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Volumn 58, Issue 1, 1998, Pages 128-134

Complete positivity of nonlinear evolution: A case study

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EID: 0001058856     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.128     Document Type: Article
Times cited : (33)

References (58)
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  • 8
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    • Some reservations with respect to a fundamental importance of CP were expressed in W. A. Majewski, Fortschr. Phys. 32, 89 (1984).FPYKA6
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  • 17
    • 85037237835 scopus 로고    scopus 로고
    • Note for math purists: The isomorphism is (Formula presented). (Formula presented) depends on the choice of the basis (Formula presented). Take two different bases. The problem with the Ando-Choi-Arveson map (Formula presented) is that the diagram (Formula presented) is noncommutative
    • Note for math purists: The isomorphism is (Formula presented). (Formula presented) depends on the choice of the basis (Formula presented). Take two different bases. The problem with the Ando-Choi-Arveson map (Formula presented) is that the diagram (Formula presented) is noncommutative.
  • 19
    • 0000722186 scopus 로고
    • JMAPAQ
    • A formalism of mean-field theories especially useful in the context of this paper was given in P. Bóna, J. Math. Phys. 29, 2223 (1988); JMAPAQ
    • (1988) J. Math. Phys. , vol.29 , pp. 2223
    • Bóna, P.1
  • 20
    • 0006340307 scopus 로고
    • J. Math. Phys.P. Bóna30, 2994 (1989).
    • (1989) , vol.30 , pp. 2994
    • Bóna, P.1
  • 26
    • 85037200001 scopus 로고    scopus 로고
    • T. Ando and M.-D. Choi, in Aspects of Positivity in Functional Analysis, edited by R. Nagel, U. Schlotterbeck, and B. V. Wolff (North-Holland, Amsterdam, 1986)
    • T. Ando and M.-D. Choi, in Aspects of Positivity in Functional Analysis, edited by R. Nagel, U. Schlotterbeck, and B. V. Wolff (North-Holland, Amsterdam, 1986).
  • 30
    • 85037201009 scopus 로고    scopus 로고
    • This statement seems to apply to the nonuniqueness of (Formula presented), which is always determined up to a transformation (Formula presented) stabilizing (Formula presented)
    • This statement seems to apply to the nonuniqueness of (Formula presented), which is always determined up to a transformation (Formula presented) stabilizing (Formula presented), see [15,32].
  • 37
    • 85037207854 scopus 로고    scopus 로고
    • this concrete example the dynamics is on coadjoint orbits of, respectively, (Formula presented) (Formula presented), and (Formula presented). Quantum mechanics with mean-field backgrounds, as well as a Jordan-Weinberg-type version of nonlinear quantum mechanics were described in a mathematically precise way in the language of coadjoint orbits in P. Bóna, Comenius University report Ph10-91 (1991). This is probably the first paper where a mathematically and physically correct version of a Lie-Poisson nonlinear quantum mechanics of density matrices was formulated
    • In this concrete example the dynamics is on coadjoint orbits of, respectively, (Formula presented) (Formula presented), and (Formula presented). Quantum mechanics with mean-field backgrounds, as well as a Jordan-Weinberg-type version of nonlinear quantum mechanics were described in a mathematically precise way in the language of coadjoint orbits in P. Bóna, Comenius University report Ph10-91 (1991). This is probably the first paper where a mathematically and physically correct version of a Lie-Poisson nonlinear quantum mechanics of density matrices was formulated.
  • 42
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    • Commun. Math. Phys.B. Mielnik37, 221 (1969).
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  • 46
    • 85037183000 scopus 로고    scopus 로고
    • We propose the following methodological principle (“Doebner-Goldin razor”): If you discover an impossibility principle stating that any nonlinear modification of quantum mechanics is impossible, first perform the following test. Take a nonlinearly gauge transformed Schrödinger or Liouville–von Neumann equation. If you use a Doebner-Goldin transformation with the parameter (Formula presented) then the transformed equation will have the ordinary kinetic and potential terms but in addition some nonlinearity will appear. Now use this nonlinear dynamics as an example you tried to rule out by your theorem
    • We propose the following methodological principle (“Doebner-Goldin razor”): If you discover an impossibility principle stating that any nonlinear modification of quantum mechanics is impossible, first perform the following test. Take a nonlinearly gauge transformed Schrödinger or Liouville–von Neumann equation. If you use a Doebner-Goldin transformation with the parameter (Formula presented) then the transformed equation will have the ordinary kinetic and potential terms but in addition some nonlinearity will appear. Now use this nonlinear dynamics as an example you tried to rule out by your theorem.
  • 47
  • 58
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    • M. Czachor, e-print quant-ph/9711054.
    • Czachor, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.