Quantum chaos on a toral phase space for general boundary conditions: Recent new results

Itzhack Dana

Research output: Contribution to journalArticlepeer-review

Abstract

This paper is a brief review of recent new results for the quantum-chaos problem on a 2D toral phase space for general boundary conditions (BCs) on the torus. The following results will be reviewed and discussed: (a) The new concept of band distribution for Hamiltonians periodic in phase space. (b) Expressions for the general smooth torus map and for the condition determining the allowed quantum BCs associated with this map. (c) An exact renormalization scheme for quantum Anosov maps on the torus, which `eliminates' the general-BCs problem, replacing it by a fixed-BCs one.

Original languageEnglish
Pages (from-to)542-547
Number of pages6
JournalPhysica E: Low-Dimensional Systems and Nanostructures
Volume9
Issue number3
DOIs
StatePublished - Mar 2001

Bibliographical note

Funding Information:
The author would like to thank M. Wilkinson, K. Zyczkowski, and Z. Rudnick for discussions. This work was partially supported by the Israel Science Foundation administered by the Israel Academy of Sciences and Humanities.

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