  We revisit the fidelity as a measure for the stability and the complexity of
the quantum motion of single and many-body systems. Within the context of cold
atoms, we present on overview of applications of two fidelities which we call
static and dynamical fidelity, respectively. The static fidelity applies to
quantum problems which can be diagonalized since it is defined via the
eigenfunctions. In particular, we show that the static fidelity is a highly
effective practical detector of avoided crossings characterizing the complexity
of the systems and their evolutions. The dynamical fidelity is defined via the
time-dependent wave functions. Focussing on the quantum kicked rotor system, we
highlight a few practical applications of fidelity measurements in order to
better understand the large variety of dynamical regimes of this paradigm of a
low-dimensional system with mixed regular-chaotic phase space.
