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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

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Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances.

A P Itin¹, A I Neishtadt

¹Zentrum für optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany. alx_it@yahoo.com

Chaos (Woodbury, N.Y.)

|July 5, 2012

Summary

Moving boundaries in a slowly rotating rectangular billiard can cause particle acceleration. Resonance phenomena disrupt adiabatic invariance, leading to unlimited particle energy gain.

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Area of Science:

Classical mechanics
Dynamical systems theory
Nonlinear dynamics

Background:

Billiard systems model complex dynamics.
Adiabatic invariance is crucial in conservative systems.
Slowly evolving systems can exhibit resonant phenomena.

Purpose of the Study:

Investigate particle dynamics in a rotating rectangular billiard with moving boundaries.
Analyze the impact of resonance conditions on particle behavior.
Examine the breakdown of adiabatic invariance.

Main Methods:

Canonical perturbation theory applied to a slowly rotating system.
Analysis of resonance conditions and their implications.
Study of scattering and capture phenomena.

Main Results:

Resonance conditions are identified during slow evolution.
Scattering and capture into resonance are observed.
Breakdown of adiabatic invariance leads to particle acceleration.

Conclusions:

Moving boundaries in rotating billiards can induce resonance.
Resonance phenomena are key to unlimited particle acceleration.
Adiabatic invariance is not preserved under these conditions.