Ratchet current in nontwist Hamiltonian systems

Area of Science:

• Physics
• Dynamical Systems
• Nonlinear Dynamics

Background:

• Non-monotonic area-preserving maps exhibit unique phase space structures.
• These maps violate the twist condition, forming shearless invariant barriers and twin island chains.

Purpose of the Study:

• Investigate shearless barriers and twin island chains in extended standard nontwist maps with two resonant perturbations.
• Compare findings with single-perturbation scenarios.
• Analyze the influence of a second wave number on barrier formation and symmetry.

Main Methods:

• Analysis of extended standard nontwist maps with distinct wave numbers.
• Phase space exploration to identify invariant barriers and island chains.
• Parameter space analysis to determine conditions for shearless barrier existence.

Main Results:

• The presence of shearless barriers and twin island chains is confirmed in extended nontwist maps.
• Symmetry of twin island chains depends on the parity of the second wave number.
• Odd second wave numbers lead to symmetrical twin island chains.
• Even second wave numbers result in asymmetrical chains, inducing a ratchet effect and directed transport.

Conclusions:

• The study elucidates the role of multiple wave numbers in shaping phase space dynamics.
• Asymmetrical twin island chains, driven by even wave numbers, offer a mechanism for directed transport.
• Findings contribute to understanding complex dynamics in perturbed Hamiltonian systems.