Scaling of the conductance and resistance of square lattices with an exponentially wide spectrum of the resistances of links

The conductance G? and \(\overline {{G^{ - 1}}} \) resistance average over realizations of disorder have been calculated for various sizes of square lattices L. In contrast with different direction of change in the two quantities at percolation in lattices with the binary spread of conductances of links (g _i = 0 or 1), it has been found that the mean conductance and resistance of lattices decrease simultaneously with an increase in L in the case of an exponential distribution of local conductances g _i = exp(?kx_i), where x _i ∈ [0,1] are random numbers. When L is smaller than the disorder length L₀ = bk^v, G?(L) and \(\overline {{G^{ - 1}}} \)(L) are proportional to L^?n with n = k/5 and k/6, respectively. A similar behavior is characteristic of the distributions of conductances of links, which simulate a transition between the open and tunneling regimes in semiconducting lattices of antidots created in a two-dimensional electron gas.     

Observation of the Talbot effect for ultrasonic waves

The diffraction of ultrasonic radiation on an amplitude diffraction grating in the near-field area (Fresnel diffraction) has been studied. The effect of self-imaging of the grating (Talbot effect) has been detected for ultrasonic radiation at distances from the grating in the range from z = 0 to z = 2L _T, where L _T is the Talbot length. The fractional Talbot effect, i.e., the ultrasonic image of the grating with the period d/2, has been observed.     

Testing the Distance-Duality Relation from Hubble,Galaxy Clusters and Type Ia Supernovae Data with Model Independent Methods

In this paper, we perform cosmological-model-independent tests for the distance-duality (DD) relation η(z)=D _L(1+z)^?2/D _A by combining the angular diameter distance D _A(or comoving distances D _c ) with the luminosity distance D _L. The D _A are provided by two galaxy clusters samples compiled by De Filippis et al. (the elliptical β model), Bonamente et al. (the spherical β model), the D _c are obtained from Hubble parameter data and D _L are given from the Union2.1 supernovae (SNe) Ia compilation. We employ two methods, i.e., method A: binning the SNe Ia data within the range Δz=|z?z _SNe|<0.005, and method B: reconstructing the D _L(z) by smoothing the noise of Union2.1 data set over redshift with the Gaussian smoothing function, to obtain D _L associated with the redshits of the observed D _A or D _c. Four parameterizations for η(z), i.e., η(z)=1+η ₀ z, η(z)=1+η ₀ z/(1+z), η(z)=1+η ₀ z/(1+z)² and η(z)=1?η ₀ ln(1+z), are adopted for the DD relation. We find that DD relation is consistent with the present observational data, and the results we obtained are not sensitive to the method and parameterization.     

Extraordinary photons with unusual angular momentum

A series of novel state-vector functions (SVFs), which is the general solution of the Schrödinger equation for a photon, are constructed. Each set of these functions consists of a triplet of eigen-SVFs: The triplet can be broken down into a pair of nonzero l-order functions and a single zero-order function. The photons, described with a triplet of eigen-SVFs, possess all the quantum characteristics of a photon: In addition to common attributes like energy E = ? _ω , and momentum p _z = ? _κ , they also exhibit different angular momenta (AM) L _z+ = l?, L _z? = l?, and L _z0 = 0, where l?1. In other words, in addition to usual eigenvalues L _z±= ±?, there are unusual nonzero l-order eigenvalues L _z± = ±l? and a zero-order eigenvalue L _z0 = 0 for AM of a photon. By a series of SVFs, the pattern from nonzero l-order and zero-order Laguerre-Gaussian modes of a laser beam is explained well from a quantum mechanical point of view.     

Influence of the nearest environment symmetry on the character of the <Emphasis Type="Italic">p-d</Emphasis> interaction in binary copper sulfides

The energy structure of copper sulfides CuS and CuS₂ has been theoretically investigated by the modified method of associated plane waves (WIEN2k program). CuS is considered in two different cubic modifications of the sphalerite and NaCl (hypothetical) types, in which Cu atoms are in different coordinations. The density distribution of the electronic p states of sulfur and d states of copper are calculated taking into account the separation into the e _g and t _2g states. The specific features of these distributions are interpreted.     

