Complex scale-free networks with tunable power-law exponent and clustering

We introduce a network evolution process motivated by the network of citations in the scientific literature. In each iteration of the process a node is born and directed links are created from the new node to a set of target nodes already in the network. This set includes m$m$ “ambassador” nodes and l$l$ of each ambassador’s descendants where m$m$ and l$l$ are random variables selected from any choice of distributions _pl$p_l$ and _qm$q_m$. The process mimics the tendency of authors to cite varying numbers of papers included in the bibliographies of the other papers they cite. We show that the degree distributions of the networks generated after a large number of iterations are scale-free and derive an expression for the power-law exponent. In a particular case of the model where the number of ambassadors is always the constant m$m$ and the number of selected descendants from each ambassador is the constant l$l$, the power-law exponent is (2l+1)/l$(2l+1)/l$. For this example we derive expressions for the degree distribution and clustering coefficient in terms of l$l$ and m$m$. We conclude that the proposed model can be tuned to have the same power law exponent and clustering coefficient of a broad range of the scale-free distributions that have been studied empirically.     

What if supersymmetry breaking appears below the GUT scale?

We consider the possibility that the soft supersymmetry-breaking parameters m_1/2$m_{1/2}$ and m₀$m_0$ of the MSSM are universal at some scale Min$M_{\mathrm{in}}$ below the supersymmetric grand unification scale MGUT$M_{\mathrm{GUT}}$, as might occur in scenarios where either the primordial supersymmetry-breaking mechanism or its communication to the observable sector involve a dynamical scale below MGUT$M_{\mathrm{GUT}}$. We analyze the (m_1/2,m₀)$(m_{1/2},m_0)$ planes of such sub-GUT CMSSM models, noting the dependences of phenomenological, experimental and cosmological constraints on Min$M_{\mathrm{in}}$. In particular, we find that the coannihilation, focus-point and rapid-annihilation funnel regions of the GUT-scale CMSSM approach and merge when Min∼¹⁰¹² GeV$M_{\mathrm{in}}\sim {10}^{12}\text{GeV}$. We discuss sparticle spectra and the possible sensitivity of LHC measurements to the value of Min$M_{\mathrm{in}}$.     

A hidden analytic structure of the Rabi model

The Rabi model describes the simplest interaction between a cavity mode with a frequency ω_c${\omega }_c$ and a two-level system with a resonance frequency ω₀${\omega }_0$. It is shown here that the spectrum of the Rabi model coincides with the support of the discrete Stieltjes integral measure in the orthogonality relations of recently introduced orthogonal polynomials. The exactly solvable limit of the Rabi model corresponding to Δ=ω₀/(2ω_c)=0$\Delta ={\omega }_0/\left(2{\omega }_c\right)=0$, which describes a displaced harmonic oscillator, is characterized by the discrete Charlier polynomials in normalized energy ?$?$, which are orthogonal on an equidistant lattice. A non-zero value of Δ$\Delta$ leads to non-classical discrete orthogonal polynomials ?_k(?)${?}_k\left(?\right)$ and induces a deformation of the underlying equidistant lattice. The results provide a basis for a novel analytic method of solving the Rabi model. The number of ca. 1350 calculable energy levels per parity subspace obtained in double precision (cca 16 digits) by an elementary stepping algorithm is up to two orders of magnitude higher than is possible to obtain by Braak’s solution. Any first n$n$ eigenvalues of the Rabi model arranged in increasing order can be determined as zeros of ?_N(?)${?}_N\left(?\right)$ of at least the degree N=n+n_t$N=n+n_t$. The value of n_t>0$n_t>0$, which is slowly increasing with n$n$, depends on the required precision. For instance, n_t?26$n_t?26$ for n=1000$n=1000$ and dimensionless interaction constant κ=0.2$\kappa =0.2$, if double precision is required. Given that the sequence of the l$l$th zeros x_nl$x_{nl}$’s of ?_n(?)${?}_n\left(?\right)$’s defines a monotonically decreasing discrete flow with increasing n$n$, the Rabi model is indistinguishable from an algebraically solvable model in any finite precision. Although we can rigorously prove our results only for dimensionless interaction constant κ<1$\kappa <1$, numerics and exactly solvable example suggest that the main conclusions remain to be valid also for κ≥1$\kappa \ge 1$.     

