Heat transport in weakly anharmonic Fermi-Pasta-Ulam-Tsingou chains
Abstract
We investigate anomalous heat transport in the one-dimensional β-Fermi--Pasta--Ulam--Tsingou chain in the weakly anharmonic regime using large-scale equilibrium molecular dynamics. By resolving the heat current into phonon-mode contributions, we show that its long-time autocorrelation is controlled by diagonal mode correlations, whose decay is quantitatively determined by the corresponding phonon damping rates. Extrapolation to the thermodynamic limit gives Γk ∝ (βT)4/3 k5/3, with a subleading k2 correction. The latter produces an extended pre-asymptotic regime, C(t) ∼ t−4/5, before the asymptotic decay C(t) ∼ t−3/5 is reached, leading to κ(N) ∼ N2/5 + O(N1/5). At weak anharmonicity, off-diagonal mode correlations persist up to a characteristic time τod ∼ (βT)−2, while increasingly large systems are required to resolve the long-wavelength phonon contribution. Weak anharmonicity therefore does not introduce a distinct asymptotic transport mechanism, but shifts the onset of the phonon-dominated regime to progressively longer times and larger length scales.
Related
- Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
- Heat Transport of the β-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit
- Random Initial Data and Average Shock Time in the Fermi-Pasta-Ulam-Tsingou Chain
- Continuum Dirac Theory and Nonlinear Extensions of a Chain of Alternating non-linear springs: an SSH version of the Fermi-Pasta-Ulam-Tsingou model
- Gap-controlled thermalization in a chain of alternating nonlinear springs: an SSH model version of the Fermi-Pasta-Ulam-Tsingou problem
BibTeX
@misc{sharma2026heat,
title = {{Heat transport in weakly anharmonic Fermi-Pasta-Ulam-Tsingou chains}},
author = {Kiratholly Nandakumar Madhav Sharma and Stefano Mossa and Jean-Louis Barrat and Markus Holzmann},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09936},
eprint = {2610.09936},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09936},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Heat transport in weakly anharmonic Fermi-Pasta-Ulam-Tsingou chains
AU - Kiratholly Nandakumar Madhav Sharma
AU - Stefano Mossa
AU - Jean-Louis Barrat
AU - Markus Holzmann
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09936
UR - https://arxiv.org/abs/2610.09936
AB - We investigate anomalous heat transport in the one-dimensional β-Fermi--Pasta--Ulam--Tsingou chain in the weakly anharmonic regime using large-scale equilibrium molecular dynamics. By resolving the heat current into phonon-mode contributions, we show that its long-time autocorrelation is controlled by diagonal mode correlations, whose decay is quantitatively determined by the corresponding phonon damping rates. Extrapolation to the thermodynamic limit gives Γ_k ∝ (βT)^4/3 k^5/3, with a subleading k^2 correction. The latter produces an extended pre-asymptotic regime, C(t) ∼ t^−4/5, before the asymptotic decay C(t) ∼ t^−3/5 is reached, leading to κ(N) ∼ N^2/5 + O(N^1/5). At weak anharmonicity, off-diagonal mode correlations persist up to a characteristic time τ_od ∼ (βT)^−2, while increasingly large systems are required to resolve the long-wavelength phonon contribution. Weak anharmonicity therefore does not introduce a distinct asymptotic transport mechanism, but shifts the onset of the phonon-dominated regime to progressively longer times and larger length scales.
ER -