  The kinetics of relaxation in quantum systems induced by anomalous
fluctuating noise is studied in detail. In this study two processes are
considered, as examples: (1) relaxation in two-level system caused by external
noise with slowly decaying correlation function P (t) ~ (wt)^{-alpha}, where 0
< alpha < 1, and (2) anomalous-diffusion controlled radical pair recombination
in which relaxation results from the reaction with slowly fluctuating reaction
rate whose fluctuations are governed by subdiffusive relative motion of
radicals in a potential well. Analysis of these two processes is made within
continuous time random walk approach (CTRWA). Rigorous CTRWA-treatment of the
processes under study results in the non-Markovian stochastic Liouville
equation (SLE) for the density matrix of the systems. This SLE predicts
important specific features of relaxation kinetics of quantum systems in the
presence of the above mentioned anomalous noise.
