From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics

Abstract

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: Firstly we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting `freezing of dimensionality' rules out the occurrence of hyperchaos. Secondly we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome - one particle followed by the other - consecutive barriers of the periodic potential resulting in collective directed motion.

References in corpus (8)

• Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response
• Dynamical mechanisms of DC current generation in driven Hamiltonian systems
• Dimer diffusion in a washboard potential
• Microscopic mechanisms of thermal and driven diffusion of non rigid molecules on surfaces
• Divergence of the Chaotic Layer Width and Strong Acceleration of the Spatial Chaotic Transport in Periodic Systems Driven by an Adiabatic ac Force
• Slowly rocking symmetric, spatially periodic Hamiltonians: The role of escape and the emergence of giant transient directed transport
• Directed transport of two interacting particles in a washboard potential
• Emergence of continual directed flow in Hamiltonian systems

Cited by in corpus (2)

• Cooperative surmounting of bottlenecks
• The coupled dynamics of two particles with different limit sets