TY - JOUR
T1 - Supersymmetric theory of stochastic ABC model
AU - Ovchinnikov, Igor V.
AU - Sun, Yuquan
AU - Enßlin, Torsten A.
AU - Wang, Kang L.
N1 - Funding Information:
KLW would like to acknowledge the support from Raytheon endowed professorship. YQS would like to thank National Science Foundation of China for support (Grant No. 11201020) and Device Research Laboratory of the Electrical Engineering Department of UCLA for hospitality during his visit in 2015–2016. IVO and TAE would like to acknowledge the partial support of this work from Excellence Cluster Universe.
Publisher Copyright:
© 2018 The Author(s). Published by IOP Publishing Ltd.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2018/6
Y1 - 2018/6
N2 - In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterizes stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differential forms over the system’s phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that SEOs of all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possess pseudo-time-reversal symmetry, and each de Rham cohomology class provides one supersymmetric eigenstate. Our results also suggest that the SEO spectra for forms of complementary degrees, i.e., k and dim X −k, may be isospectral.
AB - In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterizes stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differential forms over the system’s phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that SEOs of all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possess pseudo-time-reversal symmetry, and each de Rham cohomology class provides one supersymmetric eigenstate. Our results also suggest that the SEO spectra for forms of complementary degrees, i.e., k and dim X −k, may be isospectral.
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U2 - 10.1088/2399-6528/aac94a
DO - 10.1088/2399-6528/aac94a
M3 - Article
AN - SCOPUS:85071927174
VL - 2
JO - Journal of Physics Communications
JF - Journal of Physics Communications
SN - 2399-6528
IS - 6
M1 - 065008
ER -