Romero-Bastida M, Pazó Diego, López Juan M, Rodríguez Miguel A
SEPI-ESIME Culhuacán, Instituto Politécnico Nacional, Av. Santa Ana No. 1000, Col. San Francisco Culhuacán, Delegación Coyoacan, Distrito Federal 04430, Mexico.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036205. doi: 10.1103/PhysRevE.82.036205. Epub 2010 Sep 8.
In this work we perform a detailed study of the scaling properties of Lyapunov vectors (LVs) for two different one-dimensional Hamiltonian lattices: the Fermi-Pasta-Ulam and Φ^{4} models. In this case, characteristic (also called covariant) LVs exhibit qualitative similarities with those of dissipative lattices but the scaling exponents are different and seemingly nonuniversal. In contrast, backward LVs (obtained via Gram-Schmidt orthonormalizations) present approximately the same scaling exponent in all cases, suggesting it is an artificial exponent produced by the imposed orthogonality of these vectors. We are able to compute characteristic LVs in large systems thanks to a "bit reversible" algorithm, which completely obviates computer memory limitations.
在这项工作中，我们对两种不同的一维哈密顿晶格（费米-帕斯塔-乌拉姆晶格和Φ⁴模型）的李雅普诺夫向量（LVs）的标度性质进行了详细研究。在这种情况下，特征（也称为协变）LVs与耗散晶格的特征LVs表现出定性相似性，但标度指数不同且似乎不具有普适性。相比之下，反向LVs（通过格拉姆-施密特正交归一化获得）在所有情况下都呈现出大致相同的标度指数，这表明它是由这些向量的强制正交性产生的一个人为指数。由于一种“位可逆”算法，我们能够在大型系统中计算特征LVs，该算法完全消除了计算机内存限制。
