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Russian Journal of Mathematical Physics

, Volume 19, Issue 4, pp 440–448 | Cite as

Cubic algebra and averaged Hamiltonian for the resonance 3: (−1) Penning-ioffe trap

  • O. Blagodyreva
  • M. KarasevEmail author
  • E. Novikova
Article

Abstract

For the 3: (−1) resonance Penning trap, we describe the algebra of symmetries which turns out to be a non-Lie algebra with cubic commutation relations. The irreducible representations and coherent states of this algebra are constructed explicitly. The perturbing inhomogeneous magnetic field of Ioffe type, after double quantum averaging, generates an effective Hamiltonian of the trap. In the irreducible representation, this Hamiltonian becomes a second-order ordinary differential operator of the Heun type.

Keywords

Irreducible Representation Coherent State Transverse Mode Symmetry Algebra Paul Trap 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Moscow Institute for Electronics and Mathematics at HSEMoscowRussia

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