2,366 research outputs found

### Quantum Fields far from Equilibrium and Thermalization

I review the use of the 2PI effective action in nonequilibrium quantum field
theory. The approach enables one to find approximation schemes which circumvent
long-standing problems of non-thermal or secular (unbounded) late-time
evolutions encountered in standard loop or 1/N expansions of the 1PI effective
action. It is shown that late-time thermalization can be described from a
numerical solution of the three-loop 2PI effective action for a scalar
$\phi^4$--theory in 1+1 dimensions (with Jurgen Cox, hep-ph/0006160).
Quantitative results far from equilibrium beyond the weak coupling expansion
can be obtained from the 1/N expansion of the 2PI effective action at
next-to-leading order (NLO), calculated for a scalar O(N) symmetric quantum
field theory (hep-ph/0105311). Extending recent calculations in classical field
theory by Aarts et al. (hep-ph/0007357) and by Blagoev et al. (hep-ph/0106195)
to $N>1$ we show that the NLO approximation converges to exact (MC) results
already for moderate values of $N$ (with Gert Aarts, hep-ph/0107129). I comment
on characteristic time scales in scalar quantum field theory and the
applicability of classical field theory for sufficiently high initial
occupation numbers.Comment: 12 pages, 5 figures, invited talk at the 6th Workshop on
Non-Perturbative QCD, Paris, 5-9 June 2001 (to appear in the Proceedings

### Progress in Nonequilibrium Quantum Field Theory

We review recent developments for the description of far-from-equilibrium
dynamics of quantum fields and subsequent thermalization.Comment: To appear in the proceedings of Strong and Electroweak Matter (SEWM
2002), Heidelberg, Germany, 2-5 Oct 2002, 16 pages, 11 figure

### Renormalized thermodynamics from the 2PI effective action

High-temperature resummed perturbation theory is plagued by poor convergence
properties. The problem appears for theories with bosonic field content such as
QCD, QED or scalar theories. We calculate the pressure as well as other
thermodynamic quantities at high temperature for a scalar one-component field
theory, solving a three-loop 2PI effective action numerically without further
approximations. We present a detailed comparison with the two-loop
approximation. One observes a strongly improved convergence behavior as
compared to perturbative approaches. The renormalization employed in this work
extends previous prescriptions, and is sufficient to determine all counterterms
required for the theory in the symmetric as well as the spontaneously broken
phase.Comment: 20 pages, 7 figures; PRD version, references added, very minor
change

### Parametric resonance in quantum field theory

We present the first study of parametric resonance in quantum field theory
from a complete next-to-leading order calculation in a 1/N-expansion of the 2PI
effective action, which includes scattering and memory effects. We present a
complete numerical solution for an O(N)-symmetric scalar theory and provide an
approximate analytic description of the nonlinear dynamics in the entire
amplification range. We find that the classical resonant amplification at early
times is followed by a collective amplification regime with explosive particle
production in a broad momentum range, which is not accessible in a
leading-order calculation.Comment: 4 pages, 5 figures, version to appear in Phys. Rev. Lett., results
unchange

### Nonequilibrium quantum fields from first principles

Calculations of nonequilibrium processes become increasingly feasable in
quantum field theory from first principles. There has been important progress
in our analytical understanding based on 2PI generating functionals. In
addition, for the first time direct lattice simulations based on stochastic
quantization techniques have been achieved. The quantitative descriptions of
characteristic far-from-equilibrium time scales and thermal equilibration in
quantum field theory point out new phenomena such as prethermalization. They
determine the range of validity of standard transport or semi-classical
approaches, on which most of our ideas about nonequilibrium dynamics were based
so far. These are crucial ingredients to understand important topical phenomena
in high-energy physics related to collision experiments of heavy nuclei, early
universe cosmology and complex many-body systems.Comment: 10 pages, 5 figures, Acta Phys. Hung. version, minor change

### 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

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