Secondary resonances in Penning traps. Non-Lie symmetry algebras and quantum states

DOI10.1134/S1061920813030047zbMath1292.81043MaRDI QIDQ2441292

E. M. Novikova, Mikhail V. Karasev

Publication date: 24 March 2014

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Ion traps (78A37)

Related Items (10)

Bi-states and 2-level systems in rectangular Penning traps ⋮ Instantons via breaking geometric symmetry in hyperbolic traps ⋮ Bi-orbital states in hyperbolic traps ⋮ Quantization due to breaking the commutativity of symmetries. Wobbling oscillator and anharmonic Penning trap ⋮ Non-Lie top tunneling and quantum bilocalization in planar Penning trap ⋮ Eigenstates of the quantum Penning-Ioffe nanotrap at resonance ⋮ Algebra of symmetries of three-frequency hyperbolic resonance ⋮ Advances in quantization: quantum tensors, explicit star-products, and restriction to irreducible leaves ⋮ Inserted perturbations generating asymptotical integrability ⋮ Planar Penning trap with combined resonance and top dynamics on quadratic algebra

Cites Work

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• Cubic algebra and averaged Hamiltonian for the resonance \(3: ( - 1)\) Penning-Ioffe trap
• Coherent transform of the spectral problem and algebras with nonlinear commutation relations.
• Algebra and quantum geometry of multifrequency resonance
• Coherent states approach to Penning trap
• Asymptotic and geometric quantization
• On the Penning trap coherent states
• Quantum surfaces, special functions, and the tunneling effect

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