Artículo
Incommensurate standard map
Fecha de publicación:
01/2019
Editorial:
American Physical Society
Revista:
Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics
ISSN:
2470-0053
e-ISSN:
2470-0045
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
We introduce and study the extension of the Chirikov standard map when the kick potential has two and three incommensurate spatial harmonics. This system is called the incommensurate standard map. At small kick amplitudes, the dynamics is bounded by the isolating Kolmogorov-Arnold-Moser surfaces, whereas above a certain kick strength, it becomes unbounded and diffusive. The quantum evolution at small quantum kick amplitudes is somewhat similar to the case of the Aubru-André model studied in mathematics and experiments with cold atoms in a static incommensurate potential. We show that for the quantum map there is also a metalinsulator transition in space whereas in momentum we have localization similar to the case of two-dimensional Anderson localization. In the case of three incommensurate frequencies of the space potential, the quantum evolution is characterized by the Anderson transition similar to the three-dimensional case of the disordered potential. We discuss possible physical systems with such a map description including dynamics of comets and dark matter in planetary systems.
Palabras clave:
quantum chaos
,
chaos
,
dynamical systems
,
standard map
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Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Ermann, Leonardo; Shepelyansky, Dima L.; Incommensurate standard map; American Physical Society; Physical Review E: Statistical Physics, Plasmas, Fluids and Related Interdisciplinary Topics; 99; 1; 1-2019; 12215-12224
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