Real-time gauge theory simulations from stochastic quantization using optimized updating

Stochastic quantisation is applied to the problem of calculating real-time evolution on a Minkowskian space-time lattice. We employ optimized updating using reweighting, or gauge fixing, respectively. These procedures do not affect the underlying theory, but strongly improve the stability properties of the stochastic dynamics.Comment: 4 pages, 3 figures, contributed talk to SEWM 2008, Amsterda

Turbulent spectra in real-time gauge field evolution

We investigate ultraviolet fixed points in the real-time evolution of non-Abelian gauge fields. Classical-statistical lattice simulations reveal equal-time correlation functions with a spectral index 3/2. Analytical understanding of this result is achieved by employing a 2PI- loop expansion for the quantum theory.Comment: 4 pages, 2 figures. Talk presented at SEWM 2008, August 26-29, Amsterda

QCD at high Baryon Density and Temperature: Competing Condensates and the Tricritical Point

The phase diagram of strongly interacting matter is explored as a function of temperature and baryon number density. We investigate the possible simultaneous formation of condensates in the conventional quark--anti-quark channel (breaking chiral symmetry) and in a quark--quark channel leading to color superconductivity: the spontaneous breaking of color symmetry via the formation of quark Cooper pairs. We point out that for two massless quark flavors a tricritical point in the phase diagram separates a chiral symmetry restoring first order transition at high densities from the second order transition at high temperatures. Away from the chiral limit this tricritical point becomes a second order phase transition with Ising model exponents, suggesting that a long correlation length may develop in heavy ion collisions in which the phase transition is traversed at the appropriate density.Comment: Talk given at the Workshop on QCD at Finite Baryon Density: A Complex System with a Complex Action, Bielefeld, Germany, 27-30 Apr 1998; 7 pages; references adde

Introduction to the nonequilibrium functional renormalization group

In these lectures we introduce the functional renormalization group out of equilibrium. While in thermal equilibrium typically a Euclidean formulation is adequate, nonequilibrium properties require real-time descriptions. For quantum systems specified by a given density matrix at initial time, a generating functional for real-time correlation functions can be written down using the Schwinger-Keldysh closed time path. This can be used to construct a nonequilibrium functional renormalization group along similar lines as for Euclidean field theories in thermal equilibrium. Important differences include the absence of a fluctuation-dissipation relation for general out-of-equilibrium situations. The nonequilibrium renormalization group takes on a particularly simple form at a fixed point, where the corresponding scale-invariant system becomes independent of the details of the initial density matrix. We discuss some basic examples, for which we derive a hierarchy of fixed point solutions with increasing complexity from vacuum and thermal equilibrium to nonequilibrium. The latter solutions are then associated to the phenomenon of turbulence in quantum field theory.Comment: Lectures given at the 49th Schladming Winter School `Physics at all scales: The Renormalization Group' (to appear in the proceedings); 24 pages, 3 figure

What the inflaton might tell us about RHIC/LHC

Topical phenomena in high-energy physics related to collision experiments of heavy nuclei ("Little Bang") and early universe cosmology ("Big Bang") involve far-from-equilibrium dynamics described by quantum field theory. One example concerns the role of plasma instabilities for the process of thermalization in heavy-ion collisions. The reheating of the early universe after inflation may exhibit rather similar phenomena following a tachyonic or parametric resonance instability. Certain universal aspects associated to nonthermal fixed points even quantitatively agree, and considering these phenomena from a common perspective can be fruitful.Comment: Plenary talk at SEWM08, 9 pages, 6 figure

Renormalisation of out-of-equilibrium quantum fields

We consider the initial value problem and its renormalisation in the framework of the two-particle-irreducible (2PI) effective action. We argue that in the case of appropriately chosen self-consistent initial conditions, the counterterms needed to renormalise the system in equilibrium are also sufficient to renormalise its time evolution. In this way we improve on Gaussian initial conditions which have the disadvantage of generically not showing a continuum limit. For a more detailed discussion see arXiv:0809.0496.Comment: To appear in the proceedings of SEWM08, Amsterdam, The Netherlands, 26-29 August 200

Isotropization far from equilibrium

Isotropization occurs on time scales much shorter than the thermal equilibration time. This is a crucial ingredient for the understanding of collision experiments of heavy nuclei or other nonequilibrium phenomena in complex many body systems. We discuss in detail the limitations of estimates based on standard ``linear'' or relaxation-time approximations, where isotropization and thermal equilibration rates agree. For a weak-coupling $\phi^4$-model the relaxation-time approximation underestimates the thermal equilibration time by orders of magnitude, in contrast to the isotropization time. The characteristic nonequilibrium isotropization rate can be enhanced as compared to the close-to-equilibrium value. Our results are obtained from the two-particle irreducible effective action, which includes off-shell and memory effects and does not involve a gradient expansion. This allows us to determine the range of validity of a description to lowest-order in gradients, which is typically employed in kinetic equations.Comment: 27 pages, 7 figures, NPB version, minor text change

Ultracold atomic quantum gases far from equilibrium

We calculate the time evolution of a far-from-equilibrium initial state of a non-relativistic ultracold Bose gas in one spatial dimension. The non-perturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory and off-shell effects that are not captured in mean-field theory.Comment: 4 pages, Proc. Int. Conf. Strong and Electroweak Matter, SEWM 2006; Nucl. Phys. A, to be publishe