Classical and Quantum Hamiltonian Ratchets

2000/11/30 by Holger Schanz, Marc-Felix Otto, Roland Ketzmerick +1 · 7 citations
Mathematics · Physics and Astronomy · #Chaotic #Classical mechanics #Computer science #Hamiltonian (control theory) #Mathematics #Phase space #Physics #Quantum #Quantum chaos #Quantum chaos and dynamical systems #Quantum dynamics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #nlin.CD #stochastic dynamics and bifurcation

paper · pdf · doi:10.1103/physrevlett.87.070601

published as Phys. Rev. Lett. 87 (2001) 070601 · published version

openalex publication_date 2001/07/26 · arxiv created 2001/09/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We explain the mechanism leading to directed chaotic transport in Hamiltonian systems with spatial and temporal periodicity. We show that a mixed phase space comprising both regular and chaotic motion is required and we derive a classical sum rule which allows one to predict the chaotic transport velocity from properties of regular phase-space components. Transport in quantum Hamiltonian ratchets arises by the same mechanism as long as uncertainty allows one to resolve the classical phase-space structure. We derive a quantum sum rule analogous to the classical one, based on the relation between quantum transport and band structure.

Citations

• Steady States and Quasienergies of a Quantum-Mechanical System in an Oscillating Field

Cited by

• Chaotic Dynamics and Quantum Transport
• Quantum properties of double kicked systems with classical translational invariance in momentum
• Initial-state dependence of a quantum resonance ratchet
• Nanowires with surface disorder: Giant localization length and dynamical tunneling in the presence of directed chaos
• FLOQUET FORMALISM OF QUANTUM PUMPS
• Direct regular-to-chaotic tunneling rates using the fictitious-integrable-system approach
• Superexponential self-interacting oscillator