Diffusion transitions in a 2D periodic lattice

TL;DR

This paper investigates diffusion transitions in a 2D periodic lattice modeled as a soft billiard, revealing sudden shifts between normal and ballistic regimes linked to phase-space topological changes and stability variations.

Contribution

It introduces a bidimensional optical lattice Hamiltonian model to analyze diffusion transitions and characterizes the topological phase-space changes associated with these transitions.

Findings

Sudden transitions between normal and ballistic diffusion regimes.

Topological phase-space changes correlate with stability area increases.

Emergence of long-flight orbits affects average displacement without global phase-space changes.

Abstract

Spatial diffusion of particles in periodic potential models has provided a good framework for studying the role of chaos in global properties of classical systems. Here a bidimensional "soft" billiard, classically modeled from an optical lattice hamiltonian system, is used to study diffusion transitions with the control parameters variation. Sudden transitions between normal and ballistic regimes are found and characterized by inspection of the topological changes in phase-space. Transitions correlated with increases in global stability area are shown to occur for energy levels where local maxima points become accessible, deviating trajectories approaching it. These instabilities promote a slowing down of the dynamics and an island myriad bifurcation phenomenon, along with the suppression of long flights within the lattice. Other diffusion regime variations occurring during small intervals of control parameters are shown to be related to the emergence of a set of orbits with long flights, thus altering the total average displacement for long integration times but without global changes in phase-space.