On thermalization in classical scalar field theory

Thermalization of classical fields is investigated in a phi(4) scalar field theory in I + 1 dimensions, discretized on a lattice. We numerically integ rate the classical equations of motion using initial conditions sampled fro m various nonequilibrium probability distributions. Time-dependent expectat ion values of observables constructed from the canonical momentum are compa red with thermal ones. It is found that a closed system, evolving from one initial condition, thermalizes to high precision in the thermodynamic limit , in a time-averaged sense. For ensembles consisting of many members with t he same energy, we find that expectation values become stationary - and equ al to the thermal values - in the limit of infinitely many members. Initial ensembles with a nonzero (noncanonical) spread in the energy density or ot her conserved quantities evolve to noncanonical stationary ensembles. In th e case of a narrow spread, asymptotic values of primary observables are onl y mildly affected. In contrast, fluctuations and connected correlation func tions will differ substantially from the canonical values. This raises doub ts on the use of a straightforward expansion in terms of 1PI-vertex functio ns to study thermalization. (C) 2000 Elsevier Science B.V. All rights reser ved.