# Quantum L\\'evy Processes and Fractional Kinetics

Source: [Quantum L\\'evy Processes and Fractional Kinetics](<https://www.sota2.com/research/paper/68fa24bc2c2a3760193a8303>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:28:42.846Z

Authors: Dimitri Kusnezov, Aurel Bulgac, Giu Do Dang

Published: 1999-01-04T14:46:02.000Z

## Abstract

Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We find that the reduced density matrix can display dynamics given by L\\'evy stable laws. The classical limit of these dynamics can be related to fractional kinetic equations. In particular we derive a fractional extension of Kramers equation.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/chao-dyn/9901002>)

[PDF](<https://arxiv.org/pdf/chao-dyn/9901002.pdf>)