The analytic solution for the power series expansion of Heun function

The Heun function generalizes all well-known special functions such as Spheroidal Wave, Lame, Mathieu, and hypergeometric ₂F₁${}_2{F}_1$, ₁F₁${}_1{F}_1$ and ₀F₁${}_0{F}_1$ functions. Heun functions are applicable to diverse areas such as theory of black holes, lattice systems in statistical mechanics, solution of the Schrödinger equation of quantum mechanics, and addition of three quantum spins.     

The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations

In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V^k$V^k$ to a decreasing family of k$k$ foliations _Fi$F_i$ on a manifold M$M$. We have shown that there exists a (1,1)$(1,1)$ tensor J$J$ of V^k$V^k$ such that J^k≠0$J^k\ne 0$, J^k+1=0$J^{k+1}=0$ and we defined by _LJ(V^k)$L_J\left(V^k\right)$ the Lie Algebra of vector fields X$X$ on V^k$V^k$ such that, for each vector field Y$Y$ on V^k$V^k$, [X,JY]=J[X,Y]$[X,JY]=J[X,Y]$.     

On the curvature of warped product Finsler spaces and the Laplacian of the Sasaki–Finsler metrics

As an opening, we prove that a warped product Finsler space F=_F1×fF2$F=F_1{\times }_f{F}_2$ is of constant curvature c$c$ if and only if the base space _F1$F_1$ is also of constant curvature c$c$, the fiber space _F2$F_2$ is of some constant curvature α$\alpha$, and five other partial differential equations are satisfied. A rather similar result is proved for the case of warped product Finsler spaces of scalar curvature. Close relationships between the geometry of the warped product Finsler spaces of constant curvature and the spectral theory of the Laplacian (Laplace–Beltrami operator) of the well-known Sasaki–Finsler metrics of the base space _F1$F_1$ is established by detailed investigation of the above mentioned PDEs. We also define a new tensor for warped product Finsler spaces, which we call a warped-Cartan tensor. Using the tensor we define a new class of warped product Finsler spaces, calling them C-Warped spaces, which contain Landsberg, Berwald, locally Minkowski and Riemannian spaces, but not necessarily all of the constant curvature Finsler spaces of warped product type. Several results are obtained and special cases, for example the case of Riemannian, C-Warped and projectively flat spaces are also considered.     

How much information is needed to be the majority during the binary-state opinion formation?

In this paper, we try to propose a toy model, which follows the majority rule with the Fermi function, to uncover the role of the heterogeneous interaction between individuals in opinion formation. In order to do this, we define the impact factor I_Fi$I{F}_i$, says individual i$i$, as the exponential function of its connectivity _ki$k_i$ with the tunable parameter β$\beta$. β$\beta$ also shows the public information that can be collected by individuals in the system. We realize our model in scale-free networks with mean connectivity 〈k〉$〈k〉$. We find that much more public information (β>_β2$\beta >{\beta }_2$) and less public information (β<_β1$\beta <{\beta }_1$) cannot let either of the two opinions be the majority during the opinion formation. Furthermore, _β1${\beta }_1$ is a constant and equal to −0.76(±0.04)$-0.76(\pm 0.04)$, and _β2${\beta }_2$ decreases as a power-law function of the mean connectivity 〈k〉$〈k〉$ of the network. Our work can provide some perspectives and tools to understand the diversity of opinion in social networks.     

Spin polarization direction switch based on an asymmetrical quantum wire

A scheme for a spin polarization direction switch is investigated by studying the spin-dependent electron transport of an asymmetrical quantum wire with Rashba spin–orbit coupling. It is found that the spin polarization direction can be switched by changing the direction of the external current. The physical mechanism of this device arises from the fact that the symmetries in the longitudinal and transverse directions are all broken but _C2$C_2$-rotation and time-reversal symmetries are still preserved. Further studies show that the spin polarization is robust against disorder, displaying the feasibility of the proposed structure for a potential application.     

Whistler instability in a semi-relativistic bi-Maxwellian plasma

Employing linearized Vlasov–Maxwell system of equations, the whistler instability is discussed for a semi-relativistic bi-Maxwellian distribution. The dispersion relations are analyzed analytically along with the graphical representation and the estimates of the growth rate and instability threshold condition are also presented in the limiting cases i.e., _ξ±=(ω?Ω)/_k∥vt‖?1${\xi }_{\pm }=(\omega ?\Omega )/k_{\parallel }{v}_{t_{\Vert }}?1$ (resonant case) and _ξ±?1${\xi }_{\pm }?1$ (non-resonant case). Further for field free case i.e., _B0=0$B_0=0$, the growth rates for Weibel instability in a semi-relativistic bi-Maxwellian plasma are presented for both the limiting cases.     

