Attack vulnerability of scale-free networks due to cascading failures

In this paper, adopting the initial load of a node i to be with k_i being the degree of the node i, we propose a cascading model based on a load local redistribution rule and examine cascading failures on the typical network, i.e., the BA network with the scale-free property. We find that the BA scale-free network reaches the strongest robustness level in the case of α=1 and the robustness of the network has a positive correlation with the average degree 〈k〉, where the robustness is quantified by a transition from normal state to collapse. In addition, we further discuss the effects of two different attacks for the robustness against cascading failures on our cascading model and find an interesting result, i.e., the effects of two different attacks, strongly depending to the value α. These results may be very helpful for real-life networks to avoid cascading-failure-induced disasters.     

Nonperturbative equation of state of quark-gluon plasma: Applications

The vacuum-driven nonperturbative factors L_i for quark and gluon Green’s functions are shown to define the nonperturbative dynamics of QGP in the leading approximation. EoS obtained recently in the framework of this approach is compared in detail with known lattice data for μ = 0 including P/T⁴, ε/T⁴, . The basic role in the dynamics at T ? 3T_c is played by the factors L_i which are approximately equal to the modulus of Polyakov line for quark L_fund and gluon L_adj. The properties of L_i are derived from field correlators and compared to lattice data, in particular the Casimir scaling property follows in the Gaussian approximation valid for small vacuum correlation lengths. Resulting curves for P/T⁴, ε/T⁴, are in a reasonable agreement with lattice data, the remaining difference points out to an effective attraction among QGP constituents.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

Mass flows and angular momentum density for px + ipy paired fermions in a harmonic trap

We present a simple two-dimensional model of a p_x + ip_y superfluid in which the mass flow that gives rise to the intrinsic angular momentum is easily calculated by numerical diagonalization of the Bogoliubov-de Gennes operator. We find that, at zero temperature and for constant director l, the mass flow closely follows the Ishikawa-Mermin-Muzikar formula .     

Emergence of scale-free behavior in networks from limited-horizon linking and cost trade-offs

We study network growth from a fixed set of initially isolated nodes placed at random on the surface of a sphere. The growth mechanism we use adds edges to the network depending on strictly local gain and cost criteria. Only nodes that are not too far apart on the sphere may be considered for being joined by an edge. Given two such nodes, the joining occurs only if the gain of doing it surpasses the cost. Our model is based on a multiplicative parameter λ that regulates, in a function of node degrees, the maximum geodesic distance that is allowed between nodes for them to be considered for joining. For n nodes distributed uniformly on the sphere, and for within limits that depend on cost-related parameters, we have found that our growth mechanism gives rise to power-law distributions of node degree that are invariant for constant . We also study connectivity- and distance-related properties of the networks.     

Third and fourth order phase transitions: Exact solution for the Ising model on the Cayley tree

In this work we present the first exact solution of a system of interacting particles with phase transitions of order higher than two. The presented analytical derivation shows that the Ising model on the Cayley tree exhibits a line of third order phase transition points, between temperatures and , and a line of fourth order phase transitions between T_BP and ∞, where k_B is the Boltzmann constant, and J is the nearest-neighbor interaction parameter.     

Sufficient and necessary condition of separability for generalized Werner states

In a celebrated paper [Optics Communications 179, 447, 2000], A.O. Pittenger and M.H. Rubin presented for the first time a sufficient and necessary condition of separability for the generalized Werner states. Inspired by their ideas, we generalized their method to a more general case. We obtain a sufficient and necessary condition for the separability of a specific class of N d-dimensional system (qudits) states, namely special generalized Werner state (SGWS): , where is an entangled pure state of N qudits system and α_i satisfies two restrictions: (i) ; (ii) Matrix , where , is a density matrix. Our condition gives quite a simple and efficiently computable way to judge whether a given SGWS is separable or not and previously known separable conditions are shown to be special cases of our approach.     

The magnetocaloric effect and low temperature specific heat of SmNi

The magnetocaloric effect (MCE) in a magnetic SmNi sample was evaluated from magnetization and heat capacity measurements. The MCE phenomena in the vicinity of magnetic phase transitions in terms of magnetic entropy change, , and adiabatic temperature change, , are reported. Isothermal magnetization measurements at several temperatures around the transition were carried out and used for versusT calculations. A similar dependence of the magnetic entropy change was evaluated from heat capacity C_p(T) measurements under zero field and 5 T. The SmNi system provides magnetic refrigerants that induce an adiabatic cooling of about during the magnetization process with a field of 5 T in the temperature range of 35-45 K. The temperature dependence of C_p(T) is analyzed in terms of the magnetic and the lattice contributions.     

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.     

Finite and infinite dynamical systems of identical interacting particles

A dynamical system of infinite volume and of infinite number of identical interacting particles occupying energy levels has been constructed as the limit of an infinite sequence of finite, equivalent systems of increasing size and particle number. Systems both in equilibrium and in non-equilibrium state (designated S_∞=limS_k, , respectively, k=1,2,…) were investigated. The main results are:(i) The values in the T-limit (thermodynamic limit) of the physical quantities characterizing these systems are determined.(ii) The time evolution process both in and in systems is governed by the non-linear rate equations with common initial conditions p_i(t₀), where p_i(t)=n_i(t)/N are the occupation probabilities at time t. The time evolution process in the and systems is the same. The asymptotic approach to the equilibrium state is proved.(iii) For the case of the equilibrium state, the Boltzmann probability distribution p_i is given by the equation −lnp_i+a+e_ib=0 common to S_k and S_∞ systems with the same value of a and b. The term a=β⁻¹a_e, where a_e is the free energy per particle, and .(iv) The conditions for the equivalence of the systems being in equilibrium and also of the ones in non-equilibrium are stated.     

