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Classical and Quantum Hamiltonian Ratchets

Holger Schanz·Marc-Felix Otto·Roland Ketzmerick·Thomas Dittrich
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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 derive a classical sum rule which allows 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 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.

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Holger Schanz, Marc-Felix Otto, Roland Ketzmerick, Thomas Dittrich. 2001-09-11. Classical and Quantum Hamiltonian Ratchets. https://doi.org/10.1103/physrevlett.87.070601

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