Weak-chaos ratchet accelerator

Abstract

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.

Quantum properties of double kicked systems with classical translational invariance in momentum

“…It is also responsible for a variety of interesting classical and quantum phenomena. A well known example are classical transporting islands [3][4][5][6][7][9][10][11], leading to chaotic-transport effects such as superdiffusion [4-7, 9, 10] and Hamiltonian ratchets [11][12][13][14]. These effects are most significant when they take place in the momentum direction due, e.g., to acceleratormode islands.…”

Multi-Frequency Delta-Kicked Models for the Quantum Ratchet Effect

“…A ratchet system with thermal noise is also called a Brownian motor [6], which can be considered a model of the molecular motor in biology [7]. There are also other kinds of ratchet systems without noise, such as the chaotic dynamical ratchet with dissipation and the purely Hamiltonian ratchet [8,9,10,11].…”