Complete solvability of the inertial spin model with an averaged spin

Huh, Hyungjin; Kim, Dohyun

doi:10.1090/qam/1601

Authors: Hyungjin Huh and Dohyun Kim
Journal: Quart. Appl. Math. 80 (2022), 53-67
MSC (2020): Primary 34C15; Secondary 34D06, 34C40
DOI: https://doi.org/10.1090/qam/1601
Published electronically: October 14, 2021
MathSciNet review: 4360549
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Abstract: We study the inertial spin model which consists of two variables: velocity as a mechanical observable and spin as an internal variable. In this paper, we slightly modified the original inertial spin model where the spin in the dynamics of the velocity is replaced by the average of spins. Moreover, by introducing two external control functions (rotation control and alignment control), we show the emergence of velocity and spin alignments mainly depends on these control functions. Finally, we perform numerical simulations that support and complement our theoretical results.

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