Diffusion of particles moving with constant speed

Ramakrishna, S. Anantha ; Kumar, N. (1999) Diffusion of particles moving with constant speed Physical Review E, 60 (2). pp. 1381-1389. ISSN 1063-651X

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Official URL: http://pre.aps.org/abstract/PRE/v60/i2/p1381_1

Related URL: http://dx.doi.org/10.1103/PhysRevE.60.1381


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 <xn> along with an approximate expression for the marginal probability distribution function P(x,t) 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 (8t) only after which the diffusion approximation becomes valid. This factor of 8 is a well-known experimental fact. A persistence exponent of 0.435±0.005 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.

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Source:Copyright of this article belongs to American Physical Society.
ID Code:18352
Deposited On:17 Nov 2010 09:27
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