4 research outputs found
Diffusion of particles moving with constant speed
The propagation of light in a scattering medium is described as the motion of
a special kind of a Brownian particle on which the fluctuating forces act only
perpendicular to its velocity. This enforces strictly and dynamically the
constraint of constant speed of the photon in the medium. A Fokker-Planck
equation is derived for the probability distribution in the phase space
assuming the transverse fluctuating force to be a white noise. Analytic
expressions for the moments of the displacement along with an
approximate expression for the marginal probability distribution function
are obtained. Exact numerical solutions for the phase space
probability distribution for various geometries are presented. The results show
that the velocity distribution randomizes in a time of about eight times the
mean free time () only after which the diffusion approximation becomes
valid. This factor of eight is a well known experimental fact. A persistence
exponent of is calculated for this process in two dimensions
by studying the survival probability of the particle in a semi-infinite medium.
The case of a stochastic amplifying medium is also discussed.Comment: 9 pages, 9 figures(Submitted to Phys. Rev. E