Two-Level System with a Noisy Hamiltonian

We study the dynamical properties of a two-level system in interaction with its environment, whose action on the system is modeled by means of a noise term in the Hamiltonian. We solve the Schrödinger equation, obtain an evolution equation of the Lindblad type for the noise average of the density matrix, and discuss the results in terms of a “decoherence parameter.” Finally, we concentrate our attention on the possibility of hindering the transitions between the two levels in two (apparently unrelated) ways: (a) by increasing the strength of the noise; (b) by a series of frequent measurements. There is an interesting relation between these two situations.