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Discussion on generalized formulation of spin semiclassical Langevin equation
School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China.
KTH, School of Engineering Sciences (SCI), Applied Physics, Materials and Nanophysics.ORCID iD: 0000-0003-1661-9572
School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China.
School of Physics and Optoelectronics, South China University of Technology, Guangzhou 510640, China.
2023 (English)In: Wuli xuebao, ISSN 1000-3290, Vol. 72, no 14, article id 140501Article in journal (Refereed) Published
Abstract [en]

The stochastic dynamics of spin semiclassical system at finite temperature is usually described by stochastic Landau-Lifshitz equation. In this work, the stochastic differential equation for spin semiclassical system is studied. The generalized formulation of effective Langevin equation and the corresponding Fokker-Planck equation are derived. The obtained effective Langevin equation offers an accurate description of the distribution in the canonical ensemble for spin semiclassical system. When the damping term and the stochastic term vanish, the effective Langevin equation reduces to the semiclassical equation of motion for spin system. Hence, the effective Langevin equation can be seen as a generalization of the stochastic Landau-Lifshitz equation. The explicit expressions for the effective Langevin equation and the corresponding Fokker-Planck equation are shown in both Cartesian coordinates and spherical coordinates. It is demonstrated that, the longitudinal effect can be easily illustrated from the expressions in spherical coordinates. The effective Langevin equation is applied to the simple system of a single spin in a constant magnetic field. Choosing an appropriate form, the Langevin equation can be easily solved and the stationary Boltzmann distribution can be obtained. The correctness of the Langevin approach for the spin semiclassical system is thus confirmed.

Place, publisher, year, edition, pages
Acta Physica Sinica, Chinese Physical Society and Institute of Physics, Chinese Academy of Sciences , 2023. Vol. 72, no 14, article id 140501
Keywords [en]
Boltzmann distribution, Fokker-Planck equation, Langevin equation, stochastic Landau-Lifshitz equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-335318DOI: 10.7498/aps.72.20230106ISI: 001045012400022Scopus ID: 2-s2.0-85166479184OAI: oai:DiVA.org:kth-335318DiVA, id: diva2:1794304
Note

QC 20230905

Available from: 2023-09-05 Created: 2023-09-05 Last updated: 2023-09-05Bibliographically approved

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Lu, Zhiwei

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