Abstract
It is shown that the stationary fluctuations described by the diffusion equation of an effective space dimension less than one have a 1/f spectrum. A physical diffusion model equivalent to such a low dimensional diffusion process is proposed. Here, a singular disturbance of temperature fluctuation is assumed to diffuse with the space-dependent diffusion coefficient D(r)=D0(1+κr−m)θ. Here, D0 is the constant part of the diffusion coefficient and κr−m represents the effect of local temperature enhancement of the background medium caused by the singular disturbance itself, where r is the distance from the singular disturbance at r=0, and m and θ positive constants.
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