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Peer-reviewedCC BY 4.0Journal of Statistical Physics

Resonant Interactions in the α α-FPUT Lattice with Site-Dependent Coefficients

  • Lorenzo Migliorelli1,2
  • Giovanni Dematteis1,2
  • Sergio Chibbaro3
  • Miguel Onorato1,2
  1. 1Dipartimento di Fisica, Universitá degli Studi di Torino, Via P. Giuria 1, 10125 Turin, Italy
  2. 2Sezione di Torino, Istituto Nazionale di Fisica Nucleare, INFN, Via P. Giuria 1, 10125 Turin, Italy
  3. 3LISN, UMR 9015, CNRS, INRIA, Université Paris-Saclay, 91405 Orsay cedex, France
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Abstract

The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains. In this work, we extend this approach to the α α-FPUT problem when the spring stiffness χ χ and the nonlinear coefficient α α are site-dependent. Although three-wave interactions are non-resonant for constant coefficients, their spatial modulation gives rise to a non-trivial resonant manifold. In this framework, we derive a new kinetic equation that suggests the possibility of substantially faster thermalization than in the constant-coefficient case. The new kinetic equation also includes an additional term that can be associated with the Bragg-scattering mechanism, which promotes the isotropization of the wave-action spectral density function. We corroborate these results with direct numerical simulations, confirming the radically faster thermalization pathway in the presence of random coefficients.

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Cite

BibTeXRIS
BibTeX
@article{migliorelli2026resonant,
  title = {{Resonant Interactions in the α α-FPUT Lattice with Site-Dependent Coefficients}},
  author = {Lorenzo Migliorelli and Giovanni Dematteis and Sergio Chibbaro and Miguel Onorato},
  journal = {Journal of Statistical Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/s10955-026-03724-w},
  url = {https://doi.org/10.1007/s10955-026-03724-w},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Resonant Interactions in the α α-FPUT Lattice with Site-Dependent Coefficients
AU  - Lorenzo Migliorelli
AU  - Giovanni Dematteis
AU  - Sergio Chibbaro
AU  - Miguel Onorato
PY  - 2026
DA  - 2026/11/03
JO  - Journal of Statistical Physics
DO  - 10.1007/s10955-026-03724-w
UR  - https://doi.org/10.1007/s10955-026-03724-w
AB  - The wave turbulence framework has proven to be an effective tool for analyzing certain features of nonlinear energy transfer in one-dimensional nonlinear chains. In this work, we extend this approach to the α α-FPUT problem when the spring stiffness χ χ and the nonlinear coefficient α α are site-dependent. Although three-wave interactions are non-resonant for constant coefficients, their spatial modulation gives rise to a non-trivial resonant manifold. In this framework, we derive a new kinetic equation that suggests the possibility of substantially faster thermalization than in the constant-coefficient case. The new kinetic equation also includes an additional term that can be associated with the Bragg-scattering mechanism, which promotes the isotropization of the wave-action spectral density function. We corroborate these results with direct numerical simulations, confirming the radically faster thermalization pathway in the presence of random coefficients.
SN  - 0022-4715
SN  - 1572-9613
ER  -