Abstract
We write in terms of path integrals the effective quantum propagator associated to a quantum particle interacting with a fractional-dimensional reservoir modelled by a scalar and vectorial phonon field in a space-time R v , with v an arbitrary real number. We show, thus, that the classical regime related to this quantum-fractional-dimensional Brownian particle motion is given by the fractional Langevin equation (a fractional time diffusion process). As a consequence, we deduce from first (microscopic) principles fractional-dimensional diffusion phenomena.
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