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

A. A. Samokhin^a, A. V. Zyl^bc, N. L. Zamarashkin<sup>b

a</sup> 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

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.

Received: 04.09.2023
Revised: 18.10.2023

DOI: 10.4213/tmf10603

 English version: Theoretical and Mathematical Physics, 2024, 218:3, 452–463

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