  Using a generalized energy-conserving transition probability, it is shown how
nonadiabatic calculations, within the Wigner-Heisenberg representation of
quantum mechanics, can be reliably extended to far longer times than those
allowed by a primitive sampling scheme. Tackling the spin-boson model as a
paradigmatic example, substantial numerical evidence is provided that effective
integration of the dynamics can be achieved for a wide range of temperatures
and friction.
