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Title: 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 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 Mobius 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 Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.

Authors:
 [1]; ORCiD logo [1]
  1. 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) (SC-22), Materials Sciences and Engineering Division
OSTI Identifier:
1372900
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Scientific Reports
Additional Journal Information:
Journal Volume: 7; Journal Issue: 1; Journal ID: ISSN 2045-2322
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 М. Linear dynamics of classical spin as Mobius transformation. United States: N. p., 2017. Web. doi:10.1038/s41598-017-01326-x.
Galda, Alexey, & Vinokur, Valerii М. Linear dynamics of classical spin as Mobius transformation. United States. doi:10.1038/s41598-017-01326-x.
Galda, Alexey, and Vinokur, Valerii М. Wed . "Linear dynamics of classical spin as Mobius transformation". United States. doi:10.1038/s41598-017-01326-x. 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 М.},
abstractNote = {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 Mobius 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 Mobius transformations, with the critical point of the transition corresponding to the parabolic transformation. However, this establishes the understanding of non-equilibrium phase transitions as topological transitions in configuration space.},
doi = {10.1038/s41598-017-01326-x},
journal = {Scientific Reports},
number = 1,
volume = 7,
place = {United States},
year = {Wed Apr 26 00:00:00 EDT 2017},
month = {Wed Apr 26 00:00:00 EDT 2017}
}

Journal Article:
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