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On the factorization method for the quantum statistical description of dynamics of an isolated spin system

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Abstract

We study the applicability of the formula that factors the trace of the diagonal part of spin operator products in the case of a relatively small number of particles of an isolated spin system. The validity of this formula for a large number of particles follows from the basic principles of quantum statistical mechanics. The spin system under consideration includes dipole–dipole interaction and the Zeeman interaction with an external magnetic field. We establish that the accuracy of this formula monotonically increases as the magnetic field increases. At the same time, the dependence on the number of particles in the range \(2\div10\) for various configurations turns out to be sharply nonmonotone.

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Funding

This research was supported by the Russian Science Foundation under grant No. 19-11-00338, https://rscf.ru/en/project/en/19-11-00338/.

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Authors and Affiliations

  1. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, Russia

    A. A. Samokhin

  2. Marchuk Institute of Numerical Mathematics, Russian Academy of Science, Moscow, Russia

    A. V. Zyl & N. L. Zamarashkin

  3. Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia

    A. V. Zyl

Authors
  1. A. A. Samokhin
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  2. A. V. Zyl
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  3. N. L. Zamarashkin
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Correspondence to A. V. Zyl.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2024, Vol. 218, pp. 522–536 https://doi.org/10.4213/tmf10603.

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Samokhin, A.A., Zyl, A.V. & Zamarashkin, N.L. On the factorization method for the quantum statistical description of dynamics of an isolated spin system. Theor Math Phys 218, 452–463 (2024). https://doi.org/10.1134/S0040577924030061

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  • DOI: https://doi.org/10.1134/S0040577924030061

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