Exotic Stochastic Processes from Complex Quantum Environments

Details Exotic Stochastic Processes from Complex Quantum Environments Exotic Stochastic Processes from Complex Quantum Environments

1999-11-20

arxiv.org/abs/nucl-th/9911069v1

Physics E9, 436-442 (2001)

Physics

Nuclear Physics

Nuclear Theory

7 pages, Elsevier style file espcrc2.sty

Scientific paper

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 L\'evy 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 L\'evy dynamics.

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