The model is defined by the following evolution operator H ^ ^ = L ^ ^ − − ∂ ∂ U + Θ Θ [ d ^ ^ , d ^ ^ † † ] , where ( ∂ ∂ U ) i = g i j ∂ ∂ j U with g being the metric, [ d ^ ^ , d ^ ^ † † ] is the Hodge Laplacian, and the differential forms from the exterior algebra of the phase space, Ω Ω ( X ) , are viewed as wavefunctions. There exists a similarity transformation, H ^ ^ → → H ^ ^ U = e U / 2 Θ Θ H ^ ^ e − − U / 2 Θ Θ , that brings the evolution operator to the explicitly Hermitian form H ^ ^ U = Θ Θ [ d ^ ^ U , d ^ ^ U † † ] with d ^ ^ U = e U / 2 Θ Θ d ^ ^ e − − U / 2 Θ Θ = χ χ i ( ∂ ∂ / ∂ ∂ x i − − ∂ ∂ i U / 2 Θ Θ ) . In the Euclidean case, H ^ ^ U is the Hamiltonian of a N=2 supersymmetric quantum mechanics. One can introduce two Hermitian operators, q ^ ^ 1 = ( d ^ ^ U + d ^ ^ U † † ) / 2 1 / 2 and q ^ ^ 2 = i ( d ^ ^ U − − d ^ ^ U † † ) / 2 1 / 2 , such that H ^ ^ U = Θ Θ q ^ ^ 1 2 = Θ Θ q ^ ^ 2 2 . This demonstrates that the spectrum of H ^ ^ U and/or H ^ ^ is real and nonnegative. This is also true for SEOs of Langevin SDEs. For the SDEs of arbitrary form, however, this is no longer true as the eigenvalues of the SEO can be negative and even complex, which actually allows for the TS to be broken spontaneously.