Langevin Interpretation of Kadanoff-Baym Equations.pdf

a r X i v : h e p - p h / 9 9 1 2 2 2 9 v 1 3 D e c 1 9 9 9 LANGEVIN INTERPRETATION OF KADANOFF-BAYM EQUATIONS C. GREINER a, S. LEUPOLD Institut fu?r Theoretische Physik, Universita?t Giessen, D-35392 Giessen, Germany We show that the nonperturbative quantum transport equations, the ‘Kadanoff- Baym equations’, can be be understood as the ensemble average over stochastic equations of Langevin type. For this we couple a free scalar boson quantum field to an environmental heat bath with some given temperature T . The inherent presence of noise and dissipation related by the fluctuation-dissipation theorem guarantees that the modes or particles become thermally populated on average in the long-time limit. This interpretation leads to a more intuitive physical picture of the process of thermalization and of the interpretation of the Kadanoff-Baym equations. 1 Motivation Non-equilibrium many body theory had been traditionally a major topic of research for describing various (quantum) transport phenomena in plasma physics, in condensed matter physics and nuclear physics. Over the last years a lot of interest for non-equilibrium quantum field theory has now emerged also in particle physics. A very powerful diagrammatic tool is given by the ‘Schwinger- Keldysh’ or ‘closed time path’ (CTP) technique by means of non-equilibrium Green’s functions for describing a quantum system also beyond thermal equi- librium. The resulting causal and nonperturbative equations of motion (by various approximations), the so called Kadanoff-Baym (KB) equations, have to be considered as an ensemble average over the initial density matrix charac- terizing the preparation of the initial state of the system. If the system behaves dissipatively, as a consequence of the famous fluctuation-dissipation theorem, there must exist fluctuations. The Kadanoff-Baym equations have then to be understood as an ensemble average over all the possible fluctuations. This in- herent stochastic aspect of the KB e