Non-Markovian behavior of small and large complex quantum systems

Abstract

The channel induced by a complex system interacting strongly with a qubit is calculated exactly under the assumption of randomness of its eigenvectors. The resulting channel is represented as an isotropic time dependent oscillation of the Bloch ball, leading to non-Markovian behavior, even in the limit of infinite environments. Two contributions are identified: one due to the density of states and the other due to correlations in the spectrum. Prototype examples, one for chaotic and the other for regular dynamics are explored.

7 pages, 4 figures. Version 2 is closer to what was published. In particular, a typo in Eq. (8) and in Wg([2^2]) at ref 11 were fixed. Other very minor corrections were done as well