Classical-quantum localization in one dimensional systems: The kicked rotor

Hamilton, Cian; Pérez-Ríos, Jesús

doi:10.1063/5.0084028

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Classical-quantum localization in one dimensional systems: The kicked rotor

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Hamilton, Cian
Molecular Physics, Fritz Haber Institute, Max Planck Society;

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Pérez-Ríos, Jesús
Molecular Physics, Fritz Haber Institute, Max Planck Society;
Department of Physics and Astronomy, Stony Brook University;

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Hamilton, C., & Pérez-Ríos, J. (2022). Classical-quantum localization in one dimensional systems: The kicked rotor. AIP Advances, 12(3): 035040. doi:10.1063/5.0084028.

Cite as: https://hdl.handle.net/21.11116/0000-000A-55B4-B

Abstract

This work explores the origin of dynamical localization in one-dimensional systems using the kicked rotor as an example. In particular, we propose the fractal dimension of the phase space as a robust indicator to characterize the onset of classical chaos. As a result, we find that the system crosses the stability border when the fractal dimension ≥1.81, and we obtain a functional form for the fractal dimension as a function of the kick strength. At the same time, dynamical localization is explored in the quantum realm by looking into the energy–localization relationship across the classical stability border, thus finding a correlation between the classical chaos and the presence of dynamical localization.