Random Lindblad equations from complex environments

In this paper we demonstrate that Lindblad equations characterized by a random rate variable arise after tracing out a complex structured reservoir. Our results follows from a generalization of the Born-Markov approximation, which relies in the possibility of splitting the complex environment in a direct sum of sub-reservoirs, each one being able to induce by itself a Markovian system evolution. Strong non-Markovian effects, which microscopically originate from the entanglement with the different sub-reservoirs, characterize the average system decay dynamics. As an example, we study the anomalous irreversible behavior of a quantum tunneling system described in an effective two level approximation. Stretched exponential and power law decay behaviors arise from the interplay between the dissipative and unitary hopping dynamics.