School of Physics and Material Science, Anhui University, Hefei, Anhui 230601, China.
School of Nuclear Science and Technology, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev E. 2018 Jan;97(1-1):012221. doi: 10.1103/PhysRevE.97.012221.
Currently, effective phonons (renormalized or interacting phonons) rather than solitary waves (for short, solitons) are regarded as the energy carriers in nonlinear lattices. In this work, by using the approximate soliton solutions of the corresponding equations of motion and adopting the Boltzmann distribution for these solitons, the average velocities of solitons are obtained and are compared with the sound velocities of energy transfer. Excellent agreements with the numerical results and the predictions of other existing theories are shown in both the symmetric Fermi-Pasta-Ulam-β lattices and the asymmetric Fermi-Pasta-Ulam-αβ lattices. These clearly indicate that solitons are suitable candidates for energy carriers in Fermi-Pasta-Ulam lattices. In addition, the root-mean-square velocity of solitons can be obtained from the effective phonons theory.
目前，非线性晶格中的能量载体被认为是有效声子（重整化或相互作用的声子），而不是孤立波（简称孤子）。在这项工作中，我们通过使用相应运动方程的近似孤子解，并采用玻尔兹曼分布来处理这些孤子，得到了孤子的平均速度，并将其与能量传递的声速进行了比较。在对称的费米-帕斯塔-乌伦贝克-β晶格和非对称的费米-帕斯塔-乌伦贝克-αβ晶格中，我们都得到了与数值结果和其他现有理论预测非常吻合的结果。这清楚地表明，孤子是费米-帕斯塔-乌伦贝克晶格中能量载体的合适候选者。此外，孤子的均方根速度可以从有效声子理论中得到。
