Suppression of elliptic flow in a minimally viscous quark–gluon plasma

We compute the time evolution of elliptic flow in non-central relativistic heavy-ion collisions, using a (2+1$2+1$)-dimensional code with longitudinal boost-invariance to simulate viscous fluid dynamics in the causal Israel–Stewart formulation. We show that even “minimal” shear viscosity η/s=?/(4π)$\eta /s=?/(4\pi )$ leads to a large reduction of elliptic flow compared to ideal fluid dynamics, raising questions about the interpretation of recent experimental data from the Relativistic Heavy Ion Collider.     

The rapidity structure of Mach cones and other large angle correlations in heavy-ion collisions

The pattern of angular correlations of hadrons with a (semi-)hard trigger hadron in heavy-ion collisions has attracted considerable interest. In particular, unexpected large angle structures on the away side (opposite to the trigger) have been found. Several explanations have been brought forward, among them Mach shockwaves and Cherenkov radiation. Most of these scenarios are characterized by radial symmetry around the parton axis, thus angular correlations also determine the rapidity dependence of the correlation. If the observed correlations are remnants of an away side parton after interaction with the medium created in the collision, pQCD allows to calculate the distribution P(y)$P(y)$ of the away side partons in rapidity. The measured correlation then arises as a folding of P(y)$P(y)$ and the rapidity structure of the correlation taking into account the detector acceptance. This places non-trivial and rather stringent constraints on the underlying scenario. We investigate these dependences and demonstrate that Mach shockwaves survive this folding procedure well whereas Cherenkov radiation scenarios face new challenges.     

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.     

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.     

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.     

Observation of spin reorientation in layered manganites La1.2Sr1.8(Mn1−yRuy)2O7 (0.0⩽y⩽0.2) by Lorentz transmission electron microscopy

The effect of Ru substitution for Mn in bilayered oxides La_1.2Sr_1.8(Mn_1−yRu_y)₂O₇ (0?y?0.2$0?y?0.2$) was investigated by magnetization measurements and low-temperature Lorentz transmission electron microscopy. It was found that the magnetic anisotropy is controlled by the Ru content y and temperature T. The easy axis changes from 〈1 1 0〉 for the y=0$y=0$ crystal to the c  -axis for y=0.2$y=0.2$, and it rotates away from the c-  axis for the y=0.05$y=0.05$ and y=0.07$y=0.07$ crystals with decreasing temperature. Furthermore, maze-shaped magnetic domain structures were observed in the (0 0 1) thin crystals with 0.05?y?0.2$0.05?y?0.2$. Changes in domain size and structure indicate that the uniaxial magnetic anisotropy becomes stronger as Ru content y increases.     

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.     

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.     

Partition function zeros of the antiferromagnetic Ising model on triangular lattice in the complex temperature plane for nonzero magnetic field

The grand partition functions Z(T,B)$Z(T,B)$ of the Ising model on L×L$L\times L$ triangular lattices with fully periodic boundary conditions, as a function of temperature T and magnetic field B  , are evaluated exactly for L<12$L<12$ (using microcanonical transfer matrix) and approximately for L?12$L?12$ (using Wang–Landau Monte Carlo algorithm). From Z(T,B)$Z(T,B)$, the distributions of the partition function zeros of the triangular-lattice Ising model in the complex temperature plane for real B≠0$B\ne 0$ are obtained and discussed for the first time. The critical points aN(x)$a_N(x)$ and the thermal scaling exponents yt(x)$y_t(x)$ of the triangular-lattice Ising antiferromagnet, for various values of x=e−2βB$x=e^{-2\beta B}$, are estimated using the partition function zeros.