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Torus quantization for spinning particles.

Stefan Keppeler1

  • 1Abteilung Theoretische Physik, Universität Ulm, Albert-Einstein-Alle 11, D-89069 Ulm, Germany. stefan.keppeler@physik.uni-ulm.de

Physical Review Letters
|November 22, 2002
PubMed
Summary

We developed new semiclassical quantization rules for spinning particles, extending existing methods. A novel Berry phase correction, related to spin rotation, is introduced alongside the Maslov correction.

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Area of Science:

  • Quantum mechanics
  • Mathematical physics

Background:

  • Semiclassical quantization methods are crucial for understanding quantum systems.
  • The Einstein-Brillouin-Keller (EBK) method provides quantization conditions for classical systems.
  • Geometric phases, such as the Berry phase, play a significant role in quantum mechanics.

Purpose of the Study:

  • To generalize the Einstein-Brillouin-Keller quantization conditions for particles with spin.
  • To incorporate non-Abelian geometric phases into semiclassical quantization.
  • To interpret the physical meaning of the new correction term.

Main Methods:

  • Derivation of semiclassical quantization conditions.
  • Application of concepts from non-Abelian geometric phase theory.
  • Analysis of the Maslov correction in the context of spin.

Main Results:

  • New semiclassical quantization conditions for particles with spin have been derived.
  • A novel correction term, representing a remnant of a non-Abelian geometric or Berry phase, was identified.
  • This correction is interpreted as a rotation angle for a classical spin vector.

Conclusions:

  • The derived quantization conditions offer a more complete semiclassical description for spinning particles.
  • The inclusion of Berry phase effects provides deeper insight into the quantum-classical correspondence for systems with spin.
  • The findings have implications for understanding spin dynamics in semiclassical regimes.

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