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Title

Geometric phases in discrete dynamical systems

AuthorsCartwright, Julyan H. E.; Piro, Nicolás; Piro, Oreste ; Tuval, Idan
KeywordsGeometric phase
Superdiffusion
Chaos
Standard map
Circle map
Issue Date24-Oct-2016
PublisherElsevier
CitationPhysics Letters, Section A: General, Atomic and Solid State Physics 380(42): 3485-3489 (2016)
AbstractIn order to study the behaviour of discrete dynamical systems under adiabatic cyclic variations of their parameters, we consider discrete versions of adiabatically-rotated rotators. Parallelling the studies in continuous systems, we generalize the concept of geometric phase to discrete dynamics and investigate its presence in these rotators. For the rotated sine circle map, we demonstrate an analytical relationship between the geometric phase and the rotation number of the system. For the discrete version of the rotated rotator considered by Berry, the rotated standard map, we further explore this connection as well as the role of the geometric phase at the onset of chaos. Further into the chaotic regime, we show that the geometric phase is also related to the diffusive behaviour of the dynamical variables and the Lyapunov exponent.
Publisher version (URL)https://doi.org/10.1016/j.physleta.2016.08.050
URIhttp://hdl.handle.net/10261/152423
DOI10.1016/j.physleta.2016.08.050
Identifiersdoi: 10.1016/j.physleta.2016.08.050
issn: 0375-9601
Appears in Collections:(IMEDEA) Artículos
(IACT) Artículos
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