Non-positivity of Groenewold operators

Bracken, A. J. and Wood, J. G. (2004) Non-positivity of Groenewold operators. Europhysics Letters, 68 1: 1-7. doi:10.1209/epl/i2004-10175-8


Author Bracken, A. J.
Wood, J. G.
Title Non-positivity of Groenewold operators
Journal name Europhysics Letters   Check publisher's open access policy
ISSN 0295-5075
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1209/epl/i2004-10175-8
Open Access Status Not Open Access
Volume 68
Issue 1
Start page 1
End page 7
Total pages 7
Editor Pr. D.J. Jerome
Place of publication Les Ulis, France
Publisher E D P Science
Language eng
Abstract A central feature in the Hilbert space formulation of classical mechanics is the quantisation of classical Lionville densities, leading to what may be termed Groenewold operators. We investigate the spectra of the Groenewold operators that correspond to Gaussian and to certain uniform Lionville densities. We show that when the classical coordinate-momentum uncertainty product falls below Heisenberg's limit, the Groenewold operators in the Gaussian case develop negative eigenvalues and eigenvalues larger than 1. However, in the uniform case, negative eigenvalues are shown to persist for arbitrarily large values of the classical uncertainty product.
Keyword Wigner Function
Classical Mechanics
Quantum-mechanics
Phase-space
Dynamics
States
Physics, Multidisciplinary
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 13:03:41 EST