Ivanchenko M V, Kanakov O I, Mishagin K G, Flach S
Department of Radiophysics, Nizhny Novgorod University, Gagarin Avenue 23, 603950 Nizhny Novgorod, Russia.
Phys Rev Lett. 2006 Jul 14;97(2):025505. doi: 10.1103/PhysRevLett.97.025505.
In their celebrated experiment, Fermi, Pasta, and Ulam (FPU) [Los Alamos Report No. LA-1940, 1955] observed that in simple one-dimensional nonlinear atomic chains the energy must not always be equally shared among the modes. Recently, it was shown that exact and stable time-periodic orbits, coined q-breathers (QBs), localize the mode energy in normal mode space in an exponential way, and account for many aspects of the FPU problem. Here we take the problem into more physically important cases of two- and three-dimensional acoustic lattices to find existence and principally different features of QBs. By use of perturbation theory and numerical calculations we obtain that the localization and stability of QBs are enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional analogues.
在他们著名的实验中，费米、帕斯塔和乌拉姆（FPU）[洛斯阿拉莫斯报告第LA - 1940号，1955年]观察到，在简单的一维非线性原子链中，能量并不总是在各模式之间平均分配。最近，研究表明，精确且稳定的时间周期轨道，即所谓的q呼吸子（QBs），以指数方式在简正模空间中使模式能量局域化，并解释了FPU问题的许多方面。在此，我们将该问题拓展到更具物理重要性的二维和三维声学晶格情形，以探寻QBs的存在性及主要的不同特征。通过微扰理论和数值计算，我们发现，与一维类似物相反，在更高维晶格中，随着系统尺寸的增加，QBs的局域化和稳定性会增强。
