Equation of State and Collective Dynamics

This talk summarizes the present status of a program to quantitatively relate data from the Relativistic Heavy Ion Collider (RHIC) on collective expansion flow to the Equation of State (EOS) of hot and dense strongly interacting matter, including the quark-gluon plasma and the quark-hadron phase transition. The limits reached with the present state of the art and the next steps required to make further progress will both be discussed.Comment: 8 pages, 6 two-part figures. Invited talk given at the 5th International Conference on the Physics and Astrophysics of Quark-Gluon Plasma (ICPAQGP 2005), Kolkata (India), Feb 8-12, 2005. Proceedings to be published in Journal of Physics: Conference Series (Jan-E Alam et al., eds.

Relativistic Quantum Transport Theory for Electrodynamics

We investigate the relationship between the covariant and the three-dimensional (equal-time) formulations of quantum kinetic theory. We show that the three-dimensional approach can be obtained as the energy average of the covariant formulation. We illustrate this statement in scalar and spinor QED. For scalar QED we derive Lorentz covariant transport and constraint equations directly from the Klein-Gordon equation rather than through the previously used Feshbach-Villars representation. We then consider pair production in a spatially homogeneous but time-dependent electric field and show that the pair density is derived much more easily via the energy averaging method than in the equal-time representation. Proceeding to spinor QED, we derive the covariant version of the equal-time equation derived by Bialynicki-Birula et al. We show that it must be supplemented by another self-adjoint equation to obtain a complete description of the covariant spinor Wigner operator. After spinor decomposition and energy average we study the classical limit of the resulting three-dimensional kinetic equations. There are only two independent spinor components in this limit, the mass density and the spin density, and we derive also their covariant equations of motion. We then show that the equal-time kinetic equation provides a complete description only for constant external electromagnetic fields, but is in general incomplete. It must be supplemented by additional constraints which we derive explicitly from the covariant formulation.Comment: 32 pages, no figures, standard Late

Photon HBT interferometry for non-central heavy-ion collisions

Currently, the only known way to obtain experimental information about the space-time structure of a heavy-ion collision is through 2-particle momentum correlations. Azimuthally sensitive HBT interferometry (Hanbury Brown-Twiss intensity interferometry) can complement elliptic flow measurements by constraining the spatial deformation of the source and its time evolution. Performing these measurements on photons allows us to access the fireball evolution at earlier times than with hadrons. Using ideal hydrodynamics to model the space-time evolution of the collision fireball, we explore theoretically various aspects of 2-photon intensity interferometry with transverse momenta up to 2 GeV, in particular the azimuthal angle dependence of the HBT radii in non-central collisions. We highlight the dual nature of thermal photon emission, in both central and non-central collisions, resulting from the superposition of QGP and hadron resonance gas photon production. This signature is present in both the thermal photon source function and the HBT radii extracted from Gaussian fits of the 2-photon correlation function.Comment: 18 pages, 12 figure

Evolution of pion HBT radii from RHIC to LHC -- Predictions from ideal hydrodynamics

We present hydrodynamic predictions for the charged pion HBT radii for a range of initial conditions covering those presumably reached in Pb+Pb collisions at the LHC. We study central (b=0) and semi-central (b=7fm) collisions and show the expected increase of the HBT radii and their azimuthal oscillations. The predicted trends in the oscillation amplitudes reflect a change of the final source shape from out-of-plane to in-plane deformation as the initial entropy density is increased.Comment: 6 pages, incl. 5 figures. Contribution to the CERN Theory Institute Workshop "Heavy Ion Collisions at the LHC -- Last Call for Predictions", CERN, 14 May - 8 June 2007, to appear in J. Phys.

Is there elliptic flow without transverse flow?

Azimuthal anisotropy of final particle distributions was originally introduced as a signature of transverse collective flow. We show that finite anisotropy in momentum space can result solely from the shape of the particle emitting source. However, by comparing the differential anisotropy to recent data from STAR collaboration we can exclude such a scenario, but instead show that the data favour strong flow as resulting from a hydrodynamical evolution.Comment: To appear in proceedings of Quark Matter 2001, 4 pages LaTeX, uses espcrc1.st

Fitted HBT radii versus space-time variances in flow-dominated models

The inability of otherwise successful dynamical models to reproduce the ``HBT radii'' extracted from two-particle correlations measured at the Relativistic Heavy Ion Collider (RHIC) is known as the ``RHIC HBT Puzzle.'' Most comparisons between models and experiment exploit the fact that for Gaussian sources the HBT radii agree with certain combinations of the space-time widths of the source which can be directly computed from the emission function, without having to evaluate, at significant expense, the two-particle correlation function. We here study the validity of this approach for realistic emission function models some of which exhibit significant deviations from simple Gaussian behaviour. By Fourier transforming the emission function we compute the 2-particle correlation function and fit it with a Gaussian to partially mimic the procedure used for measured correlation functions. We describe a novel algorithm to perform this Gaussian fit analytically. We find that for realistic hydrodynamic models the HBT radii extracted from this procedure agree better with the data than the values previously extracted from the space-time widths of the emission function. Although serious discrepancies between the calculated and measured HBT radii remain, we show that a more ``apples-to-apples'' comparison of models with data can play an important role in any eventually successful theoretical description of RHIC HBT data.Comment: 12 pages, 16 color figure

