Eur. Phys. J. B (2015) 88: 182
https://doi.org/10.1140/epjb/e2015-60361-5

Regular Article

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

¹ Center for Phononics and Thermal Energy Science, School of Physical Sciences and Engineering, Tongji University, Shanghai 200092, P.R. China
² Department of Physics and Centre for Computational Science and Engineering, National University of Singapore, Singapore 117546, Republic of Singapore
³ Center for Advanced 2D Material and Graphene Research Centre, National University of Singapore, Singapore 117542, Republic of Singapore

^a e-mail: nbli@tongji.edu.cn
^b e-mail: phononics@tongji.edu.cn

Received: 5 May 2015
Received in final form: 21 May 2015
Published online: 13 July 2015

Abstract

In contrary to other 1D momentum-conserving lattices such as the Fermi-Pasta-Ulam β (FPU-β) 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. It is found that the momentum diffusion constant for 1D coupled rotator lattice follows a power-law temperature dependence of T^-3.2 which is close to that of Chirikov standard map which follows a behavior of T^-3.