Haldane's instanton in 2D Heisenberg model revisited: Along the avenue of topology

Deconfined quantum phase transition from Néel phase to valence bond crystal state in 2D Heisenberg model is under debate nowadays. One crucial issue is the suppression of Haldane's instanton on quantum critical point which drives the spinon deconfined. In this Letter, by making use of the ?-mapping topological current theory, we reexamine the Haldane's instanton in an alternative way along the direction of topology. We find that the monopole events are space-time singularities of Néel field , the corresponding topological charges are the wrapping number of around the singularities which can be expressed in terms of the Hopf indices and Brouwer degrees of ?-mapping. The suppression of the monopole events can only be guaranteed when the ?-field possesses no zero points. Moreover, the quadrapolarity of monopole events in the Heisenberg model due to the Berry phase is also reproduced in this topological argument.     

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.     

Multiple superconducting gap and anisotropic spin fluctuations in iron arsenides: Comparison with nickel analog

We present extensive ⁷⁵As NMR and NQR data on the superconducting arsenides PrFeAs_0.89F_0.11, LaFeAsO_0.92F_0.08, LiFeAs and Ba_0.72K_0.28Fe₂As₂ single crystal, and compare with the nickel analog LaNiAsO_0.9F_0.1. In contrast to LaNiAsO_0.9F_0.1 where the superconducting gap is shown to be isotropic, the spin lattice relaxation rate 1/T₁ in the Fe-arsenides decreases below T_c with no coherence peak and shows a step-wise variation at low temperatures. The Knight shift decreases below T_c and shows a step-wise T variation as well. These results indicate spin-singlet superconductivity with multiple gaps in the Fe-arsenides. The Fe antiferromagnetic spin fluctuations are anisotropic and weaker compared to underdoped copper-oxides or cobalt-oxide superconductors, while there is no significant electron correlations in LaNiAsO_0.9F_0.1. We will discuss the implications of these results and highlight the importance of the Fermi surface topology.     

Relaxor behavior of K0.5La0.5Bi2Ta2O9 ceramics

Potassium lanthanum bismuth tantalate (K_0.5La_0.5Bi₂Ta₂O₉), a new relaxor ferroelectric was synthesized via the solid-state reaction route. X-ray structural studies along with Rietveld refinement confirmed it to be an n=2 member of the Aurivillius family of oxides and the refined lattice parameters are , and . The appearance of 1/2{h00} and 1/2{hk0} type superlattice reflections in the electron diffraction patterns reflected the presence of ordered polar regions. A broad dielectric peak associated with frequency dependent dielectric maximum temperature was observed. The value of the diffuseness parameter γ=1.93, obtained from the fit of a modified Curie-Weiss law established the relaxor nature of the title compound. The dielectric relaxation obeyed the Vogel-Fulcher relation wherein and . The relaxor behavior was attributed to the local polar ordering on A-sites.     

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.     

Thermal and magnetothermal properties of La0.5Pr0.5Mn2Si2

The thermal and magnetothermal properties of La_0.5Pr_0.5Mn₂Si₂ and isostructural LaFe₂Si₂ intermetallic compounds in the temperature range 4.5-303 K are reported with and without applied magnetic field. The electronic, lattice, and magnetic contributions to the heat capacity of La_0.5Pr_0.5Mn₂Si₂ are determined and analyzed. We have determined and from heat capacity experiments; the values are in line with those from the magnetization measurements. We conclude that in order to observe the anomaly in the heat capacity data around in the system, the transition around should occur in a narrow temperature interval.     

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.     

Clebsch-Gordan coefficients for the extended quantum-mechanical Poincaré group and angular correlations of decay products

This paper describes Clebsch-Gordan coefficients (CGCs) for unitary irreducible representations (UIRs) of the extended quantum-mechanical Poincaré group . ‘Extended’ refers to the extension of the 10 parameter Lie group that is the Poincaré group by the discrete symmetries C, P, and T; ‘quantum mechanical’ refers to the fact that we consider projective representations of the group. The particular set of CGCs presented here is applicable to the problem of the reduction of the direct product of two massive, unitary irreducible representations (UIRs) of with positive energy to irreducible components. Of the 16 inequivalent representations of the discrete symmetries, the two standard representations with U_CU_P = ±1 are considered. Also included in the analysis are additive internal quantum numbers specifying the superselection sector. As an example, these CGCs are applied to the decay process of the ? (4S) meson.     

On singular Lagrangian underlying the Schrödinger equation

We analyze the properties that manifest Hamiltonian nature of the Schrödinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian formulation). It is used to show that any solution of the Schrödinger equation with time independent potential can be presented in the form , where the real field ?(t,xi) is some solution of nonsingular Lagrangian theory being specified below. Preservation of probability turns out to be the energy conservation law for the field ?. After introduction the field into the formalism, its mathematical structure becomes analogous to those of electrodynamics.