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Detailed Balance and Intermediate Statistics
We present a theory of particles, obeying intermediate statistics ("anyons"),
interpolating between Bosons and Fermions, based on the principle of Detailed
Balance. It is demonstrated that the scattering probabilities of identical
particles can be expressed in terms of the basic numbers, which arise naturally
and logically in this theory. A transcendental equation determining the
distribution function of anyons is obtained in terms of the statistics
parameter, whose limiting values 0 and 1 correspond to Bosons and Fermions
respectively. The distribution function is determined as a power series
involving the Boltzmann factor and the statistics parameter and we also express
the distribution function as an infinite continued fraction. The last form
enables one to develop approximate forms for the distribution function, with
the first approximant agreeing with our earlier investigation.Comment: 13 pages, RevTex, submitted for publication; added references; added
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