Geometric phases in discrete dynamical systems

In 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. (C) 2016 Elsevier B.V. All rights reserved.


Published in:
Physics Letters A, 380, 42, 3485-3489
Year:
2016
Publisher:
Amsterdam, Elsevier Science Bv
ISSN:
0375-9601
Keywords:
Laboratories:




 Record created 2016-11-21, last modified 2018-09-13


Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)