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Multitime correlation functions provide useful probes for the ensembles oftrajectories underlying the stochastic dynamics of complex systems. These canbe obtained by measuring their optical response to sequences of ultrashortoptical pulse. Using the continuous time random walk model for spectraldiffusion, we analyze the signatures of anomalous relaxation in two-dimensionalfour wave mixing signals. Different models which share the same two point jointprobability distribution show markedly different lineshapes and may bedistinguished. Aging random walks corresponding to waiting time distributionswith diverging first moment show dependence of 2D lineshapes on initialobservation time, which persist for long times.

Anomalous Lineshapes and Aging Effects in Two-Dimensional Correlation Spectroscopy