The approach to thermalization in the classical Φ⁴ theory

by Hector De Vega (LPTHE, Paris)

Thursday 16 Oct 2003, 14:00 → 15:00 Europe/Zurich

TH Auditorium (CERN)

We study the dynamics of thermalization and the approach to equilibrium in the classical Φ⁴ theory. That is, we study whether and how thermal equilibrium is reached in a scalar field theory and what is the mechanism that leads to thermalization. We find that the long time evolution is characterized by a cascade of energy towards the ultra-violet. Such a cascade exhibits features independent of the initial conditions. The front of the cascade \\overline{k} moves to the ultra-violet as a power law \\overline{k} ~ t ^α with α \\simeq 0.25 in 1+1 space-time dimensions. The wake behind the cascade is described as a state of Local Thermodynamic Equilibrium (LTE) at an effective time-dependent temperature T_eff (t), which slowly decreases with time as ~ t -^α. Two well-separated time scales emerge: while T_eff (t) varies slowly, the wavectors in the wake with k < \\overline{k} attain LTE on much shorter time scales. Virialization starts to set much earlier than LTE. We find that strict thermalization is achieved only for an infinite time scale in classical theory. The relevance of these results for quantum field theory with large occupation numbers is stressed as well as applications to the early universe cosmology and to the formation of the quark-gluon plasma.