Matching perturbative and non-perturbative descriptions of the reorganization energy

We revisit an old concept of reorganization energy that appears in Marcus theory and, more recently, in the flux qubit tunneling experiments. Reorganization energy can be observed in the initial-state-dependent shift of the tunneling rate peak from the zero-bias point of the flux qubit. Taking advantage of the various open system methods developed for quantitative prediction of the general evolution of flux qubits in quantum annealing, we investigate the specific setting of the tunneling experiment. We find that both perturbative and non-perturbative methods demonstrate a shift in the tunneling rate peak. Rigorous ranges of validity of those methods allow us to observe with controlled numerical precision the crossover between the Lorenzian and the Gaussian shapes of the peak, as well as the adjustments on the value of the shift. The ranges of validity overlap only for a special case of the bath, but the qualitative insights we draw are applicable for the realistic bath as well.