Quantum and classical ergodicity of spinning particles

Abstract

We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of freedom and the two-sphere. On this product space we introduce a combination of the translational motion and classical spin precession. We prove quantum ergodicity under the condition that this product flow is ergodic.

17 pages, no figures

References in corpus (6)

• A semiclassical approach to the Dirac equation
• Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles
• Semiclassical limit of the Dirac equation and spin precession
• Quantum ergodicity of C* dynamical systems
• Semiclassical form factor for chaotic systems with spin 1/2
• Quantum ergodicity for Pauli Hamiltonians with spin 1/2

Cited by in corpus (9)

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• Semiclassical approximations for Hamiltonians with operator-valued symbols
• The semiclassical propagator in fermionic Fock space
• Zitterbewegung and semiclassical observables for the Dirac equation
• Torus quantization for spinning particles
• Semiclassical propagation of coherent states with spin-orbit interaction
• Semiclassical limits for the QCD Dirac operator
• Semiclassics for particles with spin via a Wigner-Weyl-type calculus
• Semiclassical time evolution and quantum ergodicity for Dirac-Hamiltonians