Universality in dissipative Landau-Zener transitions

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, nonperturbative formalism is particularly well suited in the context of time-dependent Hamiltonians, at both 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.