Geodesic
On the factorization method for the quantum statistical description of dynamics of an isolated spin system
Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 522-536 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {On the factorization method for the quantum statistical description of dynamics of an isolated spin system},
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 218 (2024) no. 3, pp. 522-536. http://geodesic.mathdoc.fr/item/TMF_2024_218_3_a5/

[1] A. Abragam, Yadernyi magnetizm, IL, M., 1963

[2] J. A. Tjon, “On the quantum statistical theory of relaxation in isolated spin systems II”, Physica, 30:7 (1964), 1341–1364 | DOI | MR

[3] A. A. Samokhin, “Ob adiabaticheskom priblizhenii dlya matritsy plotnosti izolirovannoi spin-sistemy”, ZhETF, 51:3 (1966), 928–930

[4] A. A. Samokhin, “Theory of nonlinear response of an isolated spin system”, Physica, 39:4 (1968), 541–559 | DOI

[5] D. Sakellariou, P. Hodgkinson, L. Emsley, “Quasi equilibria in solid-state NMR”, Chem. Phys. Lett., 293:1–2 (1998), 110–118 | DOI

[6] J. S. Waug, “Equilibrium and ergodicity in small spin systems”, Mol. Phys., 95:5 (1998), 731–735 | DOI

[7] A. A. Samokhin, “Ob adiabaticheskom priblizhenii v statisticheskoi mekhanike”, TMF, 5:3 (1970), 439–445 | DOI

[8] A. Polkovnikov, K. Sengupta, A. Silva, M. Vengalattore, “Colloquium: Nonequilibrium dynamics of closed interacting quantum systems”, Rev. Mod. Phys., 83:3 (2011), 863–883 | DOI

[9] K. R. A. Hazzard, B. Gadway, M. Foss-Feig, Bo Yan, S. A. Moses, J. P. Covey, N. Y. Yao, M. D. Lukin, J. Ye, D. S. Jin, A. M. Rey, “Many-body dynamics of dipolar molecules in an optical lattice”, Phys. Rev. Lett., 113:19 (2014), 195302, 5 pp. | DOI

[10] L. D'Alessio, Y. Kafri, A. Polkovnikov, M. Rigol, “From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics”, Adv. Phys., 65:3 (2016), 239–362 | DOI

[11] L. S. Blackford, J. Demmel, J. Dongarra et al., “An updated set of basic linear algebra subprograms (BLAS)”, ACM Trans. Math. Software, 28:2 (2002), 135–151 | DOI | MR

[12] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, D. Sorensen, LAPACK Users{'} Guide, SIAM, Philadelphia, PA, 1999