A walker is the association of a sub-millimetric bouncing drop moving along with a co-evolving Faraday wave. When confined in a harmonic potential, its stable trajectories are periodic and quantised both in extension and mean angular momentum. In this article, we present the rest of the story, specifically the chaotic paths. They are chaotic and show intermittent behaviors between an unstable quantised set of attractors. First, we present the two possible situations we find experimentally. Then, we emphasise theoretically two mechanisms that lead to unstable situations. It corresponds either to noise-driven chaos or low-dimensional deterministic chaos. Finally, we characterise experimentally each of these distinct situations. This article aims at presenting a comprehensive investigation of the unstable paths in order to complete the picture of walkers in a two dimensional harmonic potential.
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September 2018
Research Article|
September 18 2018
Transition to chaos in wave memory dynamics in a harmonic well: Deterministic and noise-driven behavior
Special Collection:
Hydrodynamic Quantum Analogs
S. Perrard;
S. Perrard
a)
1
Laboratoire FAST, CNRS UMR 7608, CNRS, Université Paris-Saclay
, 91405 Orsay, France
2
LadHyX, CNRS UMR 7646, École Polytechnique
, 91128 Palaiseau, France
a)Current address: Département de Physique, ENS, PSL Université, CNRS, 24 rue Lhomond, 75005 Paris.
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M. Labousse
M. Labousse
3
Gulliver, CNRS UMR 7083, ESPCI Paris and PSL University
, 75005 Paris, France
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a)Current address: Département de Physique, ENS, PSL Université, CNRS, 24 rue Lhomond, 75005 Paris.
Chaos 28, 096109 (2018)
Article history
Received:
April 02 2018
Accepted:
August 22 2018
Citation
S. Perrard, M. Labousse; Transition to chaos in wave memory dynamics in a harmonic well: Deterministic and noise-driven behavior. Chaos 1 September 2018; 28 (9): 096109. https://doi.org/10.1063/1.5032088
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