Special electronic structures of inverse spinels LiMVO<Subscript>4</Subscript>(M = Ni and Cu): a first-principles study

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d₀/2 where d₀ is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.     

Distribution of Resonances for Open Quantum Maps

We analyze a simple model of quantum chaotic scattering system, namely the quantized open baker’s map. This model provides a numerical confirmation of the fractal Weyl law for the semiclassical density of quantum resonances. The fractal exponent is related to the dimension of the classical repeller. We also consider a variant of this model, for which the full resonance spectrum can be rigorously computed, and satisfies the fractal Weyl law. For that model, we also compute the shot noise of the conductance through the system, and obtain a value close to the prediction of random matrix theory.     

Effect of the dimension of the phonon spectrum on the stability of condensed media states

The effect of dimension index d _f of the phonon spectrum, which is a structural characteristic in continual models, on the stability of states of condensed media is considered in the Einstein and Debye approximations. The estimate of the phase state stability is based on the Lindemann criterion generalized to arbitrary values of 0 ≤ d _f ≤ ∞. The problem of variation of physical characteristic of a substance by controlling the structure of its phonon spectrum is considered by analyzing the possibility of obtaining molecular hydrogen in the superfluid state. The Einstein and Debye models as applied to the problem on the dynamics of atomic oscillations are compared, and the divergence of the latter model for fractal dimensions d _f < 2 of the phonon spectrum is demonstrated, as well as the incompatibility of the Debye model at high temperatures and the model of a classical oscillator for all dimensions except d _f → ∞.     

Directed spiral site percolation on the square lattice

A new site percolation model, directed spiral percolation (DSP), under both directional and rotational (spiral) constraints is studied numerically on the square lattice. The critical percolation threshold p _c ≈ 0.655 is found between the directed and spiral percolation thresholds. Infinite percolation clusters are fractals of dimension d _f ≈ 1.733. The clusters generated are anisotropic. Due to the rotational constraint, the cluster growth is deviated from that expected due to the directional constraint. Connectivity lengths, one along the elongation of the cluster and the other perpendicular to it, diverge as p → p _c with different critical exponents. The clusters are less anisotropic than the directed percolation clusters. Different moments of the cluster size distribution P _s(p) show power law behaviour with | p - p _c| in the critical regime with appropriate critical exponents. The values of the critical exponents are estimated and found to be very different from those obtained in other percolation models. The proposed DSP model thus belongs to a new universality class. A scaling theory has been developed for the cluster related quantities. The critical exponents satisfy the scaling relations including the hyperscaling which is violated in directed percolation. A reasonable data collapse is observed in favour of the assumed scaling function form of P _s(p). The results obtained are in good agreement with other model calculations. Received 10 November 2002 / Received in final form 20 February 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: santra@iitg.ernet.in     

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size N with a degree distribution P(d) ∼ d ^−γ , the scaling of the lower bound is N ^1−1/γ . Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.     

Transition from fractal to non-fractal scalings in growing scale-free networks

Real networks can be classified into two categories: fractal networks and non-fractal networks. Here we introduce a unifying model for the two types of networks. Our model network is governed by a parameter q. We obtain the topological properties of the network including the degree distribution, average path length, diameter, fractal dimensions, and betweenness centrality distribution, which are controlled by parameter q. Interestingly, we show that by adjusting q, the networks undergo a transition from fractal to non-fractal scalings, and exhibit a crossover from ‘large’ to small worlds at the same time. Our research may shed some light on understanding the evolution and relationships of fractal and non-fractal networks.     

Evolution of the population of outer 6s and 5d shells in rare-earth metals

The shifts of the Kα ₁ and Kβ ₁ lines of all rare-earth (RE) metals (from La to Lu) have been measured experimentally by the x-ray shift method. The population of the RE-metal 6s and 5d shells has been determined by comparing the experimental and theoretical shifts obtained within the Dirac-Fock (Koopmans) model. Trivalent metals exhibit a monotonic cross-over from the 6s ^≈25d ^≈1 to 6s ^≈15d ^≈2 configuration with increasing atomic number. Fiz. Tverd. Tela (St. Petersburg) 41, 1361–1362 (August 1999)     

