Nonequilibrium quantum anharmonic oscillator and scalar field: high temperature approximations

We treat a relativistic quantum boson gas, described by a scalar quantum field, with quartic self-interaction (Φ4) in three spatial dimensions: we review the known equilibrium case and present new proposals off-equilibrium. For high temperature and large spatial scales, the behaviour of the gas at equilibrium simplifies nonperturbatively (equilibrium dimensional reduction or EDR): its thermodynamics is described by classical statistical mechanics with some quantum field effects. By assumption, the initial state of the gas off-equilibrium includes interactions and inhomogeneities and is not far from thermal equilibrium. We employ real-time generating functionals and obtain the free nonequilibrium correlators at non-zero temperature. The nonequilibrium quantum gas appears to simplify nonperturbatively in the regime of high temperature and large temporal and spatial scales (nonequilibrium dimensional reduction or NEDR), its dynamics being described by classical statistical mechanics with some quantum field effects. We outline the renormalization of the Φ4 theory, the nonequilibrium statistical mechanics of a quantum anharmonic oscillator and the high temperature simplifications, all of which provide very useful hints for NEDR in the field case. Our main proposals are NEDR and the associated new (renormalized) real-time nonequilibrium generating functionals for the Φ4 theory. (Abstract Copyright [2009], Wiley Periodicals, Inc.)