Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions.

Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel-Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel-Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality, H(a(t)), where H(t) is the Hubble parameter and a(t) is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular H(t) and a(t) are obtained, where H(t) diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of H(a(t)) is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing H(a(t)) with increasing a(t) varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure.

Diffusion of Conserved Charges in Relativistic Heavy Ion Collisions.

We demonstrate that the diffusion currents do not depend only on gradients of their corresponding charge density, but that the different diffusion charge currents are coupled. This happens in such a way that it is possible for density gradients of a given charge to generate dissipative currents of another charge. Within this scheme, the charge diffusion coefficient is best viewed as a matrix, in which the diagonal terms correspond to the usual charge diffusion coefficients, while the off-diagonal terms describe the coupling between the different currents. In this Letter, we calculate for the first time the complete diffusion matrix for hot and dense nuclear matter, including baryon, electric, and strangeness charges. We find that the baryon diffusion current is strongly affected by baryon charge gradients but also by its coupling to gradients in strangeness. The electric charge diffusion current is found to be strongly affected by electric and strangeness gradients, whereas strangeness currents depend mostly on strange and baryon gradients.

Thermalization of gluons with Bose-Einstein condensation.

We study the thermalization of gluons far from thermal equilibrium in relativistic kinetic theory. The initial distribution of gluons is assumed to resemble that in the early stage of ultrarelativistic heavy ion collisions. Only elastic scatterings in static, nonexpanding gluonic matter are considered. At first we show that the occurrence of condensation in the limit of vanishing particle mass requires a general constraint for the scattering matrix element. Then the thermalization of gluons with Bose-Einstein condensation is demonstrated in a transport calculation. We see a continuously increasing overpopulation of low energy gluons, followed by a decrease to the equilibrium distribution, when the condensation occurs. The times of the completion of the gluon condensation and of the entropy production are calculated. These times scale inversely with the energy density.

Elliptic flow and nuclear modification factor in ultrarelativistic heavy-ion collisions within a partonic transport model.

The quark gluon plasma produced in ultrarelativistic heavy-ion collisions exhibits remarkable features. It behaves like a nearly perfect liquid with a small shear viscosity to entropy density ratio and leads to the quenching of highly energetic particles. We show that both effects can be understood for the first time within one common framework. Employing the parton cascade Boltzmann approach to multiparton scatterings, the microscopic interactions and the space-time evolution of the quark gluon plasma are calculated by solving the relativistic Boltzmann equation. Based on cross sections obtained from perturbative QCD with explicitly taking the running coupling into account, we calculate the nuclear modification factor and elliptic flow in ultrarelativistic heavy-ion collisions. With only one single parameter associated with coherence effects of medium-induced gluon radiation, the experimental data of both observables can be understood on a microscopic level. Furthermore, we show that perturbative QCD interactions with a running coupling lead to a sufficiently small shear viscosity to entropy density ratio of the quark gluon plasma, which provides a microscopic explanation for the observations stated by hydrodynamic calculations.

Persistent nonequilibrium effects in generalized Langevin dynamics of nonrelativistic and relativistic particles.

Persistent nonequilibrium effects such as the memory of the initial state, the ballistic diffusion, and the break of the equipartition theorem and the ergodicity in Brownian motions are investigated by analytically solving the generalized Langevin equation of nonrelativistic Brownian particles with colored noise. These effects can also be observed in the Brownian motion of relativistic particles by numerically solving the generalized Langevin equation for specially chosen memory kernels. Our analyses give rise to think about the possible anomalous motion of heavy quarks in relativistic heavy-ion collisions.

Transport coefficients of hadronic matter near Tc.

A hadron resonance gas model including all known particles and resonances with masses m < 2 GeV and an exponentially rising density of Hagedorn states for m > 2 GeV is used to obtain an upper bound on the shear viscosity to entropy density ratio, eta/s approximately 1/(4pi), of hadronic matter near Tc. We found a large trace anomaly and small speed of sound near Tc, which agree well with recent lattice calculations. We comment on the bulk viscosity to entropy density ratio close to Tc.

Kinetic approach to a relativistic Bose-Einstein condensate.

We apply a Boltzmann approach to the kinetic regime of a relativistic Bose-Einstein condensate of scalar bosons by decomposing the one-particle distribution function in a condensate part and a nonzero momentum part of excited modes, leading to a coupled set of evolution equations which are then solved efficiently with an adaptive higher order Runge-Kutta scheme. We compare our results to the partonic cascade Monte Carlo simulation BAMPS for a critical but far from equilibrium case of massless bosons. Motivated by the color glass condensate initial conditions in QCD with a strongly overpopulated initial glasma state, we also discuss the time evolution starting from an overpopulated initial distribution function of massive scalar bosons. In this system a self-similar evolution of the particle cascade with a nonrelativistic turbulent scaling in the infrared sector is observed as well as a relativistic exponent for the direct energy cascade, confirming a weak wave turbulence in the ultraviolet region.