Implantation of periodic structures formed by silver particles into quartz glass

Quartz glass samples with a thin photosensitive AgCl-Ag film, prepared by successive evaporation of AgCl (h _AgCl ≈ 35 nm) and Ag (h _Ag ≈ 8 nm) in vacuum have been investigated. A periodic structure with a period of d = 375 nm formed by Ag particles was obtained in films using a p-polarized laser beam (λ = 532 nm, P = 25 mW) at an angle of incidence of ϕ = 20°. After removing AgCl in a fixing agent, the periodic structure remained on the glass surface. Subsequent irradiation by a CO₂ laser (λ = 10.6 μm, P ≈ 20 W) led to the implantation of this structure into the glass with the conservation of its period d and partial conservation of the related dichroism. The fact of implantation is confirmed by the high mechanical and chemical stability of the structure obtained. A possible implantation mechanism, taking into account the thermionic emission, Ag ionic transport, and the presence of free voids in the quartz glass and defects in its structural network, is discussed.     

Eigenvalues of Laplacian with Constant Magnetic Field on Non-Compact Hyperbolic Surfaces with Finite Area

We consider a magnetic Laplacian −Δ _A = (id + A)^* (id + A) on a non-compact hyperbolic surface M with finite area. A is a real one-form and the magnetic field dA is constant in each cusp. When the harmonic component of A satisfies some quantified condition, the spectrum of −Δ _A is discrete. In this case, we prove that the counting function of the eigenvalues of −Δ _A satisfies the classical Weyl formula, even when dA=0.     

Tunneling investigations of the phonon spectrum of a Bi 2223 metal oxide at high pressures

Pronounced softening of the high-frequency part of the phonon spectrum at high pressures is observed by means of tunneling spectroscopy. As the pressure is increased, the characteristic frequencies of the spectrum at ħΩ>60 mV decrease at the rate d ln(ħΩ)/dP≈(−6.5±0.5)×10⁻³ kbar⁻¹. On the other hand, hydrostatic pressure causes the low frequencies of the phonon spectrum of Bi 2223 metal oxide to shift very slightly toward higher energies, consistent with Raman spectra. Fiz. Tverd. Tela (St. Petersburg) 39, 1764–1766 (October 1997)     

Flocculation and percolation in reversible cluster-cluster aggregation

Off-lattice dynamic Monte-Carlo simulations were done of reversible cluster-cluster aggregation for spheres that form rigid bonds at contact. The equilibrium properties were found to be determined by the life time of encounters between two particles (t_e). t_e is a function not only of the probability to form or break a bond, but also of the elementary step size of the Brownian motion of the particles. In the flocculation regime the fractal dimension of the clusters is d_f=2.0 and the size distribution has a power law decay with exponent τ=1.5. At larger values of t_e transient gels are formed. Close to the percolation threshold the clusters have a fractal dimension d_f=2.7 and the power law exponent of the size distribution is τ=2.1. The transition between flocculation and percolation occurs at a characteristic weight average aggregation number that decreases with increasing volume fraction.     

Role of fractal dimension in random walks on scale-free networks

Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called (x,y)-flowers; the other is random, which is a combination of (1,3)-flower and (2,4)-flower and thus called hybrid networks. The two network families display rich behavior as observed in various real systems, as well as some unique topological properties not shared by other networks. We derive analytically the average trapping time for random walks on both the (x,y)-flowers and the hybrid networks with an immobile trap positioned at an initial node, i.e., a hub node with the highest degree in the networks. Based on these analytical formulae, we show how the average trapping time scales with the network size. Comparing the obtained results, we further uncover that fractal dimension plays a decisive role in the behavior of average trapping time on fractal scale-free networks, i.e., the average trapping time decreases with an increasing fractal dimension.     

