Bounds to unitary evolution

Abstract

Upper and lower bounds are established for the survival probability $|<\psi (0)|\psi (t)>{|}^2$ of a quantum state, in terms of the energy moments $<\psi (0)|H^n|\psi (0)>$. Introducing a cut-off in the energy generally enables considerable improvement in these bounds and allows the method to be used where the exact energy moments do not exist.

5 pages, 8 figures