Band Husimi distributions and the classical-quantum correspondence on the torus

Itzhack Dana, Yaakov Rutman, Mario Feingold

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Band Husimi distributions (BHDs) are introduced in the quantum-chaos problem 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 band is defined as the uniform average of the Husimi distributions for all the eigenstates in the band. The generalized BHD for a set of adjacent bands is the average of the BHDs associated with these bands. BHDs are shown to be closer, in several aspects, to classical distributions than Husimi distributions for individual eigenstates. The generalized BHD for two adjacent bands is shown to be approximately conserved in the passage through a degeneracy between the bands as a nonintegrability parameter is varied. Finally, it is shown how generalized BHDs can be defined so as to achieve physical continuity under small variations of the scaled Planck constant. A generalization of the topological (Chern-index) characterization of the classical-quantum correspondence is then obtained.

Original languageEnglish
Pages (from-to)5655-5667
Number of pages13
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
StatePublished - 1 Jan 1998

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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