Energy dissipation in Hamiltonian chains of rotators

We discuss, in the context of energy flow in high-dimensional systems and Kolmogorov-Arnol'd-Moser (KAM) theory, the behavior of a chain of rotators (rotors) which is purely Hamiltonian, apart from dissipation at just one end. We derive bounds on the dissipation rate which become arbitrarily sm...

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Bibliographic Details
Published in:Nonlinearity 2017-11, Vol.30 (11), p.R81-R117
Main Authors: Cuneo, Noé, Eckmann, Jean-Pierre, Wayne, C Eugene
Format: Article
Language:English
Subjects:
dissipation
Hamiltonian
Kolmogorov-Arnol'd-Moser
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Summary:We discuss, in the context of energy flow in high-dimensional systems and Kolmogorov-Arnol'd-Moser (KAM) theory, the behavior of a chain of rotators (rotors) which is purely Hamiltonian, apart from dissipation at just one end. We derive bounds on the dissipation rate which become arbitrarily small in certain physical regimes, and we present numerical evidence that these bounds are sharp. We relate this to the decoupling of non-resonant terms as is known in KAM problems.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aa85d6