Scaling of Chaos in Strongly Nonlinear Lattices

Abstract

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [New J.\ Phys.\ 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

6 pages, 4 figures

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Cited by in corpus (6)

• Nonlinear lattice waves in heterogeneous media
• Chaotic wave packet spreading in two-dimensional disordered nonlinear lattices
• Identifying localized and spreading chaos in nonlinear disordered lattices by the Generalized Alignment Index (GALI) method
• Nonlinear Lattice Waves in Random Potentials
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Nonlinear dynamics and chaos in multidimensional disordered Hamiltonian systems