Non-adiabatic dynamics in mixed quantum-classical systems

Non-adiabatic dynamics in mixed quantum-classical systems is investigated. The mixed quantum-classical system comprises a quantum system coupled to a classical environment. The starting point for the analysis is an evolution equation for the density matrix expressed in a basis of adiabatic quantum states that describes the full quantum dynamics of the subsystem and its coupling to the bath. Since the quantum dynamics influences the evolution of the "classical" degrees of freedom, a description in terms of single Newtonian trajectories is not possible. Through explicit calculations of a two-level quantum system coupled to a low dimensional bath we examine the details of mixed quantum-classical dynamics and its representation in terms of an ensemble of surface-hopping classical trajectory segments.