Supersymmetric Theory of Stochastic ABC Model: A Numerical Study
  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 characterises
stochastic differential equations (SDEs) by the spectrum of the stochastic
evolution operator (SEO) on elements of the exterior algebra or differentials
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 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 possesses
pseudo-time-reversal symmetry, and each de Rahm cohomology class provides one
supersymmetric eigenstate. Our results also suggests that the SEO spectra for
forms of complementary degrees, i.e., k and dim X -k, may be isospectral.
