Phase-space spinor amplitudes for spin-1/2 systems

Watson, P. and Bracken, A. J. (2011) Phase-space spinor amplitudes for spin-1/2 systems. Physical Review A, 83 4: 042102.1-042102.8. doi:10.1103/PhysRevA.83.042102

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Author Watson, P.
Bracken, A. J.
Title Phase-space spinor amplitudes for spin-1/2 systems
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
1094-1622
1538-4446
Publication date 2011-04-12
Sub-type Article (original research)
DOI 10.1103/PhysRevA.83.042102
Open Access Status DOI
Volume 83
Issue 4
Start page 042102.1
End page 042102.8
Total pages 8
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Subject 3107 Atomic and Molecular Physics, and Optics
Formatted abstract
The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-½ is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-½ magnetic dipole in a time-dependent magnetic field.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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