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This research was funded by Lublin University of Technology, grant numbers FN-17,
FD-20/IT-3/011 and FD-20/IT-3/030. The APC was funded by Lublin University of Technology.
In this work, a new method for constructing the infinite-dimensional Ornstein–Uhlenbeck
stochastic process is introduced. The constructed process is used to perturb the harmonic system in
order to model anomalously fast heat transport in one-dimensional nanomaterials. The introduced
method made it possible to obtain a transition probability function that allows for a different approach
to the analysis of equations with such a disturbance. This creates the opportunity to relax assumptions
about temporal correlations for such a process, which may lead to a qualitatively different model of
energy transport through vibrations of the crystal lattice and, as a result, to obtain the superdiffusion
equation on a macroscopic scale with an order of the fractional Laplacian different from the value
of 3/4 obtained so far in stochastic models. Simulations confirming these predictions are presented
and discussed.