A summary and update of developing annuities markets : the experience of Chile

The rapid growth of the market for retirement products in Chile has its origins in the pension reform that was implemented in 1981. But the successful development of an active annuity market also reflects many other factors. This paper summarizes and updates an earlier longer study on the development of the Chilean annuity market. The update focuses on the numerous changes that were introduced in 2008. The most striking aspect of the Chilean experience is the very high rate of annuitization. This has been linked to the restrictions that have been applied to lump-sum withdrawals, the offer of inflation-protected annuities, and the robust prudential regulation of providers. But the level of annuitization has also been supported by the annuitization incentives provided to early retirees and the influence of brokers and sales agents. The recent regulatory changes have weakened the impact of the last two factors, while strengthening the demand for annuities at normal retirement.Debt Markets,Pensions&Retirement Systems,Insurance&Risk Mitigation,Emerging Markets,Non Bank Financial Institutions

Challenges of the mandatory funded pension system in the Russian Federation

The overwhelming number of contributors that have been allocated into the default option is one of the main characteristics of the Russian second pillar. This finding confirms that the level of financial literacy for most of the participants is not sufficient to make informed portfolio selections. The authors argue that the current system is perfectly consistent with a solid second pillar, but the authorities should focus their attention in the strategic asset allocation of pension funds. Since in the short and medium term it is unlikely to see improvements in financial literacy of individuals that may overcome the complexity of these decisions, the authorities can play an important role in designing default investment portfolios that can be aligned with expected replacement rates for the contributors. The current investment regulation of the default option induces investment in inefficient portfolios that are unlikely to bring returns above inflation, and probably will result in very low replacement rates for contributors. Further liberalization of the investments of the pension portfolio; improvements in the governance and supervision of the pension system; and greater certainty about the ownership of the funds are necessary steps to complete the pension reform launched in 2002.Debt Markets,Financial Literacy,Emerging Markets,Pensions&Retirement Systems,Access to Finance

Upgrading investment regulations in second pillar pension systems : a proposal for Colombia

The passivity of the demand for pension products is one of the striking features of mandatory pension systems. Consequently, the provision of multiple investment alternatives to households (multifund schemes) does not ensure that contributions are invested efficiently. In addition, despite the theoretical findings that short term return maximization is not conductive to long-term return maximization, the regulatory framework of pension fund management companies puts excessive emphasis on short-term maximization. Therefore, it is not obvious that typical regulatory framework of pension funds is conductive to optimal pensions. By establishing a set of default options on investment portfolios, this paper proposes a mechanism to align the incentives of the pension fund management companies with the long-term objectives of the contributors. The paper provides a methodology, which is subsequently applied to Colombia.Debt Markets,Emerging Markets,Financial Literacy,Mutual Funds,Investment and Investment Climate

Forecast quality and simple instrument rules: a real-time data approach

We start from the assertion that a useful monetary policy design should be founded on more realistic assumptions about what policymakers can know at the time when policy decisions have to be made. Since the Taylor rule – if used as an operational device - implies a forward looking behaviour, we analyze the reliability of the input information. We investigate the forecasting performance of OECD projections for GDP growth rates and inflation. We diagnose a much better forecasting record for inflation rates compared to GDP growth rates, which for most countries are almost uninformative at the time a Taylor rule should sensibly be applied. Using this data set, we find significant differences between Taylor rules estimated over revised data compared to real-time data. There is evidence that monetary policy seems to react more actively in real time than rules estimated over revised data suggest. Given the evidence of systematic errors in OECD forecasts, in a next step we attempt to correct for these forecast biases and check to which extent this can lower the errors in interest rate policy setting. An ex-ante simulation for the years 1991 to 2001 supports the proposal that correcting for forecast errors and biases based on an error model can lower the resulting policy error in interest rate setting for most countries under consideration. In addition we investigate to what extent structural changes in the policy reaction behaviour can be handled with moving instead of expanding samples. Our results point out that the information set available needs a careful examination when applied to instrument rules like those of the Taylor type. Limited forecast quality and significant data revisions recommend a more sophisticated handling of the dated information, for which we present an operational procedure that has the potential of reducing the risk of severe policy errors. --Monetary policy rules,economic forecasting,OECD,real-time data