Flach S, Ivanchenko M V, Kanakov O I
Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany.
Phys Rev Lett. 2005 Aug 5;95(6):064102. doi: 10.1103/PhysRevLett.95.064102. Epub 2005 Aug 2.
The Fermi-Pasta-Ulam (FPU) paradox consists of the non-equipartition of energy among normal modes of a weakly anharmonic atomic chain model. In the harmonic limit each normal mode corresponds to a periodic orbit in phase space and is characterized by its wave number q. We continue normal modes from the harmonic limit into the FPU parameter regime and obtain persistence of these periodic orbits, termed here q-breathers (QB). They are characterized by time periodicity, exponential localization in the q-space of normal modes and linear stability up to a size-dependent threshold amplitude. Trajectories computed in the original FPU setting are perturbations around these exact QB solutions. The QB concept is applicable to other nonlinear lattices as well.
费米-帕斯塔-乌拉姆（FPU）悖论源于弱非谐原子链模型的简正模式之间能量的非均分。在简谐极限下，每个简正模式对应于相空间中的一个周期轨道，并由其波数q表征。我们将简正模式从简谐极限延续到FPU参数区域，并得到这些周期轨道的持续性，在此称为q呼吸子（QB）。它们的特征是时间周期性、在简正模式的q空间中的指数局域化以及在依赖于尺寸的阈值振幅以下的线性稳定性。在原始FPU设置中计算的轨迹是围绕这些精确QB解的微扰。QB概念也适用于其他非线性晶格。
