BAND DISTRIBUTIONS FOR QUANTUM CHAOS ON A TORUS

Band distributions (BDs) are introduced describing quantization in a t oral phase space. A ED is the uniform average of an eigenstate phase-s pace probability distribution over a band of toral boundary conditions . A general explicit expression for the Wigner ED is obtained. It is s hown that the Wigner functions for all of the band eigenstates can be reproduced from the Wigner ED. Also, BDs are shown to be closer to cla ssical distributions than eigenstate distributions. Generalized BDs, a ssociated with sets of adjacent bands, are used to extend in a natural way the Chern-index characterization of the classical-quantum corresp ondence on the torus to arbitrary rational values of the scaled Planck constant. [S0031-9007(98)07286-X].