Random variable approach to dissipative spin dynamics and Landau-Zener transitions

We present a random variable approach to solve for the dynamics of a dissipative two-state system. Based on an exact functional integral description, our method reformulates the problem as that of non-unitary time evolution of a quantum state vector under a Hamiltonian containing random noise fields. This non-perturbative formalism goes beyond the frequently used Non-Interacting Blip Approximation (NIBA) and is particularly well suited to treat an explicitly time-dependent Hamiltonian. As an example, we consider the renowned Landau-Zener problem in the presence of an Ohmic bath with a large bath cutoff frequency $\omega_c$. We identify an intermediate time regime where the energy separation of the two spin states is much larger than their tunneling coupling $\Delta$, but still smaller than $\omega_c$ such that bath mediated spin transitions still occur. Such a situation can for example be realized with a cold atomic quantum dot setup. We also derive an approximate analytical expression for the decay of the upper spin state population in this regime, which agrees well with our numerical results.