Semiquantum versus semiclassical mechanics for simple nonlinear systems

Bracken, A. J. and Wood, J. G. (2006) Semiquantum versus semiclassical mechanics for simple nonlinear systems. Physical Review A, 73 1: 012104-1-012104-10. doi:10.1103/PhysRevA.73.012104

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Author Bracken, A. J.
Wood, J. G.
Title Semiquantum versus semiclassical mechanics for simple nonlinear systems
Journal name Physical Review A   Check publisher's open access policy
ISSN 1050-2947
Publication date 2006-01
Sub-type Article (original research)
DOI 10.1103/PhysRevA.73.012104
Open Access Status File (Publisher version)
Volume 73
Issue 1
Start page 012104-1
End page 012104-10
Total pages 10
Editor Gordon W. F. Drake
Margaret Malloy
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2006
Language eng
Subject 240201 Theoretical Physics
780101 Mathematical sciences
010503 Mathematical Aspects of Classical Mechanics, Quantum Mechanics and Quantum Information Theory
Abstract Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.
Keyword Optics
Physics, Atomic, Molecular & Chemical
Quantum-mechanics
Phase-space
Classical Mechanics
Dynamics
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Published 10 January 2006

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Physical Sciences Publications
 
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Created: Mon, 13 Aug 2007, 15:56:30 EST