Linear dynamics of classical spin as Mobius transformation
Abstract
Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to nonequilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of nonHermitian quantum mechanics enabling the identification of a class of nonequilibrium phase transitions associated with the loss of combined parity (reflection) and timereversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the LandauLifshitzGilbertSlonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the paritytime symmetrybreaking phase transition occurring in spintransfer torquedriven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of nonequilibrium phase transitions as topological transitions in configuration space.
 Authors:
 Univ. of Chicago, Chicago, IL (United States); Argonne National Lab. (ANL), Argonne, IL (United States)
 Publication Date:
 Research Org.:
 Argonne National Lab. (ANL), Argonne, IL (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22), Materials Sciences and Engineering Division
 OSTI Identifier:
 1372900
 Grant/Contract Number:
 AC0206CH11357
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Scientific Reports
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 20452322
 Publisher:
 Nature Publishing Group
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Galda, Alexey, and Vinokur, Valerii Ð. Linear dynamics of classical spin as Mobius transformation. United States: N. p., 2017.
Web. doi:10.1038/s4159801701326x.
Galda, Alexey, & Vinokur, Valerii Ð. Linear dynamics of classical spin as Mobius transformation. United States. doi:10.1038/s4159801701326x.
Galda, Alexey, and Vinokur, Valerii Ð. 2017.
"Linear dynamics of classical spin as Mobius transformation". United States.
doi:10.1038/s4159801701326x. https://www.osti.gov/servlets/purl/1372900.
@article{osti_1372900,
title = {Linear dynamics of classical spin as Mobius transformation},
author = {Galda, Alexey and Vinokur, Valerii Ð.},
abstractNote = {Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to nonequilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of nonHermitian quantum mechanics enabling the identification of a class of nonequilibrium phase transitions associated with the loss of combined parity (reflection) and timereversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the LandauLifshitzGilbertSlonczewski equation in the absence of magnetic anisotropy terms is described by a Mobius transformation in complex stereographic coordinates. We identify the paritytime symmetrybreaking phase transition occurring in spintransfer torquedriven linear spin systems as a transition between hyperbolic and loxodromic classes of Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of nonequilibrium phase transitions as topological transitions in configuration space.},
doi = {10.1038/s4159801701326x},
journal = {Scientific Reports},
number = 1,
volume = 7,
place = {United States},
year = 2017,
month = 4
}

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