BAND HUSIMI DISTRIBUTIONS AND THE CLASSICAL-QUANTUM CORRESPONDENCE ONTHE TORUS

Band Husimi distributions (BHDs) are introduced in the quantum-chaos p roblem on a toral phase space. In the framework of this phase space, a quantum state must satisfy Bloch boundary conditions (BCs) on a torus and the spectrum consists of a finite number of levels for given BCs. As the BCs are varied, a level broadens into a band. The BHD for a ba nd is defined as the uniform average of the Husimi distributions for a ll the eigenstates in the band. The generalized BHD for a set of adjac ent bands is the average of the BHDs associated with these bands. BHDs are shown to be closer, in several aspects, to classical distribution s than Husimi distributions for individual eigenstates. The generalize d BHD for two adjacent bands is shown to be approximately conserved in the passage through a degeneracy between the bands as a nonintegrabil ity parameter is varied. Finally, it is shown how generalized BHDs can be defined so as to achieve physical continuity under small variation s of the scaled Planck constant. A generalization of the topological ( Chern-index) characterization of the classical-quantum correspondence is then obtained. [S1063-651X(98)03011-6].