A Large Scale Non-equilibrium Simulation of Heat Transport in One-dimensional Fermi–Pasta–Ulam–Tsingou Lattice

Heat transport in one-dimensional Fermi–Pasta–Ulam–Tsingou (FPUT) lattice is known to be anomalous. Its thermal conductivity κ diverges as the lattice size N increases. It is believed that the asymptotic scaling law κ ∝ Nα holds for N large enough with 0 < α < 1. However, the precise value of the exponent α has still been of much debated question. In order to precisely determine the value of α, we perform a large scale non-equilibrium molecular dynamics simulation up to the size \(N = 2²⁴ 1.68 × 10⁷\), using the FPUT-β lattice which is in contact with different temperature heat baths at both ends. Our simulation indicates \(α 0.3987\), which is close to α = 2/5. The exponent α locally defined as a function of N decreases to about 0.27 up to \(N 2¹⁴\) and then increases towards the asymptotic value with increasing N.