Monte Carlo framework for noncontinuous interactions between particles and classical fields.

Particles and fields are standard components in numerical calculations like transport simulations in nuclear physics and have well-understood dynamics. Still, a common problem is the interaction between particles and fields due to their different formal description. Particle interactions are discrete, pointlike events while field dynamics is described with continuous partial-differential equations of motion. A workaround is the use of effective theories like the Langevin equation with the drawback of energy conservation violation. We present a method, which allows us to model noncontinuous interactions between particles and scalar fields, allowing us to simulate scattering-like interactions which exchange discrete "quanta" of energy and momentum between fields and particles while obeying energy and momentum conservation and allowing control over interaction strengths and times. In this paper we apply this method to different model systems, starting with a simple harmonic oscillator, which is damped by losing discrete energy quanta. The second and third system consists of an oscillator and a one-dimensional field, which are damped via discrete energy loss and are coupled to a stochastic force, leading to equilibrium states which correspond to statistical Langevin-like systems. The last example is a scalar field in (1 + 3) space-time dimensions, which is coupled to a microcanonical ensemble of particles by incorporating particle production and annihilation processes. Obeying the detailed-balance principle, the system equilibrates to thermal and chemical equilibrium with dynamical fluctuations on the fields, generated dynamically by the discrete interactions.

Simulation of stationary Gaussian noise with regard to the Langevin equation with memory effect.

We present an efficient method for simulating a stationary Gaussian noise with an arbitrary covariance function, and then we study numerically the impact of time-correlated noise on the time evolution of a (1+1)-dimensional generalized Langevin equation by comparing also to analytical results. Finally, we apply our method to the generalized Langevin equation with an external harmonic and double-well potential.

Towards a unified understanding of jet quenching and elliptic flow within a perturbative QCD parton transport.

The gluonic contribution to the nuclear modification factor R_{AA} is investigated for central Au + Au collisions at sqrt[s] = 200 AGeV employing a perturbative QCD-based parton cascade including radiative processes. A flat quenching pattern is found up to transverse momenta of 30 GeV, which is slightly smaller compared with results from the Gyulassy-Levai-Vitev formalism. We demonstrate that the present microscopic transport description provides a challenging means of investigating both jet quenching and a strong buildup of elliptic flow in terms of the same standard perturbative QCD interactions.

Shear viscosity in a gluon gas.

The relation of the shear viscosity coefficient to the recently introduced transport rate is derived within relativistic kinetic theory. We calculate the shear viscosity over entropy ratio eta/s for a gluon gas, which involves elastic gg-->gg perturbative QCD (PQCD) scatterings as well as inelastic gg<-->ggg PQCD bremsstrahlung. For alpha_{s}=0.3 we find eta/s=0.13 and for alpha_{s}=0.6, eta/s=0.076. The small eta/s values, which suggest strongly coupled systems, are due to the gluon bremsstrahlung incorporated.

Perturbative QCD calculations of elliptic flow and shear viscosity in Au+Au collisions at sqrt[s_{NN}]=200 GeV.

The elliptic flow v_{2} and the ratio of the shear viscosity over the entropy density, eta/s, of gluon matter are calculated from the perturbative QCD (pQCD) based parton cascade Boltzmann approach of multiparton scatterings. For Au+Au collisions at sqrt[s]=200A GeV the gluon plasma generates large v_{2} values measured at the BNL Relativistic Heavy Ion Collider. Standard pQCD yields eta/s approximately 0.08-0.15 as small as the lower bound found from the anti-de Sitter/conformal field theory conjecture.

Dilepton yields from brown-rho scaled vector mesons including memory effects.

Scenarios with dropping vector meson masses, motivated by the work of Brown and Rho, have been strongly discussed after recent NA60 Collaboration data were presented. In this Letter they are investigated within a nonequilibrium field theoretical description that includes quantum mechanical memory. Dimuon yields are calculated by application of a model for the fireball, and strong modifications are found in the comparison to quasiequilibrium calculations, which assume instantaneous adjustment of all meson properties to the surrounding medium. In addition, results for the situation of very broad excitations are presented.

Proof that the hydrogen-antihydrogen molecule is unstable.

In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges (m1(+), m2(-), m3(+), m4(-)), where all masses are assumed finite, to form the stable system. The obtained stability condition is physical and is expressed through the required minimal ratio of Jacobi masses. In particular, this provides the rigorous proof that hydrogen-antihydrogen and muonium-antimuonium molecules and hydrogen-positron-muon systems are unstable. It also proves that replacing hydrogen in the hydrogen-antihydrogen molecule with its heavier isotopes does not make the molecule stable. These are the first rigorous results on the instability of these systems.