Comments on the Dynamics of the Pais-Uhlenbeck Oscillator

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2009
• Main Author: Smilga, A.V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2009
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/149243
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Comments on the Dynamics of the Pais-Uhlenbeck Oscillator / A.V. Smilga // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 14 назв. — англ.

We discuss the quantum dynamics of the PU oscillator, i.e. the system with the Lagrangian 
 L = ½ [ ¨q² - (Ω₁² + Ω₂²) ·q² + Ω₁²Ω₂²q ] (+ nonlinear terms). 
 When Ω₁ ≠ Ω₂, the free PU oscillator has a pure point spectrum that is dense everywhere. When Ω₁ = Ω₂, the spectrum is contin...