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Directed transport in a classical lattice with a high-frequency driving
1Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
Directed transport of classical particles in periodic potentials is possible even with zero average force. This study derives an asymptotic formula for fast driving, revealing transport arises from an effective Hamiltonian without chaotic dynamics.
Area of Science:
- Classical mechanics
- Nonlinear dynamics
- Condensed matter physics
Background:
- Directed transport in periodic potentials with time-dependent forces is a known phenomenon.
- Previous work established transport for slow driving and explored its connection to chaos.
- The dynamics of classical particles in spatially periodic potentials under time-periodic forces are complex.
Purpose of the Study:
- To analyze the dynamics of a classical particle in a spatially periodic potential driven by a time-periodic force.
- To derive an asymptotic formula for the average drift velocity in the fast driving regime.
- To clarify the relationship between chaos and directed transport in this system.
Main Methods:
- Canonical perturbation theory was employed to analyze the system's dynamics.
- Asymptotic analysis was used to derive formulas for drift velocity.
- The properties of the effective Hamiltonian were investigated.
Main Results:
- An asymptotic formula for the average drift velocity was derived for fast driving.
- Directed transport was shown to arise from an effective Hamiltonian that lacks chaotic dynamics.
- Sufficient conditions for the occurrence of directed transport were established.
Conclusions:
- Directed transport can occur in systems with spatially periodic potentials and time-periodic driving, even without chaotic dynamics.
- The study clarifies that directed transport does not necessarily require chaotic motion.
- The derived formula provides a quantitative description of transport for fast driving regimes.
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