Chaos and exponentially localized eigenstates in smooth Hamiltonian systems

1997/03/31 by M. S. Santhanam, V B Sheorey, V. B. Sheorey +2 · 3 citations
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #Theoretical and Computational Physics #chao-dyn #nlin.CD

paper · pdf · doi:10.1103/physreve.57.345

7pages including 7 figures. Submitted to PRL

arxiv created 1997/03/31 · openalex publication_date 1998/01/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present numerical evidence to show that the wave functions of smooth classically chaotic Hamiltonian systems scarred by certain simple periodic orbits are exponentially localized in the space of unperturbed basis states. The degree of localization, as measured by the information entropy, is shown to be correlated with the local phase-space structure around the scarring orbit. Sharp localization is observed when the orbit scarring the wave function undergoes a pitchfork bifurcation and loses stability.

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