Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps |
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Authors: | L G Moyano A P Majtey C Tsallis |
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Institution: | (1) Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil;(2) Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Ciudad Universitaria, CONICET, Córdoba, 5000, Argentina;(3) Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA |
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Abstract: | We introduce, and numerically study, a system of N symplectically and globally coupled
standard maps localized in a d=1 lattice array. The global coupling is modulated
through a factor r-α, being
r the distance between maps. Thus, interactions are long-range (nonintegrable) when
0≤α≤1, and short-range (integrable) when α>1.
We verify that the largest Lyapunov exponent λM scales as λM ∝
N-κ(α), where κ(α) is positive when interactions are
long-range, yielding weak chaos in the thermodynamic
limit N↦∞ (hence λM→0). In the short-range case,
κ(α) appears to vanish,
and the behaviour corresponds to strong chaos. We show that, for certain
values of the control parameters of the system, long-lasting metastable states
can be present. Their duration tc scales as tc ∝Nβ(α),
where β(α) appears to be numerically in agreement with the following
behavior: β>0 for 0 ≤α< 1, and zero for α≥1.
These results are consistent with features typically found in nonextensive statistical mechanics.
Moreover, they exhibit strong similarity between the present
discrete-time system, and the α-XY Hamiltonian ferromagnetic model. |
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Keywords: | 05 20 -y Classical statistical mechanics 05 45 -a Nonlinear dynamics and chaos 05 70 Ln Nonequilibrium and irreversible thermodynamics 05 90 +m Other topics in statistical physics thermodynamics and nonlinear dynamical systems |
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