Glass formation in amorphous SiO<Subscript>2</Subscript> as a percolation phase transition in a system of network defects

Thermodynamic parameters of defects (presumably, defective SiO molecules) in the network of amorphous SiO₂ are obtained by analyzing the viscosity of the melt with the use of the Doremus model. The best agreement between the experimental data on viscosity and the calculations is achieved when the enthalpy and entropy of the defect formation in the amorphous SiO₂ network are H _d =220 kJ/mol and S _d =16.13R, respectively. The analysis of the network defect concentration shows that, above the glass-transition temperature (T _g ), the defects form dynamic percolation clusters. This result agrees well with the results of molecular dynamics modeling, which means that the glass transition in amorphous SiO₂ can be considered as a percolation phase transition. Below T _g , the geometry of the distribution of network defects is Euclidean and has a dimension d=3. Above the glass-transition temperature, the geometry of the network defect distribution is non-Euclidean and has a fractal dimension of d _f =2.5. The temperature T _g can be calculated from the condition that percolation arises in the defect system. This approach leads to a simple analytic formula for the glass-transition temperature: T _g =H _d /((S _d +1.735R). The calculated value of the glass-transition temperature (1482 K) agrees well with that obtained from the recent measurements of T _g for amorphous SiO₂ (1475 K).     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

Topologically appropriate coordinates for (Vzz, η) joint probability distributions

Inhomogeneous broadening (IHB) of hyperfine interactions in materials arises from a distribution of electric field gradients (EFGs) due to randomly distributed defects contributing non-uniformly to the EFG at probe sites. Hyperfine experiments reflect the inhomogeneous distribution of defects through the joint probability distribution function (PDF) of V_zz and η determined by the defect concentration, crystal structure, and defect sites in the crystal. Czjzek showed how to choose coordinates in the (V_zz, η) plane that are consistent with the physical constraints and ordering convention for these EFG parameters. Here we show how to transform to a new set of coordinates that decreases the distortion inherent in Czjzek’s representation. These new coordinates allow one to express the joint PDF for random distributions of defects in a form reasonably approximated by the product of two independent marginal distributions. This paper focuses on these topologically appropriate coordinates, with simple examples drawn from Czjzek’s work and from our simulations of point defects in cubic lattices as well as random amorphous distributions of defects. Detailed simulations have been carried out for IHB in cubic structures and point charge models relevant to perturbed angular correlation (PAC) experiments.     

Paramagnetische Resonanz von Er3+ in Y2O3

The paramagnetic resonance absorption of trivalent erbium in single crystals of Y₂O₃ on sites of crystal field symmetry C_3i and C₂ is investigated at 4.2°K and 9.2 kMc/s. The values of theg-tensors and those of the hyperfine structure parallel to the axes of crystalline fields are:g _‖=12.176,g _⊥=3.319,A=426.4·10^?4 cm^?1, andg _z =12.314,g _x =1.645,g _y =4.892, andA _z =433.2·10^?4 cm^?1 for the C_3i-ions and the C₂-ions, respectively. For ions on sites of symmetry C₂ the principal axes ofg in the plane perpendicular toz are found ± 2° beside the [100]-directions. This is different from the result on Yb³⁺ in Y₂O₃. The dependency ofg on the angle of rotation is determined for the (001)-, (110)-, and (111)-plane.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.     

Threshold perturbations in current-carrying superconducting bridges with a finite length near the critical temperature

Near the critical temperature of a superconducting transition, the energy of the threshold perturbation δF_thr that transfers a superconducting bridge to a resistive state at a current below the critical current I_c has been determined. It has been shown that δF_thr increases with a decrease in the length of a bridge for short bridges with lengths L < ξ (where ξ is the coherence length) and is saturated for long bridges with L ? ξ. At certain geometrical parameters of banks and bridge, the function δF_thr(L) at the current I → 0 has a minimum at L ~ (2–3)ξ. These results indicate that the effect of fluctuations on Josephson junctions made in the form of short superconducting bridges is reduced and that the effect of fluctuations on bridges with lengths ~(2–3)ξ is enhanced.     

