Abstract
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.
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