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5, 1, 2) single runs were selected by the requirement that the system stayed in the metastable vacuum up to the time 106 . 4 demonstrates that not only the equilibrium positions but also the fluctuations of the OP are governed by the static effective potential. Similar measurements, performed on 100 × 100 lattices showed no finite size effects in the stable regime, h > 0. The error of f (Φ) 47 CHAPTER 3. 3 The force f (Φ) as the function of the order parameter on 40 × 40 lattices with T = 1/30 and 1/3.

The crossover therefore is located at the autocorrelation time scale of the noise. A qualitative interpretation of the oscillatory IR regime can be based on the observed small amplitude beating phenomenon in the OP trajectory. 1, which persists further also on the right side. 55) due to this regularity. This feature is relevant to the value of η(bt ), responsible for the decay of all kinds of fluctuations. The appareance of peaks in η(bt ) at both the maximal destructive and constructive interferences can be modeled semi-quantitatively by identifying the beating part of the OP-motion ReδΦ = ReδΦ0 exp(iωt) with the stationary solution of a single weakly damped driven har¨ + η δΦ ˙ + ω 2 δΦ = f0 exp(iωt).

CLASSICAL KINETIC THEORY OF LANDAU DAMPING that the combined kinetic plus field theory is equivalent to the effective theory for the modes with k0 ≪ Λ < M, that is its validity goes beyond the Hard Thermal Loop approximation. 40) where v = (1, p/p0 ). Then by looking at Eq. 13) one sees that f1 (k, p) the deviation from equilibrium of the one particle distribution function is given by the equation φ¯ df0 (p0 ) f1 (k, p) = − W (k, v) . 41) The non-local part of ∆(1) (k, p) from Eq. 34)is given by the equation λ d˜ n(|p0 |) ∆(1) (k, p) = − φ¯ W (k, v) 2πδ(p2 − M02 ) .

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