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Tr. Mat. Inst. Steklova, 2014, Volume 285, Pages 232–243 (Mi tm3539)  

This article is cited in 21 scientific papers (total in 21 papers)

Feynman formulas as a method of averaging random Hamiltonians

Yu. N. Orlova, V. Zh. Sakbaevb, O. G. Smolyanovc

a M. V. Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (State University), Dolgoprudnyi, Russia
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia

Abstract: We propose a method for finding the mathematical expectation of random unbounded operators in a Hilbert space. The method is based on averaging random one-parameter semigroups by means of the Feynman–Chernoff formula. We also consider an application of this method to the description of various operations that assign quantum Hamiltonians to the classical Hamilton functions.


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English version:
Proceedings of the Steklov Institute of Mathematics, 2014, 285, 222–232

Bibliographic databases:

Document Type: Article
UDC: 517.98
Received in February 2014

Citation: Yu. N. Orlov, V. Zh. Sakbaev, O. G. Smolyanov, “Feynman formulas as a method of averaging random Hamiltonians”, Selected topics of mathematical physics and analysis, Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth, Tr. Mat. Inst. Steklova, 285, MAIK Nauka/Interperiodica, Moscow, 2014, 232–243; Proc. Steklov Inst. Math., 285 (2014), 222–232

Citation in format AMSBIB
\by Yu.~N.~Orlov, V.~Zh.~Sakbaev, O.~G.~Smolyanov
\paper Feynman formulas as a~method of averaging random Hamiltonians
\inbook Selected topics of mathematical physics and analysis
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Vasilii Sergeevich Vladimirov's birth
\serial Tr. Mat. Inst. Steklova
\yr 2014
\vol 285
\pages 232--243
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2014
\vol 285
\pages 222--232

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    This publication is cited in the following articles:
    1. L. A. Borisov, Yu. N. Orlov, “Analyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescription”, Theoret. and Math. Phys., 184:1 (2015), 986–995  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. I. D. Remizov, “Solution to a parabolic differential equation in Hilbert space via Feynman formula - I”, Model. i analiz inform. sistem, 22:3 (2015), 337–355  mathnet  crossref  mathscinet  elib
    3. L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Formuly Feinmana dlya usredneniya polugrupp, porozhdaemykh operatorami tipa Shredingera”, Preprinty IPM im. M. V. Keldysha, 2015, 057, 23 pp.  mathnet
    4. L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Ekvivalentnost po Chernovu primenitelno k uravneniyam evolyutsii matritsy plotnosti i funktsii Vignera dlya lineinogo kvantovaniya”, Preprinty IPM im. M. V. Keldysha, 2015, 066, 28 pp.  mathnet
    5. L. S. Efremova, V. Zh. Sakbaev, “Notion of blowup of the solution set of differential equations and averaging of random semigroups”, Theoret. and Math. Phys., 185:2 (2015), 1582–1598  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    6. V. Zh. Sakbaev, “On the law of large numbers for compositions of independent random semigroups”, Russian Math. (Iz. VUZ), 60:10 (2016), 72–76  mathnet  crossref  mathscinet  isi  elib  elib
    7. 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
    8. V. G. Sakbaev, O. G. Smolyanov, “_orig analogues of feynman formulas for ill-posed problems associated with the schrodinger equation”, Dokl. Math., 94:3 (2016), 654–658  crossref  mathscinet  zmath  isi  scopus
    9. I. D. Remizov, “Quasi-Feynman formulas – a method of obtaining the evolution operator for the Schrödinger equation”, J. Funct. Anal., 270:12 (2016), 4540–4557  crossref  mathscinet  zmath  isi  elib  scopus
    10. I. D. Remizov, “Feynman and quasi-Feynman formulas for evolution equations”, Dokl. Math., 96:2 (2017), 433–437  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    11. I. D. Remizov, “New method for constructing Chernoff functions”, Differ. Equ., 53:4 (2017), 566–570  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    12. Ya. A. Butko, “Chernoff approximation of subordinate semigroups”, Stoch. Dyn., 18:3 (2018), 1850021, 19 pp.  crossref  mathscinet  zmath  isi  scopus
    13. V. Zh. Sakbaev, “Averaging of random flows of linear and nonlinear maps”, European Conference - Workshop Nonlinear Maps and Applications, Journal of Physics Conference Series, 990, IOP Publishing Ltd, 2018, UNSP 012012  crossref  isi  scopus
    14. L. A. Borisov, Yu. N. Orlov, V. Zh. Sakbaev, “Feynman averaging of semigroups generated by Schrödinger operators”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:2 (2018), 1850010, 13 pp.  crossref  mathscinet  zmath  isi  scopus
    15. L. A. Borisov, Y. N. Orlov, V. J. Sakbaev, “Chernoff equivalence for shift operators, generating coherent states in quantum optics”, Lobachevskii J. Math., 39:6 (2018), 742–746  crossref  mathscinet  isi  scopus
    16. Yu. N. Orlov, “O kommutatsii kvantovykh operatorov pervykh integralov gamiltonovykh sistem”, Preprinty IPM im. M. V. Keldysha, 2018, 018, 15 pp.  mathnet  crossref
    17. Yu. N. Orlov, A. B. Kozlova, M. B. Korsakova, E. L. Masherov, A. A. Kislitsyn, “Statsionarnaya tochka urovnya znachimosti dlya nestatsionarnykh funktsii raspredeleniya”, Preprinty IPM im. M. V. Keldysha, 2018, 113, 20 pp.  mathnet  crossref
    18. Yu. N. Orlov, V. Zh. Sakbaev, “Feynman–Chernoff iterations and their applications in quantum dynamics”, Proc. Steklov Inst. Math., 301 (2018), 197–206  mathnet  crossref  crossref  isi  elib  elib
    19. I. D. Remizov, “Explicit formula for evolution semigroup for diffusion in Hilbert space”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 21:4 (2018), 1850025, 35 pp.  crossref  mathscinet  isi  scopus
    20. Ya. A. Butko, “Chernoff approximation for semigroups generated by killed Feller processes and Feynman formulae for time-fractional Fokker-Planck-Kolmogorov equations”, Fract. Calc. Appl. Anal., 21:5 (2018), 1203–1237  crossref  mathscinet  isi  scopus
    21. A. A. Kislitsyn, Yu. N. Orlov, D. A. Moltchanov, A. K. Samuylov, A. V. Chukarin, Yu. V. Gaidamaka, “On the distribution of the stationary point of significance level for empirical distribution function”, 2018 10th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT 2018): Emerging Technologies For Connected Society, International Conference on Ultra Modern Telecommunications and Control Systems & Workshops, IEEE, 2018  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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