Classical and Quantum Hamiltonian Ratchets

Details Classical and Quantum Hamiltonian Ratchets Classical and Quantum Hamiltonian Ratchets

2000-11-21

arxiv.org/abs/nlin/0011038v2

Phys. Rev. Lett. 87 (2001) 070601

Nonlinear Sciences

Chaotic Dynamics

published version

Scientific paper

10.1103/PhysRevLett.87.070601

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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