Twice Scattered Particles in a Plane Are Uniformly Distributed |
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Authors: | Ricardo García-Pelayo |
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Institution: | (1) ETS de Ingeniería Aeronáutica, Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros, 3, Madrid, 28040, Spain |
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Abstract: | It was recently shown (Physica A 216:299–315, 1995) that in two dimensions the sum of three vectors each of whose lengths is exponentially distributed, whose direction is uniformly
distributed and such that the sum of their lengths is l, is uniformly distributed on a disk of radius l. We state here this random walk result in terms of scattering of particles as follows: in two dimensions twice isotropically
scattered particles by random (i.e., Poisson distributed) scatterers are uniformly distributed. We show that there is no other
dimension d and no other number of scatterings s for which the corresponding result (i.e., uniform distribution on a d-dimensional sphere after s scatterings) holds. |
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Keywords: | Continuous time random walk Multiple scattering |
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