Directed chaos in a billiard chain with transversal magnetic field

Abstract

In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which electrons move under the influence of a perpendicular magnetic field. We analyze the phase-space structure and derive an explicit expression for the chaotic transport velocity. Unlike previous studies of directed chaos our model has a parameter regime in which the dispersion of an ensemble of chaotic trajectories around its moving center of mass is essentially diffusive. We explain how in this limit the deterministic chaos reduces to a biased random walk in a billiard with a rough surface. The diffusion constant for this simplified model is calculated analytically.

References in corpus (6)

• Brownian motors: noisy transport far from equilibrium
• Directed current due to broken time-space symmetry
• Classical and Quantum Hamiltonian Ratchets
• Directed Chaotic Transport in Hamiltonian Ratchets
• Quantum localization in rough billiards
• Uni-directional transport properties of a serpent billiard

Cited by in corpus (6)

• Directed Transport of Confined Brownian Particles with Torque
• Nano-wires with surface disorder: Giant localization lengths and dynamical tunneling in the presence of directed chaos
• Cooperative surmounting of bottlenecks
• Emergence of continual directed flow in Hamiltonian systems
• Signature of directed chaos in the conductance of a nanowire
• The coupled dynamics of two particles with different limit sets