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Immense delocalization from fractional kinetics.

A Iomin¹, G M Zaslavsky

¹Department of Physics, Technion, Haifa 32000, Israel.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|April 24, 2002

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We found immense particle delocalization in a kicked Harper model at a specific control parameter value. This phenomenon arises from a unique classical phase space topology featuring hierarchical sticky islands.

Area of Science:

Quantum chaos
Statistical mechanics
Dynamical systems

Background:

The kicked Harper model is a paradigmatic system for studying quantum chaos.
Understanding particle delocalization is crucial for predicting system behavior.

Purpose of the Study:

To investigate the phenomenon of immense particle delocalization in the kicked Harper model.
To identify the underlying mechanisms and conditions leading to this delocalization.

Main Methods:

Numerical simulations of the kicked Harper model.
Analysis of phase space topology in the classical limit.

Main Results:

Observed immense delocalization (order of 10^9) at a specific control parameter K*=6.349 972.

Related Experiment Videos

Identified a "magic" value of K* corresponding to a hierarchical, self-similar set of sticky islands in the classical phase space.

Conclusions:

The observed immense delocalization is linked to a special phase space topology.
The origin of this effect is general and applicable to other dynamical systems.