  We introduce a random variable approach to investigate the dynamics of a
dissipative two-state system. Based on an exact functional integral
description, our method reformulates the problem as that of the time evolution
of a quantum state vector subject to a Hamiltonian containing random noise
fields. This numerically exact, non-perturbative formalism is particularly well
suited in the context of time-dependent Hamiltonians, both at zero and finite
temperature. As an important example, we consider the renowned Landau-Zener
problem in the presence of an Ohmic environment with a large cutoff frequency
at finite temperature. We investigate the 'scaling' limit of the problem at
intermediate times, where the decay of the upper spin state population is
universal. Such a dissipative situation may be implemented using a cold-atom
bosonic setup.
