Estabilidade dinâmica para sistemas quânticos dependentes do tempo
Abstract
We study if a time-dependent system is either dynamically stable or unstable,
i.e., if the expected value of a positive and discrete observable is a bounded
function of time or not. Initially we consider topological properties of the orbits
of the states of the system and how these properties are related to dynamical stability.
In the case of periodic time dependence, we present a formula that allows
one to decide about stability from the behavior of the matrix elements of the resolvent
associated with the Floquet operator. Finally, we give an example of Floquet
operator with purely point spectrum and exponentially decaying eigenfunctions and
dynamical instability.