Quantum kinetics and thermalization in an exactly solvable model - art. no. 025003

We study the dynamics of relaxation and thermalization in an exactly solvab le model of a quantum particle interacting with a thermal bath of oscillato rs with the goal of understanding the effects of off-shell processes. The f ocus is to compare the exact evolution of the distribution function with di fferent approximations to the relaxational dynamics: Boltzmann, non-Markovi an and Markovian quantum kinetics. The time evolution of the distribution f unction is evaluated exactly using different approaches where each method p rovides different insights. There are two different cases that are studied in detail: (i) no stable particle states below threshold of the bath and a quasiparticle resonance above it and (ii) a stable discrete exact "particle " state below threshold. The exact solution for the evolution allows us to investigate the concept of the formation time of a quasiparticle and to stu dy the difference between the relaxation of the distribution of particles a nd quasiparticles. For the case of quasiparticles in the continuum (resonan ces) the exact quasiparticle distribution asymptotically tends to a statist ical equilibrium distribution that differs from a simple Bose-Einstein form as a result of off-shell processes such as the strength of the quasipartic le poles, the width of the unstable particle and proximity to thresholds. I n case (ii), the distribution of particles does not thermalize with the bat h. We study the kinetics of thermalization and relaxation by deriving a non -Markovian quantum kinetic equation which resums the perturbative series an d includes off-shell effects. A Markovian approximation that includes off-s hell contributions and the usual Boltzmann equation are obtained from the q uantum kinetic equation in the limit of a wide separation of time scales up on different coarse-graining assumptions. The relaxational dynamics predict ed by the non-Markovian, Markovian and Boltzmann approximations are compare d to the exact result of the model. The Boltzmann approach is seen to fail in the case of wide resonances and when threshold and renormalization effec ts are important. Implications for thermalization in field theory models ar e discussed. [S0556-2821(98)04724-9].