Energy super-diffusion in 1d deterministic nonlinear lattices with broken standard momentum
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Energy super-diffusion in 1d deterministic nonlinear lattices with broken standard momentum Hengzhe Yan 1,2 , Jie Ren 2 , and Nianbei Li 1,a 1
2
Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen 361021, P.R. China 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 Received 6 March 2020 / Received in final form 5 May 2020 Published online 10 June 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 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.
1 Introduction Since the first ever discovery of anomalous heat conduction for 1d nonlinear Fermi-Pasta-Ulam β (FPU-β) lattice [1], revealing the physical mechanism behind this anomalous heat conduction behavior has attracted great attention [2–5]. Among many properties of 1d FPU-β lattice model, the conservation of total momentum has been thought to be the key issue which eventually gives rise to the anomalous heat conduction [6,7]. The numerical simulations confirm that the anomalous heat conduction can be found for the 1d nonlinear lattice if the total momentum is conserved [1,8], except for the special 1d coupled rotator model [9,10]. On the other hand, the normal heat conduction can be obtained for 1d nonlinear lattice with on-site potential where the conservation of total momentum is broken [11–13]. Recent numerical results seem suggesting that asymmetry in momentum conserving lattices can induce normal heat conduction [14–16], but later works demonstrate that this might be a finite size effect and anomalous heat conduction will be approached for asymmetric momentum conserving lattices in the thermodynamical limit [17,18]. Although momentum conserved 1d nonlin
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