Empirical constraints on parton energy loss in nucleus–nucleus collisions at RHIC

We present empirical features of parton energy loss in nucleus–nucleus collisions at RHIC through studies of the spectra and nuclear modification factors (R_AA$R_{AA}$) for charged hadrons, neutral pions (π⁰${\pi }^0$) and non-photonic electrons. The flat distribution of R_AA$R_{AA}$ at high transverse momentum (pT$p_T$) for a given collision centrality is consistent with a scenario where parton energy loss ΔpT$\mathrm{\Delta }{p}_T$ is proportional to pT$p_T$. The centrality dependence of the parton energy loss indicates the absence of path length dependence in the magnitude of energy loss. The lack of strong path length dependence suggests a dynamical picture where the dense partonic medium undergoes rapid expansion and the density of the medium falls rapidly in the first a few Fermi interval, which may be much shorter than the full path length. Implications of the empirical constraints on the parton energy loss will also be discussed.     

Properties of baryonic,electric and strangeness chemical potentials and some of their consequences in relativistic heavy ion collisions

Analytic expressions are given for the baryonic, electric and strangeness chemical potentials which explicitly show the importance of various terms. Simple scaling relations connecting these chemical potentials are found. Applications to particle ratios and to fluctuations and related thermal properties such as the isothermal compressibility κT${\kappa }_T$ are illustrated. A possible divergence of κT${\kappa }_T$ is discussed.     

Superconducting cosmic strings and one dimensional extended supersymmetric algebras

In this article we study in detail the supersymmetric structures that underlie the system of fermionic zero modes around a superconducting cosmic string. Particularly, we extend the analysis existing in the literature on the one dimensional N=2$N=2$ supersymmetry and we find multiple N=2$N=2$, d=1$d=1$ supersymmetries. In addition, compact perturbations of the Witten index of the system are performed and we find to which physical situations these perturbations correspond. More importantly, we demonstrate that there exists a much more rich supersymmetric structure underlying the system of fermions with N_f$N_f$ flavors and these are N$N$-extended supersymmetric structures with non-trivial topological charges, with “N$N$” depending on the fermion flavors.     

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$p_T$.     

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.     

Warped string compactification via singular Calabi–Yau conformal field theory

We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2,R)$\mathit{SL}(2,\mathbf{R})$. The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27⊕1$27\oplus 1$ of E₆$E_6$ for the E₈×E₈$E_8\times E_8$ heterotic string. We speculate about a possible realization of local E₆$E_6$ GUT by using this framework.     

Phase separation in polydisperse rod–coil block copolymers

The stability limits of the homogeneous state of melts of rod–coil RC$RC$, R_C2$R{C}_2$, and CRC$CRC$ polydisperse block copolymers have been investigated in the framework of the weak segregation theory. It was assumed that the number of units in either the rod-like R$R$ or the flexible C$C$ block is a random variable distributed by the Schulz–Zimm distribution. Inspection of the spinodal curves shows that the copolymer melts with polydisperse rigid blocks are less stable with respect to formation of the nematic state than melts with the monodisperse ones. If flexible C$C$ blocks are polydisperse the homogeneous state of a rod–coil melt is less stable against microphase separation than the homogeneous state of monodisperse melt of the same architecture.     

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.     

Momentum spectra,anisotropic flow,and ideal fluids

If the matter produced in ultrarelativistic heavy-ion collisions reaches thermal equilibrium, its subsequent evolution follows the laws of ideal fluid dynamics. We show that general predictions can be made on this basis alone, irrespective of the details of the hydrodynamical model. We derive several scaling rules for momentum spectra and anisotropic flow (in particular the elliptic flow, v₂$v_2$, and the hexadecupole flow, v₄$v_4$) of identified particles. Comparison with existing data is briefly discussed, and qualitative predictions are made for LHC.     

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.     

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.     

Asymmetric Gepner models II. Heterotic weight lifting

A systematic study of “lifted” Gepner models is presented. Lifted Gepner models are obtained from standard Gepner models by replacing one of the N=2$N=2$ building blocks and the E₈$E_8$ factor by a modular isomorphic N=0$N=0$ model on the bosonic side of the heterotic string. The main result is that after this change three family models occur abundantly, in sharp contrast to ordinary Gepner models. In particular, more than 250 new and unrelated moduli spaces of three family models are identified. We discuss the occurrence of fractionally charged particles in these spectra.     

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.     

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Rényi entropies. We recall that in both Shannon and Rényi cases, and for a given dimension n$n$, the only case of equality occurs for Gaussian random vectors. We show that as n$n$ grows, however, the bound is also asymptotically attained in the cases of n$n$-dimensional Student-t$t$ and Student-r$r$ distributions. A complete analytical study is performed in a special case of a Student-t$t$ distribution. We also show numerically that this effect exists for the particular case of a n$n$-dimensional Cauchy variable, whatever the Rényi entropy considered, extending the results of Abe and illustrating the analytical asymptotic study of the Student-t$t$ case. In the Student-r$r$ case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a “Gaussianization” of the vector when the dimension increases.     

Singular unitarity in “quantization commutes with reduction”

Let M$M$ be a connected compact quantizable Kähler manifold equipped with a Hamiltonian action of a connected compact Lie group G$G$. Let M//G=?⁻¹(0)/G=_M0$M//G={?}^{-1}\left(0\right)/G=M_0$ be the symplectic quotient at value 0 of the moment map ?$?$. The space _M0$M_0$ may in general not be smooth. It is known that, as vector spaces, there is a natural isomorphism between the quantum Hilbert space over _M0$M_0$ and the G$G$-invariant subspace of the quantum Hilbert space over M$M$. In this paper, without any regularity assumption on the quotient _M0$M_0$, we discuss the relation between the inner products of these two quantum Hilbert spaces under the above natural isomorphism; we establish asymptotic unitarity to leading order in Planck’s constant of a modified map of the above isomorphism under a “metaplectic correction” of the two quantum Hilbert spaces.     

On the anatomy of multi-spin magnon and single spike string solutions

We study rigid string solutions rotating in AdS₅×S⁵${\mathit{AdS}}_5\times S^5$ background. For particular values of the parameters of the solutions we find multispin solutions corresponding to giant magnons and single spike strings. We present an analysis of the dispersion relations in the case of three spin solutions distributed only in S⁵$S^5$ and the case of one spin in AdS₅${\mathit{AdS}}_5$ and two spins in S⁵$S^5$. The possible relation of these string solutions to gauge theory operators and spin chains are briefly discussed.     

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.     

Pseudo-topological transitions in 2D gravity models coupled to massless scalar fields

We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to d   massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a c=1$c=1$ “barrier”, analogous to the c=1$c=1$ barrier encountered in non-critical string theory, only the CDT transition is easier to be detected numerically. For d?1$d?1$ we observe time-translation invariance and geometries entirely governed by quantum fluctuations around the uniform toroidal topology put in by hand. For d>1$d>1$ the effective average geometry is no longer toroidal but “semiclassical” and spherical with Hausdorff dimension _dH=3$d_H=3$. In the d>1$d>1$ sector we study the time dependence of the semiclassical spatial volume distribution and show that the observed behavior is described by an effective mini-superspace action analogous to the actions found in the de Sitter phase of three- and four-dimensional pure CDT simulations and in the three-dimensional CDT-like Ho?ava–Lifshitz models.