TY - JOUR

T1 - Transient-chaos induced directed transport in a spatially-open Hamiltonian system

AU - Hennig, Dirk

AU - Burbanks, Andrew

AU - Osbaldestin, Andrew

AU - Mulhern, Colm

PY - 2010

Y1 - 2010

N2 - We study the autonomous Hamiltonian dynamics of non-interacting particles trapped initially in one well of a symmetric multiple-well washboard potential. The particles interact locally with an anharmonic oscillator acting as an energy deposit. For a range of interaction strengths, the particles gain sufficient energy during a chaotic transient to escape from the well and afterwards settle onto regular (rotational) dynamics. Strikingly, microcanonical ensembles of initial conditions that are unbiased with respect to the washboard coordinate nevertheless give rise to net directed motion. We demonstrate that for unbiased spatially localized initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories within the ensemble, despite the time-reversibility symmetry of the equations of motion, allowing for a nonzero current. Recent studies have shown that particle current may be induced in other systems with preserved spatial symmetry by an external periodic but asymmetric driving force, however, averaging over the phase of the latter yields zero current. The system we propose is novel in that averaging over the phase of the oscillator still yields nonzero current. Furthermore, no mixed phase space is required, and chaos is needed only in an initial stage of the dynamics to guide trajectories from the interior of separatrices onto sustained integrable rotational motion.

AB - We study the autonomous Hamiltonian dynamics of non-interacting particles trapped initially in one well of a symmetric multiple-well washboard potential. The particles interact locally with an anharmonic oscillator acting as an energy deposit. For a range of interaction strengths, the particles gain sufficient energy during a chaotic transient to escape from the well and afterwards settle onto regular (rotational) dynamics. Strikingly, microcanonical ensembles of initial conditions that are unbiased with respect to the washboard coordinate nevertheless give rise to net directed motion. We demonstrate that for unbiased spatially localized initial conditions, violation of parity prevents the existence of pairs of counter-propagating trajectories within the ensemble, despite the time-reversibility symmetry of the equations of motion, allowing for a nonzero current. Recent studies have shown that particle current may be induced in other systems with preserved spatial symmetry by an external periodic but asymmetric driving force, however, averaging over the phase of the latter yields zero current. The system we propose is novel in that averaging over the phase of the oscillator still yields nonzero current. Furthermore, no mixed phase space is required, and chaos is needed only in an initial stage of the dynamics to guide trajectories from the interior of separatrices onto sustained integrable rotational motion.

U2 - 10.1088/1751-8113/43/34/345101

DO - 10.1088/1751-8113/43/34/345101

M3 - Article

SN - 1751-8113

VL - 43

SP - 345101

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 34

ER -