On the nuclear modification factor at RHIC and LHC

We show that pQCD factorization incorporated with pre-hadronization energy-loss effect naturally leads to flatness of the nuclear modification factor RAA$R_{\mathit{AA}}$ for produced hadrons at high transverse momentum pT$p_T$. We consider two possible scenarios for the pre-hadronization: In scenario 1, the produced gluon propagates through dense QCD medium and loses energy. In scenario 2, all gluons first decay to quark–antiquark pairs and then each pair loses energy as propagating through the medium. We show that the estimates of the energy-loss in these two different models lead to very close values and is able to explain the suppression of high-pT$p_T$ hadrons in nucleus–nucleus collisions at RHIC. We show that the onset of the flatness of RAA$R_{\mathit{AA}}$ for the produced hadron in central collisions at midrapidity is about pT≈15$p_T\approx 15$ and 25 GeV at RHIC and the LHC energies, respectively. We show that the smallness (RAA<0.5$R_{\mathit{AA}}<0.5$ ) and the high-pT$p_T$ flatness of RAA$R_{\mathit{AA}}$ obtained from the kT$k_T$ factorization supplemented with the Balitsky–Kovchegov (BK) equation is rather generic and it does not strongly depend on the details of the BK solutions. We show that energy-loss effect reduces the nuclear modification factor obtained from the kT$k_T$ factorization about 30–50% at moderate pT$p_T$.     

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).     

Surface and bulk properties of ballistic deposition models with bond breaking

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability p$p$. These systems present a crossover, for small values of p$p$, from random to correlated (KPZ) growth of surface roughness, which is studied through scaling arguments and Monte Carlo simulations on one- and two-dimensional substrates. We show that the crossover characteristic time _t×$t_{\times }$ scales with p$p$ according to _t×∼p^−y$t_{\times }\sim p^{-y}$ with y=(n+1)$y=(n+1)$ and that the interface width at saturation _Wsat$W_{sat}$ scales as _Wsat∼p^−δ$W_{sat}\sim p^{-\delta }$ with δ=(n+1)/2$\delta =(n+1)/2$, where n$n$ is either the maximal number of broken bonds or of dislodged suspended particles. This result shows that the sets of exponents y=1$y=1$ and δ=1/2$\delta =1/2$ or y=2$y=2$ and δ=1$\delta =1$ found in all previous works focusing on systems with this same type of crossover are not universal. Using scaling arguments, we show that the bulk porosity P$P$ of the deposits scales as P∼p^y−δ$P\sim p^{y-\delta }$ for small values of p$p$. This general scaling relation is confirmed by our numerical simulations and explains previous results present in literature.     

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.     

First-order density matrices in one dimension for independent fermions and impenetrable bosons in harmonic traps

To complement existing knowledge of the density matrix γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ of independent fermions for N   particles in one dimension under harmonic confinement, the corresponding matrix γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ for impenetrable bosons is given for N=2$N=2$ and 3 (with the N=4$N=4$ form available also). For fermions the momentum density is then obtained and illustrated numerically for N=10$N=10$. The boson momentum density is studied analytically at high momentum p  , the coefficients of the p⁻⁴$p^{\mathrm{-4}}$ and p⁻⁶$p^{\mathrm{-6}}$ terms being tabulated for N=2–5$N=2\text{–}5$ inclusive. Their dependence on powers of N   is exhibited numerically. Finally, the functional relationship between γIB(x,y)${\gamma }_{\mathrm{IB}}(x,y)$ and γF(x,y)${\gamma }_{\mathrm{F}}(x,y)$ is formally set out and illustrated.     

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.     

Critical behavior of an anisotropic Ising antiferromagnet in both external longitudinal and transverse fields

In this paper we study the critical behavior of a two-sublattice Ising model on an anisotropic square lattice in both uniform longitudinal (H  ) and transverse (Ω$\Omega$) fields by using the effective-field theory. The model consists of ferromagnetic interaction J_x in the x direction and antiferromagnetic interaction J_y in the y direction in the presence of the H   and Ω$\Omega$ fields. We obtain the phase diagrams in the H–T$H–T$ and Ω–T$\Omega –T$ planes changing values of the Ω$\Omega$ and H   parameters, respectively for fixed value at λ=_Jx/_Jy=1$\lambda =J_x/J_y=1$. At null temperature, the ground state phase diagram in the Ω–H$\Omega –H$ plane for several values of λ$\lambda$ parameter is analyzed. In the particular case of λ=1$\lambda =1$ we compare our results with mean-field theory (MFT) and was not observed reentrant behavior around of the critical field _Hc/_Jy=2.0$H_c/J_y=2.0$ for Ω=0$\Omega =0$ by using EFT.     

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.     

