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Time independent description of rapidly oscillating potentials
Saar Rahav1, Ido Gilary, Shmuel Fishman
1Department of Physics, Technion, Haifa 32000, Israel.
Physical Review Letters
|October 4, 2003
Summary
Researchers developed an effective time-independent Hamiltonian to describe classical and quantum dynamics in high-frequency fields. This method simplifies analyzing systems with oscillating fields, particularly benefiting cold atom research.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Atomic physics
Background:
- Analyzing systems with rapidly oscillating fields is complex.
- Previous work on the Kapitza pendulum was limited to lower orders of frequency expansion.
Purpose of the Study:
- To derive an effective time-independent Hamiltonian for systems in high-frequency fields.
- To extend classical results for the Kapitza pendulum to higher orders.
- To provide a framework for analyzing dynamics in oscillating fields using established methods.
Main Methods:
- Systematic expansion of dynamics in inverse frequency (omega).
- Method of separation of time scales.
- Quantum gauge transformation within Floquet theory.
Main Results:
- An effective time-independent Hamiltonian was calculated to order omega(-4).
- This Hamiltonian accurately describes both classical and quantum dynamics.
- The approach extends the Kapitza pendulum solution to higher orders.
Conclusions:
- The derived effective Hamiltonian simplifies the study of systems with high-frequency fields.
- This framework allows the application of time-independent theories to oscillating systems.
- The findings are particularly relevant for the dynamics of cold atoms.