Charmonium states in quark-gluon plasma

We discuss how the spectral changes of quarkonia at T _c can reflect the ‘critical’ behaviour of QCD phase transition. Starting from the temperature dependencies of the energy density and pressure from lattice QCD calculation, we extract the temperature dependencies of the scalar and spin-2 gluon condensates near T _c. We also parametrize these changes into the electric and magnetic condensate near T _c. While the magnetic condensate hardly changes across T _c, we find that the electric condensate increases abruptly above T _c. Similar abrupt change is also seen in the scalar condensate. Using the QCD second-order Stark effect and QCD sum rules, we show that these sudden changes induce equally abrupt changes in the mass and width of J/ψ, both of which are larger than 100 MeV at slightly above T _c.      

Orientational dynamics of superfluid He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

A remark on the large difference between the glueball mass and T<Subscript>c</Subscript> in quenched QCD

The lattice QCD studies indicate that the critical temperature T _c ≃ 260-280 MeV of the deconfinement phase transition in quenched QCD is considerably smaller than the lowest-lying glueball mass m _G ≃ 1500-1700 MeV, i.e., T _c ≪ m _G. As a consequence of this large difference, the thermal excitation of the glueball in the confinement phase is strongly suppressed by the statistical factor e ^-mG/Tc ≃ 0.00207 even near T ≃ T _c. We consider its physical implication, and argue the abnormal feature of the deconfinement phase transition in quenched QCD from the statistical viewpoint. To appreciate this, we demonstrate a statistical argument of the QCD phase transition using the recent lattice QCD data. From the phenomenological relation between T _c and the glueball mass, the deconfinement transition is found to take place in quenched QCD before a reasonable amount of glueballs is thermally excited. In this way, quenched QCD reveals a question “what is the trigger of the deconfinement phase transition ?” Received: 18 November 2002 / Accepted: 4 February 2003 / Published online: 29 April 2003     

Discussion of thermodynamic features within the PNJL model

We discuss some thermodynamical features of a QCD system within the two-flavor Polyakov loop extended Nambu–Jona-Lasinio(PNJL) model. Several thermodynamical quantities of interest(pressure, energy density,specific heat, speed of sound, etc.) are investigated and discussed in detail with two different forms of Polyakov loop potential. The effective coupling strength G incorporating a quark feedback(quark condensate) through operator product expansion is also discussed, as well as the relationship between color deconfinement and chiral phase crossover.We find that some thermodynamical quantities have quite different behavior for different Polyakov loop potentials.By changing the characteristic temperature T_0 of the pure Yang-Mills field, we find that when T_0 becomes small,color deconfinement might happen earlier than chiral phase crossover, while their relationship can be determined via some thermodynamical quantities. Furthermore, the behavior of the thermodynamical quantities is quite different in the two different forms of Polyakov loop potential studied. Especially, one of the potentials, specific heat, has two peaks, which correspond to color deconfinement and chiral phase crossover respectively. This interesting phenomenon may shed some light on whether the inflection points of the chiral condensate and deconfinement transitions happen at the same temperature or not for lattice QCD and experimental studies.     

Simulation of first order confinement transition in relativistic heavy ion collision

We have carried out numerical simulation of first order phase transition in 2+1 dimensions to study the formation and evolution of Z(3) domain walls in relativistic Heavy Ion Collision using the effective potential proposed by Pisarski for QCD where Polyakov loop is the order parameter of the weak first order phase transition. Bubbles of the QGP phase are randomly nucleated on the lattice, which grow and coalesce. The spontaneous breaking of Z(3) symmetry in QGP phase gives rise to domain walls and topological strings. We discuss P _T enhancement due to reflection of quarks from the collapsing domain walls. We also discuss enhancement of doubly strange and triply strange hadrons due to larger concentration of s quarks inside collapsing wall. The decay of the domain walls when temperature drops below T _c results in the fluctuations of energy density.     

The wrong kind of gravity

The KPZ formula [V.G. Knizhnik, A.M. Polyakov, and A.B. Zamolodchikov, Mod. Phys. Lett. A 3 (1988) 819] shows that coupling central charge c≤1 spin models to 2D quantum gravity dresses the conformal weights to get new critical exponents, where the relation between the original and dressed weights depends only on c. At the discrete level the coupling to 2D gravity is effected by putting the spin models on annealed ensembles of Φ³ planar random graphs or their dual triangulations, where the connectivity fluctuates on the same time-scale as the spins.Since the sole determining factor in the dressing is the central charge, one could contemplate putting a spin model on a quenched ensemble of 2D gravity graphs with the “wrong” c value. We might then expect to see the critical exponents appropriate to the c value used in generating the graphs. In such cases the KPZ formula could be interpreted as giving a continuous line of critical exponents which depend on this central charge. We note that rational exponents other than the KPZ values can be generated using this procedure for the Ising, tricritical Ising and 3-state Potts models.     

