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Volumn 57, Issue 6, 1998, Pages 4122-4129

Nonlocal-looking equations can make nonlinear quantum dynamics local

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EID: 0000914322     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.57.4122     Document Type: Article
Times cited : (38)

References (47)
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    • The notion of weak and strong separability was investigated by Goldin and Svetlichny [G. A. Goldin (private communication)] and discussed in G. A. Goldin (unpublished)
    • The notion of weak and strong separability was investigated by Goldin and Svetlichny [G. A. Goldin (private communication)] and discussed in G. A. Goldin (unpublished).
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    • H.-D. Doebner, G. A. Goldin, and P. Nattermann, in Quantization, Coherent States, and Complex Structures, edited by J.-P. Antoine et al. (Plenum, New York, 1995), p. 27
    • H.-D. Doebner, G. A. Goldin, and P. Nattermann, in Quantization, Coherent States, and Complex Structures, edited by J.-P. Antoine et al. (Plenum, New York, 1995), p. 27.
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    • Density matrices can, of course, evolve in a nonlinear way. A spectacular example of a nonlinear evolution of a density matrix is the interference in a Bose-Einstein condensate. It is known that the interference fringes recently observed by Andrews et al. and Mewes et al. 19 20 are well approximated by a nonlinear (Formula presented) Schrödinger equation. The atomic clouds in a trap cannot be in a pure state because the atoms are highly entangled with laser photons
    • Density matrices can, of course, evolve in a nonlinear way. A spectacular example of a nonlinear evolution of a density matrix is the interference in a Bose-Einstein condensate. It is known that the interference fringes recently observed by Andrews et al. and Mewes et al. 1920 are well approximated by a nonlinear (Formula presented) Schrödinger equation. The atomic clouds in a trap cannot be in a pure state because the atoms are highly entangled with laser photons.
  • 33
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  • 35
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    • For technical reasons I restrict my analysis to nondissipative equations since inclusion of imaginary terms in Hamiltonians does not allow for an immediate application of the triple bracket results. This does not mean that such an extension is impossible
    • For technical reasons I restrict my analysis to nondissipative equations since inclusion of imaginary terms in Hamiltonians does not allow for an immediate application of the triple bracket results. This does not mean that such an extension is impossible.
  • 36
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    • This nonlinearity results from a (Formula presented) limit of a (Formula presented)-deformed Schrödinger equation; cf. R. Twarock, Ph.D. thesis, Technical University of Clausthal, 1997 (unpublished)
    • This nonlinearity results from a (Formula presented) limit of a (Formula presented)-deformed Schrödinger equation; cf. R. Twarock, Ph.D. thesis, Technical University of Clausthal, 1997 (unpublished).
  • 39
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    • A general result guarantees that (Formula presented) is time independent and a Casimir invariant. This means, in particular, that the triple-bracket dynamics preserves the purity of states
    • A general result guarantees that (Formula presented) is time independent and a Casimir invariant. This means, in particular, that the triple-bracket dynamics preserves the purity of states 1428.
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    • This appears to be in conflict with the analysis given in
    • This appears to be in conflict with the analysis given in 2 where, assuming (Formula presented) and weak separability, it was concluded that (Formula presented). There is no contradiction, however. Take (Formula presented). According to our general scheme the two-particle nonlinearity is (Formula presented), as expected. In 2 it was assumed that the two-particle nonlinearity is (Formula presented).
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