Inverse Scattering at Fixed Energy on Surfaces with Euclidean Ends

On a fixed Riemann surface (M ₀, g ₀) with N Euclidean ends and genus g, we show that, under a topological condition, the scattering matrix S _V (λ) at frequency λ > 0 for the operator Δ+V determines the potential V if \({V\in C^{1,\alpha}(M_0)\cap e^{-\gamma d(\cdot,z_0)^j}L^\infty(M_0)}\) for all γ > 0 and for some \({j\in\{1,2\}}\) , where d(z, z ₀) denotes the distance from z to a fixed point \({z_0\in M_0}\) . The topological condition is given by \({N\geq \max(2g+1,2)}\) for j = 1 and by N ≥ g + 1 if j = 2. In \({\mathbb {R}^2}\) this implies that the operator S _V (λ) determines any C ^{1, α} potential V such that \({V(z)=O(e^{-\gamma|z|^2})}\) for all γ > 0.     

Renormalization group functions of the φ<Superscript>4</Superscript> theory in the strong coupling limit: Analytical results

The previous attempts of reconstructing the Gell-Mann-Low function β(g) of the φ⁴ theory by summing perturbation series give the asymptotic behavior β(g) = β_∞ g in the limit g→∞, where α = 1 for the space dimensions d = 2, 3, 4. It can be hypothesized that the asymptotic behavior is β(g) ～ g for all d values. The consideration of the zero-dimensional case supports this hypothesis and reveals the mechanism of its appearance: it is associated with vanishing of one of the functional integrals. The generalization of the analysis confirms the asymptotic behavior β(g) ～ g in the general d-dimensional case. The asymptotic behaviors of other renormalization group functions are constant. The connection with the zero-charge problem and triviality of the φ⁴ theory is discussed.     

Das Auger-Spektrum derL III- Schale von Wismut

A thin Bi layer is irradiated by X-rays so thatL-Auger electrons are emitted. A magnetic lens spectrometer is used to measure the electron spectrum. Energy, transition, and relativ intensity are given for 14 lines. Under the most favourable conditions the number ofL _III ionisations is about ten times that ofL _II ionisations. In this case only a small intensity ofL _II-Auger electrons is superposed on theL _III-Auger spectrum. The ratiod of intensities of line groupL _III M N to line groupL _III M M is found by extrapolation to bed=0·46±0·02. This combined with earlier results gives anL _III-Auger yielda ₃= 0·64±0·04. TheL _III fluorescenc yield isω ₃=0·36±0·04, correspondingly. A further application of the experimental method is described.     

Studies of the defect structure from the calculations of optical and electron paramagnetic resonance spectra for Ni<Superscript>2+</Superscript> centre in <Emphasis Type="Italic">α</Emphasis>-LiIO<Subscript>3</Subscript> crystal

By calculating the optical spectrum band positions and EPR parameters (g factors, g‖, g⊥ and zero-field splitting D) by diagonalizing the complete energy matrix of 3d⁸ ions in trigonal symmetry, the defect structure of Ni²⁺ centre in α-LiIO₃ crystal is studied. It is found that to reach the good fits of optical and EPR data between calculation and experiment, the Ni²⁺ ion should shift by Δz ≈ 0.298 Å along C₃-axis and the O^2? ions between the Ni²⁺ ion and Li⁺ vacancy (V _Li) should be displaced away from the V _Li by Δx ≈ 0.097 Å because of the electrostatic interaction. The results are discussed.     

Josephson effects in unconventional heavy fermion superconductors

We discuss the Josephson effect for pairing states which break crystal symmetries in addition to gauge symmetry. We consider theE _1g andE _2u models for the low-temperature phase ofUPt ₃, with order parameters Δ(E _1g )～p _z (p _x +ip _y ) and Δ(E _2u )～p _z (p _x +ip _y )². We report calculations of Josephson critical currents, taking into account the effects of depairing at the interface. For singlet-triplet junctions the critical current is non-zero only for spin-orbit, spin-flip tunneling, and is found to be much smaller than the Ambegaokar-Baratoff value even when the spin-orbit tunneling amplitude is comparable to the spin-independent amplitude.     

