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1998 | 43 | 1 | 119-133
Tytuł artykułu

Quantum stochastic processes arising from the strong resolvent limits of the Schrödinger evolution in Fock space

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EN
Abstrakty
EN
By using F. A. Berezin's canonical transformation method [5], we derive a nonadapted quantum stochastic differential equation (QSDE) as an equation for the strong limit of the family of unitary groups satisfying the Schrödinger equation with singularly degenerating Hamiltonians in Fock space. Stochastic differentials of QSDE generate a nonadapted associative Ito multiplication table, and the coefficients of these differentials satisfy the formal unitarity conditions of the Hudson-Parthasarathy type [10].
Słowa kluczowe
Rocznik
Tom
43
Numer
1
Strony
119-133
Opis fizyczny
Daty
wydano
1998
Twórcy
  • Moscow State University, Faculty of Physics, Quantum Statistics Department, Moscow 119899, Russia
  • Moscow State University, Faculty of Physics, Quantum Statistics Department, Moscow 119899, Russia
Bibliografia
  • [1] L. Accardi, Y.-G. Lu and I. Volovich, Non-linear Extensions of Classical and Quantum StochastCalculus and Essentially Infinite Dimensional Analysis, V. Volterra Center, Università di Roma Tor Vergata, Preprint No 268, 1996.
  • [2] S. Albeverio, F. Gesztesy and R. Hoegh-Krohn, Solvable models in Quantum mechanics, Springer-Verlag, New-York, Berlin, London, 1988.
  • [3] S. Albeverio, W. Karwowski and V. D. Koshmanenko, Square powers of singularly perturbed operators, Math. Nachr., Vol. 173, 1995, 5-24.
  • [4] V. P. Belavkin and P. Staszewski, Nondemolition observation of a free quantum particle, Phys. Rev. A, Vol. 45, 1992, 1347-1356.
  • [5] F. A. Berezin, The Method of Second Quantization, Academic Press, New-York, 1996.
  • [6] A. M. Chebotarev, Quantum stochastic differential equation as a strong resolvent limit of the Schrödinger evolution, in: IV Simposio de Probabilidad y Procesos Estochasticos, Gunajuato, Mexico, 1996, Societad Mat. Mexicana, 1996, 71-89.
  • [7] A. M. Chebotarev, Symmetric form of the Hudson-Parthasarathy equation, Mathematical Notes, Vol. 60, N5, 1996, 544-561.
  • [8] A. M. Chebotarev, Quantum stochastic differential equation is unitarily equivalent to a boundary value problem for the Schrödinger equation, Mathematical Notes, Vol. 61, N4, 1997, 510-519.
  • [9] C. W. Gardiner and M. J. Collett, Input and output in damped quantum systems: quantum statistical differential equations and the master equation, Phys. Rev. A, Vl. 31, 1985, 3761-3774.
  • [10] R. L. Hudson and K. R. Parthasarathy, Quantum Ito's formula and stochastic evolutions, Commun. Math. Phys., Vol. 93, N3, 1984, 301-323.
  • [11] Ka T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer-Verlag, Berlin-Heidelberg-New York, 1980.
  • [12], Naukova dumka, Kiev, 1993.
  • [13] P. A. Meyer, Quantum probability for probabilists, Lecture Notes in Math., vol. 1338, 1993.
  • [14] K. R. Parthasarathy, An introduction to quantum stochastic calculus, Birkhäuser, Basel, 1992.
  • [15] P. Zoller and C. W. Gardiner, Quantum Noise in Quantum Optics: the Stochastic Schödinger Equation, To appear in: Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluctuations in July 1995, Edited by E. Giacobino and S. Reynaud, Elsevier Science Publishers B.V., 1997.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv43i1p119bwm
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