2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/83284Stochastic processes are shown to emerge from the time evolution of complex quantum systems. Using parametric, banded random matrix ensembles to describe a quantum chaotic environment, we show that the dynamical evolution of a particle coupled to such environments displays a variety of stochastic behaviors, ranging from turbulent diffusion to Lévy processes and Brownian motion. Dissipation and diffusion emerge naturally in the stochastic interpretation of the dynamics. This approach provides a derivation of a fractional kinetic theory in the classical limit and leads to classical Lévy dynamics.7 pages, Elsevier style file espcrc2.styNuclear TheoryCondensed MatterQuantum Physicstext