Linear dynamics of classical spin as Möbius transformation

Abstract Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enab...

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Autores principales:	Alexey Galda, Valerii М. Vinokur
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/c6b39563d9d24a2a8a99620fd2ae4499
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spelling	oai:doaj.org-article:c6b39563d9d24a2a8a99620fd2ae44992021-12-02T15:05:09ZLinear dynamics of classical spin as Möbius transformation10.1038/s41598-017-01326-x2045-2322https://doaj.org/article/c6b39563d9d24a2a8a99620fd2ae44992017-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01326-xhttps://doaj.org/toc/2045-2322Abstract Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Möbius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Möbius transformations, with the critical point of the transition corresponding to the parabolic transformation. This establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.Alexey GaldaValerii М. VinokurNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-5 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Alexey Galda Valerii М. Vinokur Linear dynamics of classical spin as Möbius transformation
description	Abstract Though the overwhelming majority of natural processes occur far from the equilibrium, general theoretical approaches to non-equilibrium phase transitions remain scarce. Recent breakthroughs introduced a description of open dissipative systems in terms of non-Hermitian quantum mechanics enabling the identification of a class of non-equilibrium phase transitions associated with the loss of combined parity (reflection) and time-reversal symmetries. Here we report that the time evolution of a single classical spin (e.g. monodomain ferromagnet) governed by the Landau-Lifshitz-Gilbert-Slonczewski equation in the absence of magnetic anisotropy terms is described by a Möbius transformation in complex stereographic coordinates. We identify the parity-time symmetry-breaking phase transition occurring in spin-transfer torque-driven linear spin systems as a transition between hyperbolic and loxodromic classes of Möbius transformations, with the critical point of the transition corresponding to the parabolic transformation. This establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.
format	article
author	Alexey Galda Valerii М. Vinokur
author_facet	Alexey Galda Valerii М. Vinokur
author_sort	Alexey Galda
title	Linear dynamics of classical spin as Möbius transformation
title_short	Linear dynamics of classical spin as Möbius transformation
title_full	Linear dynamics of classical spin as Möbius transformation
title_fullStr	Linear dynamics of classical spin as Möbius transformation
title_full_unstemmed	Linear dynamics of classical spin as Möbius transformation
title_sort	linear dynamics of classical spin as möbius transformation
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/c6b39563d9d24a2a8a99620fd2ae4499
work_keys_str_mv	AT alexeygalda lineardynamicsofclassicalspinasmobiustransformation AT valeriimvinokur lineardynamicsofclassicalspinasmobiustransformation
_version_	1718388920608096256

Linear dynamics of classical spin as Möbius transformation

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