Quantum diffusion with drift and the Einstein relation. II (Q2879379)

The long-time diffusion and drift of a driven quantum particle coupled to an array of thermal reservoirs, that are described quantum-mechanically, are investigated. A positive temperature \(T\) is the same for all the reservoirs and reservoirs at different sites are independent of each other.NEWLINENEWLINEThe main physical results were given in Part I [ibid. 55, No. 7, 075206, 34 p. (2014; Zbl 1305.82051)]. In the present paper, the authors analyze some more detailed mathematical aspects: an asymptotic perturbation theory for small driving force, the construction of time-dependent correlation functions of particle observables, and to determine asymptotic properties of the motion of the particle, when time \(t\) tends to \(\infty\).NEWLINENEWLINEThe Dyson expansion of the propagator describing the time-evolution of mixed states of the system is derived and the Dyson expansions are represented in the form of ``polymer expansions''. The time Laplace transform of the effective particle dynamics is obtained as well as the Einstein relation. Some results have already been proven in [loc. cit.].