Regular Article

Energy super-diffusion in 1d deterministic nonlinear lattices with broken standard momentum

¹ Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, P.R. China
² Center for Phononics and Thermal Energy Science, China-EU Joint Center for Nanophononics, Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology, School of Physics Sciences and Engineering, Tongji University, Shanghai 200092, P.R. China

^a e-mail: nbli@hqu.edu.cn

Received: 6 March 2020
Received in final form: 5 May 2020
Published online: 10 June 2020

Abstract

The property of total momentum conservation is a key issue in determining the energy diffusion behavior for 1d nonlinear lattices. The super-diffusion of energy has been found for 1d momentum conserving nonlinear lattices with the only exception of 1d coupled rotator model. However, for all the other 1d momentum non-conserving nonlinear lattices studied so far, the energy diffusion is normal. Here we investigate the energy diffusion in a 1d nonlinear lattice model with inverse couplings. For the standard definition of momentum, this 1d inverse coupling model does not preserve the total momentum while it exhibits energy super-diffusion behavior. In particular, with a parity transformation, this 1d inverse coupling model can be mapped into the well-known 1d FPU-β model although they have different phonon dispersion relations. In contrary to the 1d FPU-β model where the long-wave length phonons are responsible for the super-diffusion behavior, the short-wave length phonons contribute to the super-diffusion of energy in the 1d inverse coupling model.