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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 6, Pages 3–20 (Mi izv663)  

This article is cited in 6 scientific papers (total in 6 papers)

Randomized Hamiltonian Feynman integrals and Shrödinger–Itô stochastic equations

J. E. Gougha, O. O. Obrezkovb, O. G. Smolyanovc

a Nottingham Trent University
b M. V. Lomonosov Moscow State University
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: In this paper, we consider stochastic Schrödinger equations with two-dimensional white noise. Such equations are used to describe the evolution of an open quantum system undergoing a process of continuous measurement. Representations are obtained for solutions of such equations using a generalization to the stochastic case of the classical construction of Feynman path integrals over trajectories in the phase space.

DOI: https://doi.org/10.4213/im663

Full text: PDF file (1673 kB)
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English version:
Izvestiya: Mathematics, 2005, 69:6, 1081–1098

Bibliographic databases:

UDC: 517.987.4
MSC: 35A8, 35C15, 35C20, 35R15, 35R60, 46L45, 46N50, 60H15, 60H99, 81Q05, 81Q10, 81Q30, 81S40
Received: 11.01.2005

Citation: J. E. Gough, O. O. Obrezkov, O. G. Smolyanov, “Randomized Hamiltonian Feynman integrals and Shrödinger–Itô stochastic equations”, Izv. RAN. Ser. Mat., 69:6 (2005), 3–20; Izv. Math., 69:6 (2005), 1081–1098

Citation in format AMSBIB
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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. Smolyanov O.G., “Feynman type formulae for quantum evolution and diffusion on manifolds and graphs”, Quantum bio-informatics III, QP–PQ: Quantum Probab. White Noise Anal., 26, World Sci. Publ., Hackensack, NJ, 2010, 337–347  crossref  mathscinet  adsnasa  isi
    2. Dürr D., Hinrichs G., Kolb M., “On a stochastic Trotter formula with application to spontaneous localization models”, J. Stat. Phys., 143:6 (2011), 1096–1119  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Unbounded random operators and Feynman formulae”, Izv. Math., 80:6 (2016), 1131–1158  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Obrezkov O.O., Smolyanov O.G., “Representations of solutions of Lindblad equations by randomized Feynman formulas”, Dokl. Math., 93:1 (2016), 74–77  crossref  mathscinet  zmath  isi  elib  scopus
    5. Fraas M., “Adiabatic Theorem For a Class of Stochastic Differential Equations on a Hilbert Space”, Functional Analysis and Operator Theory For Quantum Physics: the Pavel Exner Anniversary Volume, EMS Ser. Congr. Rep., eds. Dittrich J., Kovarik H., Laptev A., Eur. Math. Soc., 2017, 223–243  mathscinet  zmath  isi
    6. Loboda A.A., “Ito Method For Proving the Feynman-Kac Formula For the Euclidean Analog of the Stochastic Schrodinger Equation”, Differ. Equ., 54:4 (2018), 557–561  crossref  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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