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Mat. Zametki, 1996, Volume 60, Issue 5, Pages 726–750 (Mi mz1885)  

This article is cited in 16 scientific papers (total in 16 papers)

Symmetric form of the Hudson-Parthasarathy stochastic equation

A. M. Chebotarev

M. V. Lomonosov Moscow State University, Faculty of Physics

Abstract: We prove that the Hudson–Parthasarathy equation corresponds, up to unitary equivalence, to the strong resolvent limit of Schrödinger Hamiltonians in Fock space and that the symmetric form of this equation corresponds to the weak limit of the Schrödinger Hamiltonians.

DOI: https://doi.org/10.4213/mzm1885

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English version:
Mathematical Notes, 1996, 60:5, 544–561

Bibliographic databases:

UDC: 519.217
Received: 19.12.1995

Citation: A. M. Chebotarev, “Symmetric form of the Hudson-Parthasarathy stochastic equation”, Mat. Zametki, 60:5 (1996), 726–750; Math. Notes, 60:5 (1996), 544–561

Citation in format AMSBIB
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\by A.~M.~Chebotarev
\paper Symmetric form of the Hudson-Parthasarathy stochastic equation
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\yr 1996
\vol 60
\issue 5
\pages 726--750
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\jour Math. Notes
\yr 1996
\vol 60
\issue 5
\pages 544--561
\crossref{https://doi.org/10.1007/BF02309169}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. M. Chebotarev, “The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation”, Math. Notes, 61:4 (1997), 510–518  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. D. V. Viktorov, “On the Ito multiplication table for second-order quantum stochastic processes”, Math. Notes, 63:5 (1998), 688–692  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. Chebotarev, AM, “Quantum stochastic differential equation is unitarily equivalent to a symmetric boundary value problem in Fock space”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 1:2 (1998), 175  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Gough, J, “Asymptotic stochastic transformations for nonlinear quantum dynamical systems”, Reports on Mathematical Physics, 44:3 (1999), 313  crossref  mathscinet  zmath  adsnasa  isi
    5. Albeverio, S, “On form-sum approximations of singularly perturbed positive self-adjoint operators”, Journal of Functional Analysis, 169:1 (1999), 32  crossref  mathscinet  zmath  isi  scopus  scopus
    6. O. Yu. Shvedov, “Renormalization of Lee-type models in spaces of arbitrary dimension”, Math. Notes, 68:1 (2000), 139–141  mathnet  crossref  mathscinet  zmath  isi
    7. Gregoratti, M, “On the Hamiltonian operator associated to some quantum stochastic differential equations”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 3:4 (2000), 483  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Shvedov, OY, “Exactly solvable quantum mechanical models with infinite renormalization of the wavefunction”, Journal of Physics A-Mathematical and General, 34:16 (2001), 3483  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. A. M. Chebotarev, G. V. Ryzhakov, “On the Strong Resolvent Convergence of the Schrödinger Evolution to Quantum Stochastics”, Math. Notes, 74:5 (2003), 717–733  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Shvedov, OY, “Approximations for strongly singular evolution equations”, Journal of Functional Analysis, 210:2 (2004), 259  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Gough, J, “Quantum flows as Markovian limit of emission, absorption and scattering interactions”, Communications in Mathematical Physics, 254:2 (2005), 489  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    12. Von Waldenfels W., “The Hamiltonian of a Simple Pure Number Process”, Quantum Probability and Infinite Dimensional Analysis, Qp-Pq Quantum Probability and White Noise Analysis, 18, ed. Schurmann M. Franz U., World Scientific Publ Co Pte Ltd, 2005, 518–524  mathscinet  isi
    13. Gough, J, “Quantum Stratonovich calculus and the quantum Wong-Zakai theorem”, Journal of Mathematical Physics, 47:11 (2006), 113509  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Derezinski J., De Roeck W., “Reduced and Extended Weak Coupling Limit”, Noncommutative Harmonic Analysis with Applications to Probability, Banach Center Publications, 78, eds. Bozejko M., Krystek A., Mlotkowski W., Wysoczanski J., Panstwowe Wydawnictwo Naukowe Polish Sci Publ, 2007, 91–119  crossref  mathscinet  isi
    15. Derezinski, J, “Extended weak coupling limit for Pauli-Fierz operators”, Communications in Mathematical Physics, 279:1 (2008), 1  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. von Waldenfels W., “The Singular Coupling Limit for a Simple Pure Number Process”, Stochastics, 84:2-3, SI (2012), 417–423  crossref  mathscinet  zmath  isi  scopus  scopus
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