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

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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.

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Authors and Affiliations

  1. Institute of Systems Science and Department of Physics, College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, P.R. China

    Hengzhe Yan & Nianbei Li

  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

    Hengzhe Yan & Jie Ren

Authors
  1. Hengzhe Yan
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  2. Jie Ren
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  3. Nianbei Li
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Correspondence to Nianbei Li.

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Yan, H., Ren, J. & Li, N. Energy super-diffusion in 1d deterministic nonlinear lattices with broken standard momentum. Eur. Phys. J. B 93, 108 (2020). https://doi.org/10.1140/epjb/e2020-10117-3

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  • DOI: https://doi.org/10.1140/epjb/e2020-10117-3

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