We investigate the relaxation of multilevel systems under the influence of stochastic fields with finite correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$. First, we study a system with spin S=1/2 in a static magnetic field in the presence of dichotomic perturbations. The spectra of the components of the averaged spin vector S\ifmmode\bar\else\textasciimacron\fi{} are evaluated exactly by resorting to the memory-function approach. The model is then extended to include the influence on the relaxation of S\ifmmode\bar\else\textasciimacron\fi{} of a different species with spin I=1/2. The relaxation rates
T1 and
T2 are given in terms of cumulant expansions and compared with the exact results. Fourth-order calculations recover the inequality
T2/2
T1\ensuremath{\le}1 for correlated noise fields. Furthermore, it is found that
T1 can be defined also for long ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$.
T1 is longer than ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$ provided that ${\mathit{r}}^{(\mathrm{est})}$1, where
r(est) is the squared ratio between the total amplitude of the fluctuating fields and the largest one between the Larmor frequency and 1/${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$. It is also found that 2
r(est) is an upper bound of the relative error between the exact and the second-order cumulant expansion of
T1. Generalizations on systems with S=1/2, I>1/2, and arbitrary kinds of noise are discussed.
The nonlinear response to external disturbances of a system of interest scrA (the ``atom'') in contact with a thermal bath is studied. The central issue is the relationship between the nonlinear susceptibility and the equilibrium relaxation spectra of observables of scrA. Paralleling the results of the linear-response theory, the nth-order nonlinear susceptibility is factorized by quantum-mechanical arguments into two terms pertaining to the disturbances and the spin-bath system, respectively. The role of slow atom states, i.e., states relaxing on times T longer than the bath correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$, is pointed out, by recurring to recent findings on their general features [Phys. Rev. A 46, 6222 (1992)]. In the frame of a stochastic picture of the bath and a multilevel scheme of the system scrA, the conditions under which the nonlinear susceptibility provides the spectrum of the slow atom states are clarified. Illustrations are drawn from magnetic resonance to demonstrate that techniques based on the nonlinear response of a spin system to multiple continuous waves compete favorably with pulsed techniques to provide information on longitudinal spin relaxation.