Panoiu N.-C.
Department of Physics, New York University, 4 Washington Place, New York, New York 10003Institute of Atomic Physics, Department of Theoretical Physics, P.O. Box MG-6, Bucharest, Romania.
Chaos. 2000 Mar;10(1):166-179. doi: 10.1063/1.166484.
The diffusion process in a Hamiltonian dynamical system describing the motion of a particle in a two-dimensional (2D) potential with hexagonal symmetry is studied. It is shown that, depending on the energy of the particle, various transport processes can exist: normal (Brownian) diffusion, anomalous diffusion, and ballistic transport. The relationship between these transport processes and the underlying structure of the phase space of the Hamiltonian dynamical system is investigated. The anomalous transport is studied in detail in two particular cases: in the first case, inside the chaotic sea there exist self-similar structures with fractal properties while in the second case the transport takes place in the presence of multilayered structures. It is demonstrated that structures of the second type can lead to a physical situation in which the transport becomes ballistic. Also, it is shown that for all cases in which the diffusive transport is anomalous the trajectories of the diffusing particles contain long segments of regular motion, the length of these segments being described by Levy probability density functions. Finally, the numerical values of the parameters which describe the diffusion processes are compared with those predicted by existing theoretical models. (c) 2000 American Institute of Physics.
研究了哈密顿动力学系统中的扩散过程，该系统描述了粒子在具有六边形对称性的二维势场中的运动。结果表明，根据粒子的能量，可能存在各种输运过程：正常（布朗）扩散、反常扩散和弹道输运。研究了这些输运过程与哈密顿动力学系统相空间基础结构之间的关系。在两种特殊情况下详细研究了反常输运：第一种情况是，在混沌海中存在具有分形性质的自相似结构；第二种情况是，输运发生在多层结构存在的情况下。结果表明，第二种类型的结构可导致输运变为弹道输运的物理情形。此外，结果表明，对于所有扩散输运为反常的情况，扩散粒子的轨迹包含长段的规则运动，这些段的长度由列维概率密度函数描述。最后，将描述扩散过程的参数数值与现有理论模型预测的值进行了比较。（c）2000美国物理研究所。