Influence of interface states on the temperature dependence and current–voltage characteristics of Ni/p-InP Schottky diodes

The ideality factor n$n$ and the barrier height _Φap${\Phi }_{ap}$ of the sputtered Ni/p-InP Schottky diodes have been calculated from their experimental Current–voltage (I–V)$\left(I\text{–}V\right)$ characteristics in the temperature range of 60–400 K with steps of 10 K. The n$n$ and _Φap${\Phi }_{ap}$ values for the device have been obtained as 1.27 and 0.87 eV at 300 K and 1.13 and 0.91 eV at 400 K, respectively. The n$n$ values larger than unity at high temperatures indicate the presence of a thin native oxide layer at the semiconductor/metal interface. The barrier height (BH) has been assumed to be bias dependent due to the presence of an interfacial layer and interface states located at the interfacial layer-semiconductor interface. Interfacial layer-thermionic emission current mechanism has been fitted to experimental I–V$I\text{–}V$ data by considering the bias-dependence of the BH at each temperature. The best fitting values of the series resistance _Rs$R_s$ and interface state density _Ns$N_s$ together with the bias-dependence of the BH have been used at each temperature, and the _Rs$R_s$ and _Ns$N_s$ versus temperature plots have been drawn. It has been seen that the experimental and theoretical forward bias I–V$I\text{–}V$ data are in excellent agreement with each other in the temperature range of 60–400 K. It has been seen that the _Rs$R_s$ and _Ns$N_s$ values increase with a decrease in temperature, confirming the results in the literature.     

Three PT-symmetric Hamiltonians with completely different spectra

We discuss three Hamiltonians, each with a central-field part H₀$H_0$ and a PT-symmetric perturbation igz$igz$. When H₀$H_0$ is the isotropic Harmonic oscillator the spectrum is real for all g$g$ because H$H$ is isospectral to H₀+g²/2$H_0+g^2/2$. When H₀$H_0$ is the Hydrogen atom then infinitely many eigenvalues are complex for all g$g$. If the potential in H₀$H_0$ is linear in the radial variable r$r$ then the spectrum of H$H$ exhibits real eigenvalues for 0<g<g_c$0<g<g_c$ and a PT phase transition at g_c$g_c$.     

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).     

Comparative study between a two-dimensional anisotropic Heisenberg antiferromagnet with easy-axis single-ion anisotropy and one with easy-axis exchange anisotropy

Generally, in literature, easy-axis single ion anisotropy and easy-axis exchange anisotropy was treated in indistinct way. In this work we propose to perform a comparative study of the effects of these two easy-axis anisotropies on the behavior of the magnetization and the critical temperature (_Tc)$(T_{\mathrm{c}})$ in the 2D classical Heisenberg antiferromagnetic model. In order to study the low-temperature thermodynamics of this model, we should consider the contribution of anisotropic spin waves, using a self-consistent harmonic approximation (SCHA) theory. We compare the predictions of SCHA with numerical simulations on L×L$L\times L$ square lattices using Monte Carlo (MC) simulations, which include effects due to all thermodynamically allowed excitations. Our SCHA results are in good agreement with our MC simulations results and have shown that the strong K$K$ limit gives two different Ising-like behavior. In the exchange anisotropic case, the dependence of _Tc$T_{\mathrm{c}}$ on anisotropic parameter K$K$ becomes linear and in the single-ion anisotropic case, _Tc$T_{\mathrm{c}}$ becomes independent of K$K$. Also, using MC simulations and finite size scaling, we show that the critical exponents in the two anisotropic case are compatible with the 2D Ising values α=0.125$\alpha =0.125$ and γ=1.75$\gamma =1.75$.     

Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite   two-dimensional lattices of size L×N$L\times N$ with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N)$Z(L,N)$ cannot be written simply as a trace of the transfer matrix TL${\mathrm{T}}_L$. Using a combinatorial method, we establish the decomposition Z(L,N)=_∑l,Dkb(l,Dk)K_l,Dk$Z(L,N)={\sum }_{l,D_k}{b}^{(l,D_k)}{K}_{l,D_k}$, where the characters K_l,Dk=i_∑N(λi)$K_{l,D_k}={\sum }_i{({\lambda }_i)}^N$ are simple traces. In this decomposition, the amplitudes b(l,Dk)$b^{(l,D_k)}$ of the eigenvalues λi${\lambda }_i$ of TL${\mathrm{T}}_L$ are labelled by the number l=0,1,…,L$l=0,1,\dots ,L$ of clusters which are non-contractible with respect to the transfer (N  ) direction, and a representation Dk$D_k$ of the cyclic group Cl$C_l$. We obtain rigorously a general expression for b(l,Dk)$b^{(l,D_k)}$ in terms of the characters of Cl$C_l$, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur.     

Non-Abelian fusion rules from an Abelian system

We demonstrate the emergence of non-Abelian fusion rules for excitations of a two dimensional lattice model built out of Abelian degrees of freedom. It can be considered as an extension of the usual toric code model on a two dimensional lattice augmented with matter fields. It consists of the usual C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ gauge degrees of freedom living on the links together with matter degrees of freedom living on the vertices. The matter part is described by a n$n$ dimensional vector space which we call H_n$H_n$. The Z_p${\mathbb{Z}}_p$ gauge particles act on the vertex particles and thus H_n$H_n$ can be thought of as a C(Z_p)$\mathbb{C}\left({\mathbb{Z}}_p\right)$ module. An exactly solvable model is built with operators acting in this Hilbert space. The vertex excitations for this model are studied and shown to obey non-Abelian fusion rules. We will show this for specific values of n$n$ and p$p$, though we believe this feature holds for all n>p$n>p$. We will see that non-Abelian anyons of the quantum double of C(S₃)$\mathbb{C}\left(S_3\right)$ are obtained as part of the vertex excitations of the model with n=6$n=6$ and p=3$p=3$. Ising anyons are obtained in the model with n=4$n=4$ and p=2$p=2$. The n=3$n=3$ and p=2$p=2$ case is also worked out as this is the simplest model exhibiting non-Abelian fusion rules. Another common feature shared by these models is that the ground states have a higher symmetry than Z_p${\mathbb{Z}}_p$. This makes them possible candidates for realizing quantum computation.     

