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TMF, 2015, Volume 184, Number 1, Pages 106–116 (Mi tmf8803)  

This article is cited in 4 scientific papers (total in 4 papers)

Analyzing the dependence of finite-fold approximations of the harmonic oscillator equilibrium density matrix and of the Wigner function on the quantization prescription

L. A. Borisova, Yu. N. Orlovb

a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow Oblast, Russia
b Keldysh Institute for Applied Mathematics, RAS, Moscow, Russia

Abstract: For an arbitrary statistical mixture of $\tau$-quantizations, we obtain an explicit expression for the leading parts of the equilibrium density matrix and for the corresponding Wigner function of a harmonic oscillator in the approach of Feynman approximations using the Chernoff theorem. Taking the oscillator Hamiltonian as an example, we determine the convergence rate for approximations of means of operators of observables depending on the approximation order and depending on the quantization rule. We demonstrate that the convergence rate of approximations of the mean of the energy operator is not uniform with respect to the Gibbs parameter.

Keywords: Feynman approximation, Chernoff theorem, quantization rule, density matrix, harmonic oscillator

DOI: https://doi.org/10.4213/tmf8803

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English version:
Theoretical and Mathematical Physics, 2015, 184:1, 986–995

Bibliographic databases:

Received: 20.10.2014

Citation: 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”, TMF, 184:1 (2015), 106–116; Theoret. and Math. Phys., 184:1 (2015), 986–995

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. Yu. N. Orlov, “O kommutatsii kvantovykh operatorov pervykh integralov gamiltonovykh sistem”, Preprinty IPM im. M. V. Keldysha, 2018, 018, 15 pp.  mathnet  crossref  elib
    4. Ya. G. Batischeva, “Zadacha Koshi dlya novoi modeli agregatsii-drobleniya v sluchae ravnykh konstant reaktsii”, Preprinty IPM im. M. V. Keldysha, 2020, 006, 28 pp.  mathnet  crossref
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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