The quantisation of the Lorenz equations is shown to take the form of a set of two complex and one real stochastic differential equations with multiplicative noise. Phase diffusion is the dominant feature for small values of the noise. Quantities such as the probability of the modulus of the variables are unchanged from those in the classical Lorenz equations. Moreover a fractal dimension can be associated with the stochastic process for sufficiently small noise. For large noises there is a radical breakdown of this picture.
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Sarkar et al. (1986) studied this question.
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