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

Craig S. Hamilton | Zendy; Jesús PérezRíos | Zendy

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

Author(s) -

Craig S. Hamilton,

Jesús PérezRíos

Publication year - 2022

Publication title -

aip advances

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.421

H-Index - 58

ISSN - 2158-3226

DOI - 10.1063/5.0084028

Subject(s) - phase space , quantum chaos , fractal , fractal dimension , quantum , statistical physics , physics , anderson localization , classical mechanics , dimension (graph theory) , quantum system , work (physics) , dynamical systems theory , stability (learning theory) , space (punctuation) , standard map , mathematical analysis , mathematics , quantum mechanics , quantum dynamics , chaotic , computer science , pure mathematics , artificial intelligence , machine learning , operating system

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 [Formula: see text], 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.

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