  New exact formulas are derived for systems involving Landau-Zener transition
rates and for absorption spectra in quantum dots. These rectify previous
inaccurate approximations utilized in experimental studies. The exact formulas
give an explicit expression for the maxima and minima of the transition rate at
any oscillating period and reveal a number of striking physical consequences,
such as the suppression of oscillations for half-integer values of the detuning
parameter and that the periodic dependence on the detuning parameter changes at
special values of the driving field amplitude. The fluorescence spectra of
quantum dots exhibit similar properties.