Enhanced suppression of superconductivity in amorphous films with nano-scale patterning

We have measured the thickness dependence of the superconducting critical temperature, T_c(d_Bi)$T_c(d_{\text{Bi}})$, in amorphous Bi/Sb films patterned with a regular array of holes as well as nanoscale thickness variations. We find that the mean field T_c$T_c$ is suppressed relative to simultaneously produced unstructured films of the same thickness. Surprisingly, however, the functional form for T_c(d_Bi)$T_c(d_{\text{Bi}})$, remains unaffected. The role of the thickness variations in suppressing T_c$T_c$ is compared to the role of the holes, through parameterization of the surface, as measured through AFM/SEM and a proximity effect calculation. These results suggest that these two nanoscale modifications suppress T_c$T_c$ about equally and are consistent with T_c$T_c$ being determined on a microscopic length scale.     

On the parallel transport of the Ricci curvatures

Geometrical characterizations are given for the tensor R⋅S$R\cdot S$, where S$S$ is the Ricci tensor   of a (semi-)Riemannian manifold (M,g)$(M,g)$ and R$R$ denotes the curvature operator   acting on S$S$ as a derivation, and of the Ricci Tachibana tensor  _∧g⋅S${\wedge }_g\cdot S$, where the natural metrical operator  _∧g${\wedge }_g$ also acts as a derivation on S$S$. As a combination, the Ricci curvatures   associated with directions on M$M$, of which the isotropy determines that M$M$ is Einstein, are extended to the Ricci curvatures of Deszcz   associated with directions and planes on M$M$, and of which the isotropy determines that M$M$ is Ricci pseudo-symmetric in the sense of Deszcz.     

The Bethe lattice treatment of sound attenuation for a spin- 3/2 Ising model

The sound attenuation phenomena is investigated for a spin- 3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T$T$), frequency (w$w$), Onsager coefficient (γ$\gamma$) and external magnetic field (H$H$) near the second-order (_Tc)$\left(T_c\right)$ and first-order (_Tt)$\left(T_t\right)$ phase transition temperatures are examined for given coordination numbers q$q$ on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (α)$\left(\alpha \right)$. Our investigations revealed that only one peak is obtained near _Tt$T_t$ and three peaks are found near _Tc$T_c$ when the Onsager coefficient is varied at a given constant frequency for q=3$q=3$. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q=3,4$q=3,4$ and 6 near _Tc$T_c$. The sound attenuation peaks are observed near _Tt$T_t$ at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear.     

Effect of target density on YBCO thin films deposited from nanograined targets

Nanograined YBa₂Cu₃O_6+x${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+x}$ (YBCO) targets with grain sizes of 25–45 nm and different densities were prepared with sol–gel method. The properties of the thin films laser deposited from these targets were systematically studied. It was found that most parameters are not clearly affected by the target density, although the surface roughness decreased with target density. A small effect of decreasing J_c$J_{\text{c}}$ with increasing target density was observed, but this can be interpreted as film to film variation. On the other hand, a negative correlation between the accommodation field, B^∗$B^{\ast }$, and zero field J_c$J_{\text{c}}$ was observed and B^∗$B^{\ast }$ was found to increase with increasing number of lattice defects. Thus target density is found not to have a large effects on the superconducting or structural properties of YBCO thin films.     

Universal behavior in a model of city traffic with unequal green/red times

The effect of green/red asymmetry is studied for the single-car traffic model proposed in [B.A. Toledo, V. Muñoz, J. Rogan, C. Tenreiro, J.A. Valdivia, Modeling traffic through a sequence of traffic lights, Phys. Rev. E 70 (1) (2004) 016107], on two different signal synchronization strategies, namely, all signals in phase, and a green wave. The asymmetry is characterized by the parameter g=_tgr/T$g=t_{\text{gr}}/T$, where _tgr$t_{\text{gr}}$ is the green time and T$T$ the signal period. Although the car dynamics turns simpler or more complex, as compared with the equivalent situation for the symmetric case g=0.5$g=0.5$, critical behavior around resonance is shown to be preserved. However, unlike the case g=0.5$g=0.5$, critical exponents at both sides of the resonance are not equal and depend on g$g$. Analytical expressions for them are found, and shown to be both consistent with simulation results and independent of the distribution of distances between signals for the green wave case. Also, it is found that the green wave strategy is more robust to changes in g$g$, with respect to the synchronized lights strategy, in the sense that larger departures from g=0.5$g=0.5$ are needed to have noticeable effects on the car dynamics.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.