Twist Property of Periodic Motion of an Atom Near a Charged Wire |
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Authors: | Lei Jinzhi Zhang Meirong |
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Institution: | (1) Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, People's Republic of China |
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Abstract: | We study the Lyapunov stability of periodic motion of an atom in the vicinity of an infinite straight wire with an oscillating uniform charge, which serves as a mechanism for trapping cold neutral atoms. It is proved by King and Leséniewski that the system has classical periodic motion for a certain range of parameters. In this Letter, we will prove, using the Birkhoff Normal Forms and Morse Twist Theorem, that such a periodic state is of twist type. As a result, besides the stability of the periodic state in the sense of Lyapunov, the system has infinitely many interesting bound states such as subharmonics and quasi-periodic states. |
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Keywords: | invariant closed curve oscillating charge periodic motion stability subharmonics twist coefficient |
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