Effects of superstrings in collisions

Superstring theory in d = 10 dimensions after Calabi—Yau compactification yields a minimum low-energy gauge group SU(3)_C × SU(2)_L × U(1)_Y × U(1)_E. The low-energy theory includes particles with the quantum numbers of 27 representations of E₆, each of which contains an extra neutrino ν^c conventionally called a “right-handed neutrino”. The contributions of ν and ν^c to through Z⁰ and Z_E mixing is calculated. Small contributions are found of the new right-handed neutrino and of the superstring boson Z_E to σ(e⁺e⁻ → γ + nothing).     

Lattice quantum chromodynamics equation of state: A better differential method

We propose a better differential method for the computation of the equation of state of QCD from lattice simulations. In contrast to the earlier differential method, our technique yields positive pressure for all temperatures including the temperatures in the transition region. Employing it on temporal lattices of 8, 10 and 12 sites and by extrapolating to zero lattice spacing we obtained the pressure, energy density, entropy density, specific heat and speed of sound in quenched QCD for 0.9 ≤ T/T _c ≤ 3. At high temperatures comparisons of our results are made with those from the dimensional reduction approach and also with those from a conformal symmetric theory.      

Deconfinement transition for nonzero baryon density in the field correlator method

Deconfinement phase transition due to the disappearance of confining colorelectric field correlators is described using a nonperturbative equation of state. The resulting transition temperature T _c (μ) at any chemical potential μ is expressed in terms of the change of the gluon condensate ΔG ₂ and absolute value of the Polyakov loop L _fund(T _c ), which is known from the lattice and analytic data, and is in good agreement with the lattice data for ΔG ₂ ≈ 0.0035 GeV⁴; e.g., T _c (0) = 0.27, 0.19, and, 0.17 GeV for n _f = 0, 2, and 3, respectively. The text was submitted by the authors in English.     

New ferromagnetic La3Co2TaO9 double perovskite: Structural and magnetic properties

The new double perovskite La₃Co₂TaO₉ has been prepared by a solid-state procedure. The crystal and magnetic structures have been studied from X-ray powder diffraction (XRPD) and neutron powder diffraction (NPD) data. Rietveld refinements were performed in the monoclinic space group P2₁/n. The structure consists of an ordered array of alternating B′O₆ and B″O₆ octahedra sharing corners, tilted along the three pseudocubic axes according to the Glazer notation a⁻b⁻c⁺. Rietveld refinements show that at RT the cell parameters are a=5.6005(7) Å, b=5.6931(7) Å, c=7.9429(9) Å and β=89.9539(7)°, and the refined crystallographic formula of this “double perovskite” can be written as La₂(Co)_2d(Co_1/3Ta_2/3)_2cO₆. Magnetization measurements and low-temperature NPD data show that the perovskite is a ferromagnet with T_C=72 K. At high T it follows the Curie–Weiss law with an effective magnetic moment of 3.82μ_B per Co ion which is very close to spin only Co²⁺ (HS).     

Magnetotransport and magnetotunneling in single-layer, two-layer, and three-layer Bi2Sr2Can−1CunOz (n=1,2,3) single crystals

In continuous magnetic fields H up to 28 T, we have studied the out-of-plane transport properties and tunneling characteristics of high-quality nondoped single crystals of the Bi-cuprate family: Bi₂Sr₂CuO_6+δ (Bi2201), Bi₂Sr₂CaCu₂O_8+δ (Bi2212) and Bi₂Sr₂Ca₂Cu₃O_10+δ (Bi2223) grown by an identical method. For all compounds the out-of-plane magnetotransport ρ_c(H) is negative in the temperature region where ρ_c(T) shows in the normal state a semiconducting-like temperature dependence. The negative magnetoresistance of ρ_c corresponds to the suppression of the semiconducting temperature dependence of ρ_c(T) which is found to be isotropic. For the Bi2201 compound, where the normal state can be reached in the available magnetic fields (28 T), a nearly complete suppression of the low-temperature upturn in ρ_c(T) is observed in the highest magnetic fields with a tendency towards a metallic behavior down to the lowest temperatures (0.4 K). Using the break-junction technique, especially for the Bi2212 and Bi2232 compounds, a clear superconducting gap structure can be observed. Both for temperatures above the critical temperature and for magnetic fields above the upper critical field, a pseudogap structure remains present in the tunneling spectra. The applied magnetic fields yield a stronger suppression of the superconducting state compared to that of the normal-state gap structures as manifested in ρ_c(T) transport and tunneling.     

Isospin breaking in nuclear physics: The Nolen-Schiffer effect

Using the QCD sum rules we calculate the neutron-proton mass difference at zero density as a function of the difference in bare quark massm _d—m _u. We confirm results of Hatsuda, Høgaasen and Prakash that the largest term results from the difference in up and down quark condensates, the explicitC(m _d—m _u) entering with the opposite sign. The quark condensates are then extended to finite density to estimate the Nolen-Schiffer effect. The neutron-proton mass difference is extremely density dependent, going to zero at roughly nuclear matter density.The Ioffe formula for the nucleon mass is interpreted as a derivation, within the QCD sum rule approach, of the Nambu-Jona-Lasinio formula. This clarifies theN _c counting and furthermore provides an alternative interpretation of the Borel mass.     

