Exact and Truncated Dynamics in Nonequilibrium Field Theory

Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These truncation schemes can be implemented equally well in a classical statistical system, where results can be tested by comparison with the complete nonlinear evolution obtained by numerical methods. For a 1+1 dimensional scalar field we find that the early-time behaviour is reproduced qualitatively by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the fixed point, the full nonlinear evolution shows thermalization with a (surprisingly) slow relaxation.Comment: 30 pages with 12 eps figures, minor changes; to appear in Phys.Rev.

Integrated sensors for robotic laser welding

A welding head is under development with integrated sensory systems for robotic laser welding applications. Robotic laser welding requires sensory systems that are capable to accurately guide the welding head over a seam in three-dimensional space and provide information about the welding process as well as the quality of the welding result. In this paper the focus is on seam tracking. It is difficult to measure three-dimensional parameters of a ream during a robotic laser welding task, especially when sharp corners are present. The proposed sensory system is capable to provide the three dimensional parameters of a seam in one measurement and guide robots over sharp corners

The Hartree ensemble approximation revisited: The "symmetric phase"

The Hartree ensemble approximation is studied in the ``symmetric phase'' of 1+1 dimensional lambda phi^4 theory. In comparison with the ``broken phase'' studied previously, it is shown that the dynamical evolution of observables such as the particle distribution, energy exchange and auto-correlation functions, is substantially slower. Approximate thermalization is found only for relatively large energy densities and couplings.Comment: 17 pages RevTeX, 16 figures, 3 tables, uses amsmath and feynmp. Extended some sections, reordered Sec.IV, added 3 refs, numerical typo corrected, published versio

Nonequilibrium time evolution of the spectral function in quantum field theory

Transport or kinetic equations are often derived assuming a quasi-particle (on-shell) representation of the spectral function. We investigate this assumption using a three-loop approximation of the 2PI effective action in real time, without a gradient expansion or on-shell approximation. For a scalar field in 1+1 dimensions the nonlinear evolution, including the integration over memory kernels, can be solved numerically. We find that a spectral function approximately described by a nonzero width emerges dynamically. During the nonequilibrium time evolution the Wigner transformed spectral function is slowly varying, even in presence of strong qualitative changes in the effective particle distribution. These results may be used to make further analytical progress towards a quantum Boltzmann equation including off-shell effects and a nonzero width.Comment: 20 pages with 6 eps figures, explanation and references added; to appear in Phys.Rev.

Thermal effects on slow-roll dynamics

A description of the transition from the inflationary epoch to radiation domination requires the understanding of quantum fields out of thermal equilibrium, particle creation and thermalisation. This can be studied from first principles by solving a set of truncated real-time Schwinger-Dyson equations, written in terms of the mean field (inflaton) and the field propagators, derived from the two-particle irreducible effective action. We investigate some aspects of this problem by considering the dynamics of a slow-rolling mean field coupled to a second quantum field, using a \phi^2\chi^2 interaction. We focus on thermal effects. It is found that interactions lead to an earlier end of slow-roll and that the evolution afterwards depends on details of the heatbath.Comment: 25 pages, 11 eps figures. v2: paper reorganized, title changed, conclusions unchanged, to appear in PR

On the Complexity of Local Search for Weighted Standard Set Problems

In this paper, we study the complexity of computing locally optimal solutions for weighted versions of standard set problems such as SetCover, SetPacking, and many more. For our investigation, we use the framework of PLS, as defined in Johnson et al., [JPY88]. We show that for most of these problems, computing a locally optimal solution is already PLS-complete for a simple neighborhood of size one. For the local search versions of weighted SetPacking and SetCover, we derive tight bounds for a simple neighborhood of size two. To the best of our knowledge, these are one of the very few PLS results about local search for weighted standard set problems

The 2PI finite temperature effective potential of the O(N) linear sigma model in 1+1 dimensions, at next-to-leading order in 1/N

We study the O(N) linear sigma model in 1+1 dimensions. We use the 2PI formalism of Cornwall, Jackiw and Tomboulis in order to evaluate the effective potential at finite temperature. At next-to-leading order in a 1/N expansion one has to include the sums over "necklace" and generalized "sunset" diagrams. We find that - in contrast to the Hartree approximation - there is no spontaneous symmetry breaking in this approximation, as to be expected for the exact theory. The effective potential becomes convex throughout for all parameter sets which include N=4,10,100, couplings lambda=0.1 and 0.5, and temperatures between 0.2 and 1. The Green's functions obtained by solving the Schwinger-Dyson equations are enhanced in the infrared region. We also compare the effective potential as function of the external field phi with those obtained in various other approximations.Comment: 19 pages, 9 figures; v2: references added, some changes in the tex

The approach to thermalization in the classical phi^4 theory in 1+1 dimensions: energy cascades and universal scaling

We study the dynamics of thermalization and the approach to equilibrium in the classical phi^4 theory in 1+1 spacetime dimensions. At thermal equilibrium we exploit the equivalence between the classical canonical averages and transfer matrix quantum traces of the anharmonic oscillator to obtain exact results for the temperature dependence of several observables, which provide a set of criteria for thermalization. We find that the Hartree approximation is remarkably accurate in equilibrium. The non-equilibrium dynamics is studied by numerically solving the equations of motion in light-cone coordinates for a broad range of initial conditions and energy densities.The time evolution is described by several stages with a cascade of energy towards the ultraviolet. After a transient stage, the spatio-temporal gradient terms become larger than the nonlinear term and a stage of universal cascade emerges.This cascade starts at a time scale t_0 independent of the initial conditions (except for very low energy density). Here the power spectra feature universal scaling behavior and the front of the cascade k(t) grows as a power law k(t) sim t^alpha with alpha lesssim 0.25. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium (LTE) with all correlations being determined by the equilibrium functional form with an effective time dependent temperatureTeff(t) which slowly decreases as sim t^{-alpha}.Two well separated time scales emerge while Teff(t) varies slowly, the wavectors in the wake with k < k(t) attain LTE on much shorter time scales.This universal scaling stage ends when the front of the cascade reaches the cutoff at a time t_1 sim a^{-1/alpha}. Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale.Comment: relevance for quantum field theory discussed providing validity criteria. To appear in Phys. Rev.