We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi–Pasta–Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.
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March 2005
Research Article|
March 28 2005
The anti-FPU problem
Thierry Dauxois;
Thierry Dauxois
Laboratoire de Physique
, UMR-CNRS 5672, ENS Lyon, 46 Allée d’Italie, 69364 Lyon Cédex 07, France
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Ramaz Khomeriki;
Ramaz Khomeriki
Tbilisi State University
, Department of Physics, 3 Chavchavadze Avenue, Tbilisi 128, Republic of Georgia
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Francesco Piazza;
Francesco Piazza
Laboratoire de Biophysique Statistique, ITP,
École Polytechnique Fédérale de Lausanne
, BSP CH-1015 Lausanne, Switzerland
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Stefano Ruffo
Stefano Ruffo
Laboratoire de Physique
, UMR-CNRS 5672, ENS Lyon, 46 Allée d’Italie, 69364 Lyon Cédex 07, France and Dipartimento di Energetica, “S. Stecco” and CSDC, Università di Firenze
, and INFN, via S. Marta, 3, 50139 Firenze, Italy
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Chaos 15, 015110 (2005)
Article history
Received:
September 21 2004
Accepted:
December 11 2004
Citation
Thierry Dauxois, Ramaz Khomeriki, Francesco Piazza, Stefano Ruffo; The anti-FPU problem. Chaos 1 March 2005; 15 (1): 015110. https://doi.org/10.1063/1.1854273
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