The spin-ladder and spin-chain system (La,Y,Sr,Ca)14Cu24O41: Electronic phases,charge and spin dynamics

The quasi-one-dimensional cuprates (La,Y,Sr,Ca)₁₄Cu₂₄O₄₁, consisting of spin-chains and spin-ladders, have attracted much attention, mainly because they represent the first superconducting copper oxide with a non-square lattice. Theoretically, in isolated hole-doped two-leg ladders, superconductivity is tightly associated with the spin gap, although in competition with a charge-density wave (CDW). Indeed, both the gapped spin-liquid and CDW states have been established in the doped spin-ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$, however the relevance of these objects to electronic properties and superconductivity is still subject of intensive discussion. In this treatise, an appreciable set of experimental data is reviewed, which has been acquired in recent years, indicating a variety of magnetic and charge arrangements found in the chains and ladders of underdoped (La,Y)_y(S,Ca)_14−yCu₂₄O₄₁ and fully doped _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$. Based on these data, phase diagrams are constructed for the chains of underdoped systems (as a function of La, Y-substitution), as well as for the chains and ladders of the fully doped ones (as a function of Ca-substitution). We try to reconcile contradictory results concerning the charge dynamics in the ladders, like the hole redistribution between ladders and chains, collective modes and pseudogap, field-dependent transport and the temperature scales and doping levels at which the two-dimensional CDW develops in the ladder planes. The remaining open issues are clearly extracted. In the discussion the experimental results are contrasted with theoretical predictions, which allows us to conclude with two important remarks concerning the nature of the competing CDW and superconducting ground states. A density wave in ladders, characterized by a sinusoidal charge modulation, belongs to the class of broken symmetry patterns, which is theoretically predicted for strongly correlated low-dimensional electron systems; however its precise texture and nature is still an open issue. As for superconductivity, the presence of the spin gap in the normal state points towards d  -wave symmetry and magnetic origin of the attractive interaction. However, there is a finite density of mobile quasi-particles that appears for high Ca contents and increases with pressure, concomitantly with increased two-dimensionality and metallicity. For this reason the superconductivity in the doped ladders of _{Sr14-xCaxCu24O41}${\mathrm{Sr}}_{14-x}{\mathrm{Ca}}_x{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ which occurs under high pressure cannot simply be a stabilization of the d-wave superconductivity expected for a pure single ladder system.     

Classification of the nonlinear dynamics and bifurcation structure of ultrasound contrast agents excited at higher multiples of their resonance frequency

Through numerical simulation of the Hoff model we show that when ultrasound contrast agents (UCAs) are excited at frequencies which are close to integer (m>2$m>2$) multiples of their natural resonance frequency, the bifurcation structure of the UCA oscillations as a function of pressure may be characterized by 3 general distinct regions. The UCA behavior starts with initial period one oscillations which undergoes a saddle node bifurcation to m   coexisting attractors for an acoustic pressure above a threshold, _Pt1$P_{t_1}$. Further increasing the pressure above a second threshold _Pt2$P_{t_2}$, is followed by a sudden transition to period 1 oscillations.     

Spin-polarized scanning tunneling spectroscopy of dislocation lines in Fe films on W(1 1 0)

We have studied the spin-resolved electronic properties of dislocation lines on the Fe double-layer (DL) on W(1 1 0) by spin-polarized scanning tunneling spectroscopy. The data reveal that the dislocation lines are ferromagnetically ordered with the magnetic contrast exhibiting a pronounced bias-dependence. By comparing tunneling spectra which were measured on the pseudomorphic DL and at different lateral separation from the dislocation line, we find a pronounced shift of a peak which originally appears at positive sample bias towards the Fermi level _EF$E_{\mathrm{F}}$. In contrast, the binding energy of a peak just below _EF$E_{\mathrm{F}}$ remains constant but increases in intensity. This causes a pronounced modification of the bias voltage-dependent magnetic asymmetry.     

Mixed density wave state in quasi-2D organic conductor

The density wave phase of α-$\alpha \mathrm{-}$(BEDT-TTF)₂KHg(SCN)₄ was investigated by transport properties and magnetic susceptibility. The density wave transition was observed as a broad increase at T_DW$T_{\mathrm{DW}}$=9 K by resistance measurement. Temperature dependence of the static magnetic susceptibility χ$\chi$ shows a large Curie tail below 100 K. By subtracting the Curie component, we found that the magnetic susceptibility increases like weak ferromagnetism with decreasing temperature below 7.4 K. The gradual increase of χ$\chi$ below T_DW$T_{\mathrm{DW}}$ is not expected in simple CDW or SDW, where the magnetic susceptibility decreases with decreasing temperature due to the reduction of Pauli paramagnetic component. To explain the weak ferromagnetic behavior, we consider the coexistence of CDW and SDW. We propose a model of the mixed density wave, where CDW exists with antiferromagnetically coupled canting spins.     

