First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model

Abstract

The thermal conductance of a one-dimensional classical inertial Heisenberg model of linear size $L$ is computed, considering the first and last particles in thermal contact with heat baths at higher and lower temperatures, $T_h$ and $T_l$ ($T_h>T_l$), respectively. These particles at extremities of the chain are subjected to standard Langevin dynamics, whereas all remaining rotators ($i=2,\cdots ,L-1$) interact by means of nearest-neighbor ferromagnetic couplings and evolve in time following their own equations of motion, being investigated numerically through molecular-dynamics numerical simulations. Fourier's law for the heat flux is verified numerically with the thermal conductivity becoming independent of the lattice size in the limit $L\to \infty$, scaling with the temperature as $\kappa (T)\sim T^{-2.25}$, where $T=(T_h+T_l)/2$. Moreover, the thermal conductance, $\sigma (L,T)=\kappa (T)/L$, is well-fitted by a function, typical of nonextensive statistical mechanics, according to $\sigma (L,T)=A{\exp }_q(-B{x}^{\eta })$, where $A$ and $B$ are constants, $x=L^{0.475}T$, $q=2.28\pm 0.04$, and $\eta =2.88\pm 0.04$.

References in corpus (14)

• How to Characterize Thermal Transport Capability of 2D Materials Fairly? - Sheet Thermal Conductance and the Choice of Thickness
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Fourier's Law confirmed for a class of small quantum systems
• Heat conduction and Fourier's law by consecutive local mixing and thermalization
• Non-Fourier heat transport in nanosystems
• Evidence for Ballistic Thermal Conduction in the One-Dimensional S=1/2 Heisenberg Antiferromagnetic Spin System Sr2CuO3
• Heat conduction in disordered harmonic lattices with energy conserving noise
• Fourier's Law from Closure Equations
• Reconstructing Fourier's law from disorder in quantum wires
• Controlling the Range of Interactions in the Classical Inertial Ferromagnetic Heisenberg Model: Analysis of Metastable States
• Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map
• Thermal conductivity of a classical one dimensional spin-phonon system
• Ising chain: Thermal conductivity and first-principle validation of Fourier law
• First-principle validation of Fourier's law in d=1,2,3 classical systems