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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 218, Number 3, Pages 522–536
DOI: https://doi.org/10.4213/tmf10603 (Mi tmf10603) 		 
On the factorization method for the quantum statistical description of dynamics of an isolated spin system

A. A. Samokhina, A. V. Zylbc, N. L. Zamarashkinb

a Prokhorov General Physics Institute of the Russian Academy of Sciences, Moscow, Russia
b Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow, Russia
c Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
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DOI: https://doi.org/10.4213/tmf10603
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.
Keywords: spin temperature, isolated spin system, density matrix, factorization formula, dependence on the number of particles.
Funding agency Grant number
Russian Science Foundation 19-11-00338
This research was supported by the Russian Science Foundation under grant No. 19-11-00338, https://rscf.ru/en/project/en/19-11-00338/.
Received: 04.09.2023
Revised: 18.10.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 218, Issue 3, Pages 452–463
DOI: https://doi.org/10.1134/S0040577924030061
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Document Type: Article
Language: Russian
Citation: A. A. Samokhin, A. V. Zyl, N. L. Zamarashkin, “On the factorization method for the quantum statistical description of dynamics of an isolated spin system”, TMF, 218:3 (2024), 522–536; Theoret. and Math. Phys., 218:3 (2024), 452–463
Citation in format AMSBIB
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\by A.~A.~Samokhin, A.~V.~Zyl, N.~L.~Zamarashkin
\paper On the factorization method for the quantum statistical description of dynamics of an isolated spin system
\jour TMF
\yr 2024
\vol 218
\issue 3
\pages 522--536
\mathnet{http://mi.mathnet.ru/tmf10603}
\crossref{https://doi.org/10.4213/tmf10603}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4721383}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...218..452S}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 218
\issue 3
\pages 452--463
\crossref{https://doi.org/10.1134/S0040577924030061}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85188461135}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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