  A long-standing challenge in mixed quantum-classical trajectory simulations
is the treatment of entanglement between the classical and quantal degrees of
freedom. We present a novel approach which describes the emergence of entangled
states entirely in terms of independent and deterministic Ehrenfest-like
classical trajectories. For a two-level quantum system in a classical
environment, this is derived by mapping the quantum system onto a path-integral
representation of a spin-1/2. We demonstrate that the method correctly accounts
for coherence and decoherence and thus reproduces the splitting of a wavepacket
in a nonadiabatic scattering problem. This discovery opens up a new class of
simulations as an alternative to stochastic surface-hopping, coupled-trajectory
or semiclassical approaches.
