Quantum Fluctuations and the Lorenz Equations

Abstract

The quantization of the Lorenz equations is shown to take the form 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 unique fractal dimension can be associated with the stochastic process. For large noises there is a radical breakdown of this picture.