  Anomalous-diffusion, the departure of the spreading dynamics of diffusing
particles from the traditional law of Brownian-motion, is a signature feature
of a large number of complex soft-matter and biological systems.
Anomalous-diffusion emerges due to a variety of physical mechanisms, e.g.,
trapping interactions or the viscoelasticity of the environment. However,
sometimes systems dynamics are erroneously claimed to be anomalous, despite the
fact that the true motion is Brownian -- or vice versa. This ambiguity in
establishing whether the dynamics as normal or anomalous can have far-reaching
consequences, e.g., in predictions for reaction- or relaxation-laws.
Demonstrating that a system exhibits normal- or anomalous-diffusion is highly
desirable for a vast host of applications. Here, we present a criterion for
anomalous-diffusion based on the method of power-spectral analysis of single
trajectories. The robustness of this criterion is studied for trajectories of
fractional-Brownian-motion, a ubiquitous stochastic process for the description
of anomalous-diffusion, in the presence of two types of measurement errors. In
particular, we find that our criterion is very robust for subdiffusion. Various
tests on surrogate data in absence or presence of additional positional noise
demonstrate the efficacy of this method in practical contexts. Finally, we
provide a proof-of-concept based on diverse experiments exhibiting both normal
and anomalous-diffusion.
