Quantum kinetics and thermalization in a particle bath model

We study the dynamics of relaxation and thermalization in an exactly solvab le model of a particle interacting with a harmonic oscillator bath. Our goa l is to understand the effects of non-Markovian processes on the relaxation al dynamics and to compare the exact evolution of the distribution function with approximate Markovian and non-Markovian quantum kinetics. There are t wo different cases that are studied in detail: (i) a quasiparticle (resonan ce) when the renormalized frequency of the particle is above the frequency threshold of the bath and (ii) a stable renormalized "particle" state below this threshold. The time evolution of the occupation number for the partic le is evaluated exactly using different approaches that yield to complement ary insights. The exact solution allows us to investigate the concept of th e formation time of a quasiparticle and to study the difference between the relaxation of the distribution of bare particles add that of quasiparticle s. For the case of quasiparticles, the exact occupation number asymptotical ly tends to a statistical equilibrium distribution that differs from a simp le Bose-Einstein form as a result of off-shell processes whereas in the sta ble particle case, the distribution of particles does not thermalize with t he bath. We derive a non-Markovian quantum kinetic equation which resums th e perturbative series and includes off-shell effects. A Markovian approxima tion that includes off-shell contributions and the usual Boltzmann equation (energy conserving) are obtained from the quantum kinetic equation in the Limit of wide separation of time scales upon different coarse-graining assu mptions. The relaxational dynamics predicted by the non-Markovian, Markovia n, and Boltzmann approximations are compared to the exact result. The Boltz mann approach is seen to fail in the case of wide resonances and when thres hold and renormalization effects are important. [S1063-651X(99)02107-8].