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Exotic Stochastic Processes from Complex Quantum Environments

Dimitri Kusnezov·Aurel Bulgac·Giu Do Dang
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Abstract

Stochastic 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.

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Dimitri Kusnezov, Aurel Bulgac, Giu Do Dang. 1999-11-20. Exotic Stochastic Processes from Complex Quantum Environments. https://arxiv.org/abs/nucl-th/9911069

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