On the longitudinal magnetic susceptibility of fractal ferrodielectrics

The longitudinal component of the magnetic susceptibility tensor χ _zz of a fractal ferrodielectric with dimension d _F = 3 − ɛ, where ɛ > 0, is calculated. The magnon dispersion in this case is shown to be a strongly anisotropic function of the parameter ɛ which, in turn, leads to nontrivial frequency dependences of χ _zz .     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

Transience, Recurrence and Critical Behavior¶for Long-Range Percolation

We study the behavior of the random walk on the infinite cluster of independent long-range percolation in dimensions d= 1,2, where x and y are connected with probability . We show that if d<s<2d, then the walk is transient, and if s≥ 2d, then the walk is recurrent. The proof of transience is based on a renormalization argument. As a corollary of this renormalization argument, we get that for every dimension d≥ 1, if d>s>2d, then there is no infinite cluster at criticality. This result is extended to the free random cluster model. A second corollary is that when d≥& 2 and d>s>2d we can erase all long enough bonds and still have an infinite cluster. The proof of recurrence in two dimensions is based on general stability results for recurrence in random electrical networks. In particular, we show that i.i.d. conductances on a recurrent graph of bounded degree yield a recurrent electrical network. Received: 27 October 2000 / Accepted: 29 November 2001     

Anomalies, symmetries and strangeness content of the proton

The matrix elements of the operators of strange quark fieldssГs where Г is 1 orγμγ ⁵ between a proton state is calculated. The sigma term is found to be ≈ 41 MeV and theSU(3) singlet axial matrix element is found to be ≈ 0.22, both in agreement with experiment. The sigma term is found using the trace anomaly, while the determination of the axial vector current matrix element is from QCD sum rules. These correspond to (ie.943-1)≈ 0.12 and for the axial current Δs ≈ −0.12, respectively. The role of the anomalies in maintaining flavor symmetry in the presence of substantial differences in quark masses is pointed out. This suggests that there is no need to invoke an intrinsic strange quark component in the proton wave function.     

Photoconductivity of poly-<Emphasis Type="Italic">p</Emphasis>-xylylene + CdS nanocomposite films over a wide temperature range

For poly-p-xylylene + CdS (PPX + CdS) nanocomposite films, the dependences of the photo-conductivity σ _ph (T) on the concentration C of CdS nanoparticles, intensity and wavelength of exciting light, and temperature T within 15–300 K are examined. An appreciable photocurrent appears at C ≥ 10 vol %, when a large percolation cluster of CdS nanoparticles is formed. The photocurrent spectrum is compared to the absorption spectrum of the film. The photocurrent I _ph (P) increases with the intensity of light flux P in a wavelength range near 435 nm according to the I _ph (P) ∼ P ⁿ power law, where n < 1. At 15 K, the photoconductivity of films with C ≈ 11.5 and 13.5 vol % is higher than that of a pure CdS film (C = 100 vol %) by factors of ≈100 and ≈30, respectively. For films with C > 11.5 vol %, the σ _ph (T) dependence at low T exhibits a metal-like character (σ _ph (T) decreases with increasing temperature). Atomic force microscopy is used to examine the surface topography of PPX + CdS films, which is found to be strongly dependent on the concentration of nanoparticles. The dark conductivity and photoconductivity of nanocomposite films arise due to the thermo- and photoexcitation transfer of electrons from the CdS nanoparticles to the PPX matrix with the formation of an electronic double layer at the PPX matrix-large percolation CdS cluster interface, a process that populates the phenyl rings of the adjacent PPX layer with excess electrons. As a result, various mechanisms of electron transfer in the polymer matrix can be realized: Mott’s hopping conduction mechanism with variable-range hopping in the matrix between CdS clusters and the metal-like behavior of the conductivity in the polymer shell of the large cluster at low temperatures. The polymer shell contains excess electrons on the phenyl rings -C₆H₄- in the composition of anion-resonances -C₆H₄⁻-.     

Probabilistic Weyl Laws for Quantized Tori

For the Toeplitz quantization of complex-valued functions on a 2n-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law (1.3). In numerical experiments the same Weyl law also holds for “false” eigenvalues created by pseudospectral effects.     

Spectrum and mechanism of the acceleration of protons in a solar flare

Investigations based on neutron monitor data show that two components of relativistic cosmic rays are generated by a solar flare. The so-called prompt component comes from a flare with flight times and is characterized by an exponential spectrum with a parameter of E ₀ ≈ 0.5 Gev. Numerical simulation of the conditions in the flare current sheet of the Bastille flare demonstrated that such a spectrum is formed at a magnetic reconnection velocity of ∼10⁷ cm s⁻¹. The delayed component has a power law spectrum and is apparently formed during the diffusion of protons in the plasma of the interplanetary magnetic field.