Glueballs and the superfluid phase of Two-Color QCD

We present the first results on scalar glueballs in cold, dense matter using lattice simulations of two-color QCD. The simulations are carried out on a 6³×12 lattice and use a standard hybrid molecular dynamics algorithm for staggered fermions for two values of quark mass. The glueball correlators are evaluated via a multi-step smearing procedure. The amplitude of the glueball correlator peaks in correspondence with the zero temperature chiral transition, μ _c=m _π /2, and the propagators change in a significant way in the superfluid phase, while the Polyakov loop is nearly insensitive to the transition. Standard analysis suggest that lowest mass in the 0⁺⁺ gluonic channel decreases in the superfluid phase, but these observations need to be confirmed on larger and more elongated lattices. These results indicate that a non-zero density induces non-trivial modifications of the gluonic medium.     

Thermodynamics on noncommutative geometry in coherent state formalism

The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual “attraction (repulsion) potential” between boson (fermion) in the high temperature limit. The characters could be traced to the fact that, the particle with mass m in noncommutative thermal geometry with noncommutativity θ and temperature T will correspond to that in the commutative background with temperature T(1+kTmθ)⁻¹. Such a correspondence implies that the ideal gas energy will asymptotically approach to a finite limiting value as that on commutative geometry at T_θ=(kmθ)⁻¹. We also investigate the squeezed coherent states and see that they could have arbitrary mean energy. The thermal properties of those systems are calculated and compared to each other. We find that the heat capacity of the squeezed coherent states of boson and fermion on the noncommutative geometry have different values, contrast to that on the commutative geometry.     

Vortex dynamics in single crystal Hg-1201

Anisotropic superconducting materials often show an enhanced pinning along their crystallographic ab-planes. To obtain information about such a behavior of the high-T_c system Hg-1201 (HgBa₂CuO₄) magnetic investigations on a single crystal are performed for the two field orientations, parallel to the c-axis and parallel to the ab-planes. The dependence of the ac magnetization on temperature, magnetic field and frequency is determined. Compared to former results on powder samples of this system no indication of a second peak in the imaginary part of the susceptibility χ′′ is found. It seems to be shifted to higher temperatures overlapping now with the first peak. The corresponding irreversibility lines for both orientations, parallel to c and parallel to ab, are determined and discussed within the framework of a “diffusion” model.     

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper''s operator

Harper's operator is the self-adjoint operator on defined by

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. We first show that the determination of the spectrum of the transition operator on the Cayley graph of the discrete Heisenberg group in its standard presentation, is equivalent to the following upper bond on the norm of H_θ,: H_{θ,≤ 2(1 + √2 + cos(2πθ))}. We then prove this bound by reducing it to a problem on periodic Jacobi matrices, viewing H_θ, as the image of H_θ = U_θ + _θ^* + V_θ + V_θ^* in a suitable representation of the rotation algebra A_θ. We also use powers of H_θ to obtain various upper and lower bounds on H_θ = maxH_θ,. We show that “Fourier coefficients” of H_θ^k in A_θ have a combinatorial interpretation in terms of paths in the square lattice ². This allows us to give some applications to asymptotics of lattice paths combinatorics.     

Hard-thermal-loop QCD trace anomaly

In this proceedings I summarize results of QCD trace anomaly from recent three-loop hard-thermal-loop perturbation theory (HTLpt) calculations. I focus on the trace anomaly scaled by T ² for pure-glue and N _f = 3 QCD. The comparison to available lattice data suggests that for pure-glue QCD agreement between HTLpt results and lattice data for the trace anomaly begins at temperatures above 8 T _c while when including quarks (N _f = 3) agreement begins already at temperatures above 2 T _c . The results in both cases indicate that at very high temperatures the T ²-scaled trace anomaly increases with temperature in accordance with the predictions of HTLpt.     

Dynamical behavior of the phase transition of strained from atomistic simulations

Using an atomistic shell model we study the temperature dependence of the ferroelectric properties of BaTiO₃ under biaxial compressive strain applicable to growth on perovskites substrate. Molecular dynamics simulations show a “r→c→p” sequence of phase transitions when temperature is increased, and the absence of an “ac phase”. The first-order paraelectric-to-ferroelectric phase transition presents in bulk changes to a second-order one as a consequence of the in-plane constraint imposed by the mechanical boundary conditions. From the tetragonal ferroelectric c phase, the transition takes place in a finite range of temperature where the lattice parameter normal to the plane keeps approximately constant until T_c is reached. Analysis of the local polarization behavior reveals an order–disorder dynamics as the dominant mechanism of the transition.