Temperature dependence of thermal conductivities of coupled rotator lattice and the momentum diffusion in standard map

Abstract

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) lattice, the 1D coupled rotator lattice is a notable exception which conserves total momentum while exhibits normal heat conduction behavior. The temperature behavior of the thermal conductivities of 1D coupled rotator lattice had been studied in previous works trying to reveal the underlying physical mechanism for normal heat conduction. However, two different temperature behaviors of thermal conductivities have been claimed for the same coupled rotator lattice. These different temperature behaviors also intrigue the debate whether there is a phase transition of thermal conductivities as the function of temperature. In this work, we will revisit the temperature dependent thermal conductivities for the 1D coupled rotator lattice. We find that the temperature dependence follows a power law behavior which is different with the previously found temperature behaviors. Our results also support the claim that there is no phase transition for 1D coupled rotator lattice. We also give some discussion about the similarity of diffusion behaviors between the 1D coupled rotator lattice and the single kicked rotator also called the Chirikov standard map.

6 pages, 5 figures

References in corpus (12)

• Length-dependent thermal conductivity in suspended single-layer graphene
• Heat Transport in low-dimensional systems
• A momentum conserving model with anomalous thermal conductivity in low dimension
• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain
• Self-Consistent Mode-Coupling Approach to 1D Heat Transport
• Effective phonons in anharmonic lattices: anomalous vs normal heat conduction
• Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential
• 1D momentum-conserving systems: the conundrum of anomalous versus normal heat transport
• Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections
• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Temperature-dependent thermal conductivities of one-dimensional nonlinear Klein-Gordon lattices with soft on-site potential

Cited by in corpus (4)

• Fragile Many Body Ergodicity
• Ising chain: Thermal conductivity and first-principle validation of Fourier law
• First-Principle Validation of Fourier's Law: One-Dimensional Classical Inertial Heisenberg Model
• First-principle validation of Fourier's law in d=1,2,3 classical systems