Entanglement thresholds for displaying the quantum nature of teleportation

A protocol for transferring an unknown single qubit state evidences quantum features when the average fidelity of the outcomes is, in principle, greater than 2/3$2/3$. We propose to use the probabilistic and unambiguous state extraction scheme   as a mechanism to redistribute the fidelity in the outcome of the standard teleportation when the process is performed with an X$X$-state as a noisy quantum channel. We show that the entanglement of the channel is necessary but not sufficient in order for the average fidelity f_X$f_X$ to display quantum features, i.e., we find a threshold C_X$C_X$ for the concurrence of the channel. On the other hand, if the mechanism for redistributing fidelity is successful then we find a filterable outcome with average fidelity f_X,0$f_{X,0}$ that can be greater than f_X$f_X$. In addition, we find the threshold concurrence of the channel C_X,0$C_{X,0}$ in order for the average fidelity f_X,0$f_{X,0}$ to display quantum features and surprisingly, the threshold concurrence C_X,0$C_{X,0}$ can be less than C_X$C_X$. Even more, we find some special cases for which the threshold values become zero.     

A systematic study on matrix models for Chern–Simons-matter theories

We investigate the planar solution of matrix models derived from various Chern–Simons-matter theories compatible with the planar limit. The saddle-point equations for most of such theories can be solved in a systematic way. A relation to Fuchsian systems play an important role in obtaining the planar resolvents. For those theories, the eigenvalue distribution is found to be confined in a bounded region even when the ?t Hooft couplings become large. As a result, the vevs of Wilson loops are bounded in the large ?t Hooft coupling limit. This implies that many of Chern–Simons-matter theories have quite different properties from ABJM theory. If the gauge group is of the form U_(N1)k1×U_(N2)k2$\mathrm{U}{(N_1)}_{k_1}\times \mathrm{U}{(N_2)}_{k_2}$, then the resolvents can be obtained in a more explicit form than in the general cases.     

Thermodynamics properties of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

We have studied the anisotropic two-dimensional nearest-neighbor Ising model with competitive interactions in both uniform longitudinal field H$H$ and transverse magnetic field Ω$\Omega$. Using the effective-field theory (EFT) with correlation in cluster with N=1$N=1$ spin we calculate the thermodynamic properties as a function of temperature with values H$H$ and Ω$\Omega$ fixed. The model consists of ferromagnetic interaction _Jx$J_x$ in the x$x$ direction and antiferromagnetic interaction _Jy$J_y$ in the y$y$ direction, and it is found that for H/_Jy∈[0,2]$H/J_y\in [0,2]$ the system exhibits a second-order phase transition. The thermodynamic properties are obtained for the particular case of λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$ (isotropic square lattice).     

Percolation theory and fragmentation measures in social networks

We study the statistical properties of a recently proposed social networks measure of fragmentation F after removal of a fraction q of nodes or links from the network. The measure F   is defined as the ratio of the number of pairs of nodes that are not connected in the fragmented network to the total number of pairs in the original fully connected network. We compare this measure with the one traditionally used in percolation theory, _P∞$P_{\infty }$, the fraction of nodes in the largest cluster relative to the total number of nodes. Using both analytical and numerical methods, we study Erd?s–Rényi (ER) and scale-free (SF) networks under various node removal strategies. We find that for a network obtained after removal of a fraction q   of nodes above criticality, _P∞≈(1-F)^1/2$P_{\infty }\approx (1-F{)}^{1/2}$. For fixed _P∞$P_{\infty }$ and close to criticality, we show that 1-F$1-F$ better reflects the actual fragmentation. For a given _P∞$P_{\infty }$, 1-F$1-F$ has a broad distribution and thus one can improve significantly the fragmentation of the network. We also study and compare the fragmentation measure F   and the percolation measure _P∞$P_{\infty }$ for a real national social network of workplaces linked by the households of the employees and find similar results.     

Accurate calibration of the velocity-dependent one-scale model for domain walls

We study the asymptotic scaling properties of standard domain wall networks in several cosmological epochs. We carry out the largest field theory simulations achieved to date, with simulation boxes of size 2048³, and confirm that a scale-invariant evolution of the network is indeed the attractor solution. The simulations are also used to obtain an accurate calibration for the velocity-dependent one-scale model for domain walls: we numerically determine the two free model parameters to have the values _cw=0.34±0.16$c_w=0.34\pm 0.16$ and _kw=0.98±0.07$k_w=0.98\pm 0.07$, which are of higher precision than (but in agreement with) earlier estimates.