Jiang Shi-xiao W, Lu Hai-hao, Zhou Douglas, Cai David
Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China.
Department of Mathematics, MOE-LSC, and Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China and Courant Institute of Mathematical Sciences and Center for Neural Science, New York University, New York, New York 10012, USA and NYUAD Institute, New York University Abu Dhabi, P.O. Box 129188, Abu Dhabi, United Arab Emirates.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Sep;90(3):032925. doi: 10.1103/PhysRevE.90.032925. Epub 2014 Sep 30.
We study the nonlinear dispersive characteristics in β-Fermi-Pasta-Ulam (FPU) chains in both thermal equilibrium and nonequilibrium steady state. By applying a multiple scale analysis to the FPU chain, we analyze the contribution of the trivial and nontrivial resonance to the renormalization of the dispersion relation. Our results show that the contribution of the nontrivial resonance remains significant to the renormalization, in particular, in strongly nonlinear regimes. We contrast our results with the dispersion relations obtained from the Zwanzig-Mori formalism and random phase approximation to further illustrate the role of resonances. Surprisingly, these theoretical dispersion relations can be generalized to describe dispersive characteristics well at the nonequilibrium steady state of the FPU chain with driving-damping in real space. Through numerical simulation, we confirm that the theoretical renormalized dispersion relations are valid for a wide range of nonlinearities in thermal equilibrium as well as in nonequilibrium steady state. We further show that the dispersive characteristics persist in nonequilibrium steady state driven-damped in Fourier space.
我们研究了处于热平衡和非平衡稳态的β-费米-帕斯塔-乌拉姆（FPU）链中的非线性色散特性。通过对FPU链应用多尺度分析，我们分析了平凡共振和非平凡共振对色散关系重整化的贡献。我们的结果表明，非平凡共振对重整化的贡献仍然很大，特别是在强非线性区域。我们将我们的结果与从兹万齐格-莫里形式主义和随机相位近似得到的色散关系进行对比，以进一步说明共振的作用。令人惊讶的是，这些理论色散关系可以推广到很好地描述在实空间中具有驱动-阻尼的FPU链的非平衡稳态下的色散特性。通过数值模拟，我们证实了理论重整化色散关系在热平衡以及非平衡稳态下对于广泛的非线性都是有效的。我们进一步表明，色散特性在傅里叶空间中驱动-阻尼的非平衡稳态中持续存在。
