  We propose to study the origin of algebraic decay of two-point correlation
functions observed in glasses, proteins, and quantum dots by their nonlinear
response to sequences of ultrafast laser pulses. Power-law spectral
singularities and temporal relaxation in two-dimensional correlation
spectroscopy (2DCS) signals are predicted for a continuous time random walk
model of stochastic spectral jumps in a two level system with a power-law
distribution of waiting times $\psi (t)\sim t^{-\alpha -1}$. Spectroscopic
signatures of stationary ensembles for $1<\alpha <2$ and aging effects in
nonstationary ensembles with $0<\alpha <1$ are identified.
