Coupled symplectic maps as models for subdiffusive processes in disordered Hamiltonian lattices

TL;DR

This study demonstrates that coupled symplectic maps can model subdiffusive processes akin to disordered Hamiltonian lattices, revealing different regimes of chaos and diffusion depending on coupling strength.

Contribution

It introduces coupled symplectic McMillan maps as a new model for subdiffusive dynamics in disordered Hamiltonian systems, highlighting their similar physical properties despite different local dynamics.

Findings

Weak coupling leads to no diffusion or subdiffusion with q>1

Large coupling results in strongly chaotic subdiffusive behavior

Model mimics energy spreading in disordered Klein-Gordon systems

Abstract

We investigate dynamically and statistically diffusive motion in a chain of linearly coupled 2-dimensional symplectic McMillan maps and find evidence of subdiffusion in weakly and strongly chaotic regimes when all maps of the chain possess a saddle point at the origin and the central map is initially excited. In the case of weak coupling, there is either absence of diffusion or subdiffusion with $q>1$-Gaussian probability distributions, characterizing weak chaos. However, for large enough coupling and already moderate number of maps, the system exhibits strongly chaotic ($q\approx 1$) subdiffusive behavior, reminiscent of the subdiffusive energy spreading observed in a disordered Klein-Gordon Hamiltonian. Our results provide evidence that coupled symplectic maps can exhibit physical properties similar to those of disordered Hamiltonian systems, even though the local dynamics in the two cases is significantly different.