A critique of the two level approximation

Abstract

The conditions in favor and necessity of a realistic multileveled description of a decohering quantum system is examined. Under these conditions approximate techniques to simplify a multileveled system by its first two levels is unreliable and a realistic multilevel description in the formulation of decoherence is unavoidable. In this regard, the first crucial observation is that, the validity of the two level approximation of a multileveled system is not controlled purely by sufficiently low temperatures. That the type of system-environment coupling and the environmental spectrum have a dominant role over the temperature is demonstrated. Particularly, zero temperature quantum fluctuations induced by the Caldeira-Leggett type linear coordinate coupling can be influential in a wide energy range in the systems allowed transitions. The second crucial observation is that the decoherence times being among the system's short time scales are found to be dominated not by the resonant but non-resonant processes. © 2006 Springer Science+Business Media, Inc.