Analysis of adiabatic trapping for quasi-integrable area-preserving maps.
Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinear resonances and slow time variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These laws can be particularly relevant for physical applications. The outcome of extensive numerical simulations showing the excellent agreement with the analytical estimates and scaling laws is presented and discussed in detail.
Physics and Astronomy Department, Bologna University, V. Irnerio 46, Bologna, Italy.
Armando
A
Bazzani
Department of Physics and Department of Mathematics, University of Central Florida, Orlando, Florida, USA and Beams Department, CERN, 1211 Geneva 23, Switzerland.
Christopher
C
Frye
Beams Department, CERN, 1211 Geneva 23, Switzerland.
Massimo
M
Giovannozzi
Beams Department, CERN, 1211 Geneva 23, Switzerland and EPFL, LPAP, 1015 Lausanne, Switzerland.
Cédric
C
Hernalsteens