CHAOTIC ANALYTIC ZERO POINTS - EXACT STATISTICS FOR THOSE OF A RANDOMSPIN-STATE

A natural statistical ensemble of 2J points on the unit sphere can be associated, via the Majorana representation, with a random quantum sta te of spin J, and an exact expression is obtained here for the general k point correlation function rho(k) in this ensemble. The pair correl ation rho(2) in the large-J limit takes the relatively simple form (J/ 2 pi)(2)g(root J/29) where g(r) = [(sinh(2) r(2) + r(4)) cosh r(2) - 2 r(2) sinh(2)]/sinh(3) r(2) and theta theta is the angular separation o f the pair of points on the sphere. It appears (from the numerical wor k of others) that, in this limit, these statistics are typical of the zero points of analytic functions associated with chaotic quantum dyna mical systems.