Geodesic
Classical and quantum-mechanical description of the Arnol'd Diffusion in a~system with~2.5 degrees of freedom
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 357-368.

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We study a universal phenomenon of nonlinear dynamics – the Arnol'd Diffusion – in a model system with 2.5 degrees of freedom. In the model an influence of three main resonances which take place in a phase space of the system is considered. The results obtained during classical and quantum-mechanical observation are compared. It was shown that a dependence of a rate of the quantum Arnol'd diffusion on parameters of the model behave alike classical one, however a value of the diffusion rate using methods of quantum mechanics lesser then that in classical case approximately at one of the order. It was found that presence of a threshold by the perturbation parameters is not necessarily feature of the Arnol'd diffusion. Also it was shown that there can occur a hybrid process in the quantum system in weak chaotic regime what doesn't have classical analogue – diffusion along resonance plus oscillations across overlapped resonances.
Keywords: nonlinear resonance, quantum chaos.
Mots-clés : Arnol'd diffusion 
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Alexander I. Malyshev; Larisa A. Chizhova. Classical and quantum-mechanical description of the Arnol'd Diffusion in a~system with~2.5 degrees of freedom. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 357-368. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a9/

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