Renormalization of quantum anosov maps: Reduction to fixed boundary conditions

Itzhack Dana

Research output: Contribution to journalArticlepeer-review

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Abstract

A renormalization scheme is introduced to study quantum Anosov maps (QAMs) on a torus for general boundary conditions (BCs), whose number (k) is always finite. It is shown that the quasienergy eigenvalue problem of a QAM for all k BCs is exactly equivalent to that of the renormalized QAM (with Planck’s constant ħ𠄲 = ħ/k) at some fixed BCs that can be of four types. The quantum cat maps are, up to time reversal, fixed points of the renormalization transformation. Several results at fixed BCs, in particular the existence of a complete basis of “crystalline” eigenstates in a classical limit, can then be derived and understood in a simple and transparent way in the general-BCs framework.

Original languageEnglish
Pages (from-to)5994-5997
Number of pages4
JournalPhysical Review Letters
Volume84
Issue number26
DOIs
StatePublished - 26 Jun 2000

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