Elliptic flow arising from ridges due to semi-hard scattering

Azimuthal anisotropy in heavy-ion collisions is studied by taking into account the ridges generated by semi-hard scattering of intermediate-momentum partons, which can be sensitive to the initial spatial configuration of the medium in non-central collisions. In a simple treatment of the problem where the recombination of only thermal partons is considered, analytical formulas can be derived that yield results in accord with the data on v₂$v_2$ for pT<1–2 GeV/c$p_T<1\text{–}2\text{GeV}/c$. Centrality dependence is described by a geometrical factor. Ridge phenomenology is used to determine the initial slopes of v₂$v_2$ at low pT$p_T$ for both pion and proton. For higher pT$p_T$, shower partons from high-pT$p_T$ jets must be included, but they are not considered here.     

Diffusion-limited aggregates grown on nonuniform substrates

In the present paper, patterns of diffusion-limited aggregation (DLA) grown on nonuniform substrates are investigated by means of Monte Carlo simulations. We consider a nonuniform substrate as the largest percolation cluster of dropped particles with different structures and forms that occupy more than a single site on the lattice. The aggregates are grown on such clusters, in the range the concentration, p$p$, from the percolation threshold, _pc$p_c$ up to the jamming coverage, _pj$p_j$. At the percolation threshold, the aggregates are asymmetrical and the branches are relatively few. However, for larger values of p$p$, the patterns change gradually to a pure DLA. Tiny qualitative differences in this behavior are observed for different k$k$ sizes. Correspondingly, the fractal dimension of the aggregates increases as p$p$ raises in the same range _pc≤p≤_pj$p_c\le p\le p_j$. This behavior is analyzed and discussed in the framework of the existing theoretical approaches.     

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$g_c$.     

On m-accretive Schrödinger-type operators with singular potentials on Riemannian manifolds

We consider a Schrödinger-type differential expression _HV=∇^∗∇+V$H_V={\nabla }^{\ast }\nabla +V$, where ∇$\nabla$ is a Hermitian connection on a Hermitian vector bundle E$E$ over a complete Riemannian manifold (M,g)$(M,g)$ with metric g$g$ and positive smooth measure dμ$d\mu$, and V$V$ is a locally integrable section of the bundle of endomorphisms of E$E$. We give a sufficient condition for m$m$-accretivity of a realization of _HV$H_V$ in L²(E)$L^2\left(E\right)$.     

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.     

θ dependence of QCD at finite isospin density

We probe the θ   dependence of QCD at finite isospin chemical potential μI${\mu }_I$ using the effective chiral Lagrangian approach. The phase diagram in the θ  , μI${\mu }_I$ plane is constructed and described in detail in terms of chiral and pion condensates. The physics at θ∼π$\theta \sim \pi$ is investigated in both the normal and superfluid phase. Finally, the behaviour of the gluon condensate at finite μI${\mu }_I$ is computed.     

Target mass corrections for spin-dependent structure functions in collinear factorization

We derive target mass corrections (TMC) for the spin-dependent nucleon structure function g₁$g_1$ and polarization asymmetry A₁$A_1$ in collinear factorization at leading twist. The TMCs are found to be significant for g₁$g_1$ at large xB$x_B$, even at relatively high Q²$Q^2$ values, but largely cancel in A₁$A_1$. A comparison of TMCs obtained from collinear factorization and from the operator product expansion shows that at low Q²$Q^2$ the corrections drive the proton A₁$A_1$ in opposite directions.     

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.     

Quantum spherical model with competing interactions

We analyse the phase diagram of a quantum mean spherical model in terms of the temperature T$T$, a quantum parameter g$g$, and the ratio p=−_J2/_J1$p=-J_2/J_1$, where _J1>0$J_1>0$ refers to ferromagnetic interactions between first-neighbour sites along the d$d$ directions of a hypercubic lattice, and _J2<0$J_2<0$ is associated with competing antiferromagnetic interactions between second neighbours along m≤d$m\le d$ directions. We regain a number of known results for the classical version of this model, including the topology of the critical line in the g=0$g=0$ space, with a Lifshitz point at p=1/4$p=1/4$, for d>2$d>2$, and closed-form expressions for the decay of the pair correlations in one dimension. In the T=0$T=0$ phase diagram, there is a critical border, _gc=_gc(p)$g_c=g_c\left(p\right)$ for d≥2$d\ge 2$, with a singularity at the Lifshitz point if d<(m+4)/2$d<(m+4)/2$. We also establish upper and lower critical dimensions, and analyse the quantum critical behavior in the neighborhood of p=1/4$p=1/4$.     

On analogues of black brane solutions in the model with multicomponent anisotropic fluid

A family of spherically symmetric solutions with horizon in the model with m  -component anisotropic fluid is presented. The metrics are defined on a manifold that contains a product of n−1$n-1$ Ricci-flat “internal” spaces. The equation of state for any s  -th component is defined by a vector Us$U^s$ belonging to Rn+1${\mathbb{R}}^{n+1}$. The solutions are governed by moduli functions Hs$H_s$ obeying non-linear differential equations with certain boundary conditions imposed. A simulation of black brane solutions in the model with antisymmetric forms is considered. An example of solution imitating M₂–M₅$M_2\text{–}{M}_5$ configuration (in D=11$D=11$ supergravity) corresponding to Lie algebra A₂$A_2$ is presented.