Heat Transport of the β-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit
Abstract
Resolving the anomalous conductivity exponent of the symmetric β-Fermi--Pasta--Ulam--Tsingou chain by molecular dynamics can require very large systems because of long finite-size crossovers and thermal-contact resistance. Motivated by this computational challenge, we derive a long-wavelength continuum description and investigate whether the kinetic-theory scaling κ∝ L2/5 becomes accessible with a moderate number of numerical degrees of freedom. The nonlinear elastic field retains the cubic stress of the microscopic interaction and exchanges heat with Langevin reservoirs. A flux-conservative spatial discretization constructs the force and energy current from the same stress, providing a consistent interior transport estimator. For L>8, corresponding to approximately 103 mesh nodes and above at the reference resolution, the fitted exponent is 0.399±0.004. Mesh refinement supports the stability of this exponent between the two finer resolutions, although the conductivity amplitude remains resolution-dependent. The main result is thus an accessible finite-size regime near 2/5, rather than convergence of the absolute conductivity as the mesh spacing vanishes. This formulation provides a practical route to studying anomalous transport in anharmonic systems and a conservative continuum framework for investigating energy flow in nonlinear elastic media.
Related
- Random Initial Data and Average Shock Time in the Fermi-Pasta-Ulam-Tsingou Chain
- Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems
- 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
- Heat transport in weakly anharmonic Fermi-Pasta-Ulam-Tsingou chains
BibTeX
@misc{lima2026heat,
title = {{Heat Transport of the $β$-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit}},
author = {Henrique Santos Lima and Matheus M. R. Poltronieri Martins and Lucas Reis e Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.09405},
eprint = {2610.09405},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.09405},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Heat Transport of the β-Fermi--Pasta--Ulam--Tsingou chain in the long-wave limit
AU - Henrique Santos Lima
AU - Matheus M. R. Poltronieri Martins
AU - Lucas Reis e Silva
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.09405
UR - https://arxiv.org/abs/2610.09405
AB - Resolving the anomalous conductivity exponent of the symmetric β-Fermi--Pasta--Ulam--Tsingou chain by molecular dynamics can require very large systems because of long finite-size crossovers and thermal-contact resistance. Motivated by this computational challenge, we derive a long-wavelength continuum description and investigate whether the kinetic-theory scaling κ∝ L^2/5 becomes accessible with a moderate number of numerical degrees of freedom. The nonlinear elastic field retains the cubic stress of the microscopic interaction and exchanges heat with Langevin reservoirs. A flux-conservative spatial discretization constructs the force and energy current from the same stress, providing a consistent interior transport estimator. For L>8, corresponding to approximately 10^3 mesh nodes and above at the reference resolution, the fitted exponent is 0.399±0.004. Mesh refinement supports the stability of this exponent between the two finer resolutions, although the conductivity amplitude remains resolution-dependent. The main result is thus an accessible finite-size regime near 2/5, rather than convergence of the absolute conductivity as the mesh spacing vanishes. This formulation provides a practical route to studying anomalous transport in anharmonic systems and a conservative continuum framework for investigating energy flow in nonlinear elastic media.
ER -