2008/08/08 by Walter Acevedo, Acevedo, Walter, Thomas Dittrich +1
Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.0808.1313
22 pages 13 figures
openalex publication_date 2008/08/08 · arxiv created 2008/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an autonomous chaotic Hamiltonian ratchet as a channel billiard subdivided by equidistant walls attached perpendicularly to one side of the channel, leaving an opening on the opposite side. A static homogeneous magnetic field penetrating the billiard breaks time-reversal invariance and renders the classical motion partially chaotic. We show that the classical dynamics exhibits directed transport, owing to the asymmetric distribution of regular regions in phase space. The billiard is quantized by a numerical method based on a finite-element algorithm combined with the Landau gauge and the Bloch formalism for periodic potentials. We discuss features of the billiard eigenstates such as node lines and vortices in the probability flow. Evidence for directed quantum transport, inherited from the corresponding features of the classical dynamics, is presented in terms of level-velocity statistics.