The electrical conductance growth of a metallic granular packing

We report on measurements of the electrical conductivity on a two-dimensional packing of metallic disks when a stable current of ~1 mA flows through the system. At low applied currents, the conductance σ is found to increase by a pattern σ(t) = σ _∞ ? Δσ E _α [ ? (t/τ) ^α ], where E _α denotes the Mittag-Leffler function of order α ∈ (0,1). By changing the inclination angle θ of the granular bed from horizontal, we have studied the impact of the effective gravitational acceleration g _eff = gsinθ on the relaxation features of the conductance σ(t). The characteristic timescale τ is found to grow when effective gravity g _eff decreases. By changing both the distance between the electrodes and the number of grains in the packing, we have shown that the long term resistance decay observed in the experiment is related to local micro-contacts rearrangements at each disk. By focusing on the electro-mechanical processes that allow both creation and breakdown of micro-contacts between two disks, we present an approach to granular conduction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the conduction dynamics of granular material at low currents, we impose that the micro-contacts at the interface switch stochastically between two possible states, “on” and “off”, characterizing the conductivity of the micro-contact. We assume that the time intervals between the consecutive changes of state are governed by a certain waiting-time distribution. It is demonstrated how the microscopic random dynamics regarding the micro-contacts leads to the macroscopic observation of slow conductance growth, described by an exact fractional kinetic equations.     

Partial pseudospin polarization,latticetronics and Fano resonances in quantum dots based in graphene ribbons: a conductance spectroscopy

In this work we study, as a function of the height V and width L _b of the potentialbarriers, the transport of Dirac quasi-particles through quantum dots in graphene ribbons.We observed, as we increase V, a partial polarization (PP) of the pseudospin due to the participation of the hyperbolic bands. This generates polarizations in the sub-lattices A or B outside the dot regions for single, coupled, and open dots. Thus for energies around the Dirac point, the conductance G at both sides of the dot shows a latticetronics of conductances G _A and G _B as a function ofV and L _b . This fact can be used as a PPspectroscopy which associates hole-type waves with the latticetronics. A periodic enhancement of PP is obtained with the increase of V in dots formed bybarriers that completely occupy the nanoribbon width. For this case, a direct correspondence between G(V) and PP(V) exists. On the other hand, for the open dots, the PP(V) and the G(V) show a complex behavior that exhibit higher intensities when compared to the previous case. In the Dirac limit we have no backscattering signs, however when we move slightly away from this limit the firstsigns of confinement appear in the PP(V) (it freezes in a given sub-lattice). In the last case the backscattering fingerprints are obtained directly fromthe conductance (splittings). The open quantum dots are very sensible to their opening w _d and this generatesFano line-shapes of difficult interpretation around the Dirac point. The PP spectroscopy used here allows us to understand the influence of w _d in the relativistic analogues and to associate electron-type waves with the observed Fano line-shapes.     

Spin-spin interaction and the EPR spectrum of KDy(WO<Subscript>4</Subscript>)<Subscript>2</Subscript>

The EPR spectrum of a KDy(WO₄)₂ monoclinic crystal is investigated. It is found that the EPR spectrum of magnetically concentrated materials at a low frequency (9.2 GHz) undergoes a substantial transformation in addition to the well-known broadening of the EPR lines. At low Dy³⁺ concentrations (x<10^?2), the EPR spectrum of an isomorphic crystal, namely, KY_(1?x)Dy_x(WO₄)₂, is characterized by the parameters g_x=0, g_y=1.54, and g_z=14.6. For a magnetically concentrated crystal KDy(WO₄)₂, the g values are as follows: g_x=0, g_y=0.82, and g_z=2.52. It is demonstrated that the difference in the parameters is associated with the specific spin-spin interaction between Dy³⁺ ions, including the Dzyaloshinski interaction, which is not observed at high frequencies.     

Small-angle neutron scattering at fractal objects

The calculation of the correlation function of an isotropic fractal particle with the finite size ξ and the dimension D is presented. It is shown that the correlation function γ(r) of volume and surface fractals is described by a generalized expression and is proportional to the Macdonald function (D–3)/2 of the second order multiplied by the power function r ^(D–3)/2. For volume and surface fractals, the asymptotics of the correlation function at the limit r/ξ < 1 coincides with the corresponding correlation functions of unlimited fractals. The one-dimensional correlation function G(z), which, for an isotropic fractal particle, is described by an analogous expression with a shift of the index of the Macdonald function and the exponent of the power function by 1/2, is measured using spin-echo small-angle neutron scattering. The boundary case of the transition from a volume to a surface fractal corresponding to the cubic dependence of the neutron scattering cross section Q ^?3 leads to an exact analytical expression for the one-dimensional correlation function G(z) = exp(?z/ξ), and the asymptotics of the correlation function in the range of fractal behavior for r/ξ < 1 is proportional to ln(ξ/r). This corresponds to a special type of self-similarity with the additive law of scaling rather than the multiplicative one, as in the case of a volume fractal.