Regular and chaotic motion of coupled rotators

Mario Feingold; Asher Peres

doi:10.1016/0167-2789(83)90282-8

Regular and chaotic motion of coupled rotators

Mario Feingold, Asher Peres

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43 Scopus citations

Abstract

We consider a classical Hamiltonian H = L_z+M_z+L_xM_x, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L² and M². By studying Poincaré surfaces of section, we find that the motion is regular when L² or M² is very small or very large. It is chaotic when both L² and M² have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.

Original language	English
Pages (from-to)	433-438
Number of pages	6
Journal	Physica D: Nonlinear Phenomena
Volume	9
Issue number	3
DOIs	https://doi.org/10.1016/0167-2789(83)90282-8
State	Published - 1 Jan 1983
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(83)90282-8

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title = "Regular and chaotic motion of coupled rotators",

abstract = "We consider a classical Hamiltonian H = Lz+Mz+LxMx, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L2 and M2. By studying Poincar{\'e} surfaces of section, we find that the motion is regular when L2 or M2 is very small or very large. It is chaotic when both L2 and M 2 have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.",

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AB - We consider a classical Hamiltonian H = Lz+Mz+LxMx, where the components of L and M satisfy Poisson brackets similar to those of angular momenta. There are three constants of motion: H, L2 and M2. By studying Poincaré surfaces of section, we find that the motion is regular when L2 or M2 is very small or very large. It is chaotic when both L2 and M 2 have intermediate values. The interest of this model lies in its quantization, which involves finite matrices only.

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Regular and chaotic motion of coupled rotators

Abstract

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