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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{JSFU_2010_3_3_a9,
     author = {Alexander I. Malyshev and Larisa A. Chizhova},
     title = {Classical and quantum-mechanical description of the {Arnol'd} {Diffusion} in a~system with~2.5 degrees of freedom},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {357--368},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a9/}
}
TY  - JOUR
AU  - Alexander I. Malyshev
AU  - Larisa A. Chizhova
TI  - Classical and quantum-mechanical description of the Arnol'd Diffusion in a~system with~2.5 degrees of freedom
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2010
SP  - 357
EP  - 368
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a9/
LA  - en
ID  - JSFU_2010_3_3_a9
ER  - 
%0 Journal Article
%A Alexander I. Malyshev
%A Larisa A. Chizhova
%T Classical and quantum-mechanical description of the Arnol'd Diffusion in a~system with~2.5 degrees of freedom
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2010
%P 357-368
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a9/
%G en
%F JSFU_2010_3_3_a9
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/