Classical and quantum Hamiltonian ratchets

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 ve...

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Bibliographic Details
Published in:Physical review letters 2001-08, Vol.87 (7), p.070601-070601, Article 070601
Main Authors: Schanz, H, Otto, M F, Ketzmerick, R, Dittrich, T
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
HAMILTONIANS
PHASE SPACE
SUM RULES
TRANSPORT
VARIATIONS
VELOCITY
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Summary: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.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.87.070601