Lattice theory and statistics (Ising, Potts, etc.) - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems - 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 82.20.Wt Computational modeling; simulation     

The anisotropic quantum antiferromagnet on the Sierpiński gasket: Ground state and thermodynamics

We investigate an antiferromagnetic s = 1/2 quantum spin system with anisotropic spin exchange on a fractal lattice, the Sierpiski gasket. We introduce a novel approximative numerical method, the configuration selective diagonalization (CSD) and apply this method to a the Sierpiski gasket with N = 42. Using this and other methods we calculate ground state energies, spin gap, spin-spin correlations and specific heat data and conclude that the s = 1/2 quantum antiferromagnet on the Sierpinski gasket shows a disordered magnetic ground state with on the Sierpinski gasket shows a disordered magnetic ground state with a very short correlation length of and an, albeit very small, spin gap. This conclusion holds for Heisenberg as well a for XY exchange.Received: 18 February 2004, Published online: 20 April 2004PACS: 75.10.-b General theory and models of magnetic ordering - 05.45.Df Fractals - 75.40.Mg Numerical simulation studies     

Exotic baryons and monopole excitations in a chiral soliton model

We compute the spectra of exotic pentaquarks and monopole excitations of thelow-lying and baryons in a chiral soliton model. Once the low-lying baryon properties are fit, the other states are predicted without any more adjustable parameters. This approach naturally leads to a scenario in which the mass spectrum of the next to lowest-lying states is fairly well approximatedby the ideal mixing pattern of the representation of flavor SU(3). We compare our results to predictions obtained in other pictures for pentaquarks and speculate about the spin-parity assignment for and .Received: 21 April 2004, Revised: 19 May 2004, Published online: 23 July 2004PACS: 12.39.Dc Skyrmions - 14.20.-c Baryons (including antiparticles) - 14.80.-j Other particles (including hypothetical)