REPELLER STRUCTURE IN A HIERARCHICAL MODEL .1. TOPOLOGICAL PROPERTIES

R LIVI, A POLITI, S RUFFO

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrodinger equation is studied. Analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set, whose structure undergoes relevant changes when the growth rate R of the potential barriers is modified. The minimal region containing the repeller is determined and the mechanism originating a Cantor set structure along the unstable manifold is revealed. The repeller is continuous along the stable manifold for R < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum for R < 1 and we present the associated wavefunctions.

Original languageEnglish
Pages (from-to)53-72
Number of pages20
JournalJournal of Statistical Physics
Volume65
Issue number1-2
Publication statusPublished - Oct 1991

Keywords

  • STRANGE REPELLERS
  • LOCALIZATION
  • SCHRODINGER OPERATOR
  • HIERARCHICAL STRUCTURES
  • RENORMALIZATION GROUP
  • RENORMALIZATION-GROUP
  • SPECTRUM
  • ULTRADIFFUSION
  • SYSTEMS

Cite this

REPELLER STRUCTURE IN A HIERARCHICAL MODEL .1. TOPOLOGICAL PROPERTIES. / LIVI, R ; POLITI, A ; RUFFO, S .

In: Journal of Statistical Physics, Vol. 65, No. 1-2, 10.1991, p. 53-72.

Research output: Contribution to journalArticle

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N2 - The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrodinger equation is studied. Analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set, whose structure undergoes relevant changes when the growth rate R of the potential barriers is modified. The minimal region containing the repeller is determined and the mechanism originating a Cantor set structure along the unstable manifold is revealed. The repeller is continuous along the stable manifold for R < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum for R < 1 and we present the associated wavefunctions.

AB - The repeller associated with the renormalization dynamics of the spectral problem of a hierarchical tight-binding Schrodinger equation is studied. Analysis of escaping regions and of stable and unstable manifolds provide complementary descriptions of the recurrent set, whose structure undergoes relevant changes when the growth rate R of the potential barriers is modified. The minimal region containing the repeller is determined and the mechanism originating a Cantor set structure along the unstable manifold is revealed. The repeller is continuous along the stable manifold for R < 2. Finally, we show the existence of a pointlike component of the spectrum located at its upper extremum for R < 1 and we present the associated wavefunctions.

KW - STRANGE REPELLERS

KW - LOCALIZATION

KW - SCHRODINGER OPERATOR

KW - HIERARCHICAL STRUCTURES

KW - RENORMALIZATION GROUP

KW - RENORMALIZATION-GROUP

KW - SPECTRUM

KW - ULTRADIFFUSION

KW - SYSTEMS

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JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

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