Critical states and fractal attractors in fractal tongues: localization in the Harper map.

نویسندگان

  • S S Negi
  • R Ramaswamy
چکیده

Localized states of Harper's equation correspond to strange nonchaotic attractors in the related Harper mapping. In parameter space, these fractal attractors with nonpositive Lyapunov exponents occur in fractally organized tongue-like regions which emanate from the Cantor set of eigenvalues on the critical line epsilon=1. A topological invariant characterizes wave functions corresponding to energies in the gaps in the spectrum. This permits a unique integer labeling of the gaps and also determines their scaling properties as a function of potential strength.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

M ay 2 00 1 Dynamics of the Harper map : Localized states , Cantor spectra and Strange nonchaotic attractors

The Harper (or “almost Mathieu”) equation plays an important role in studies of localization. Through a simple transformation, this equation can be converted into an iterative two dimensional skew–product mapping of the cylinder to itself. Localized states of the Harper system correspond to fractal attractors with nonpositive maximal Lyapunov exponent in the dynamics of the associated Harper ma...

متن کامل

Critical Localization and Strange Nonchaotic Dynamics: The Fibonacci Chain

The discrete Schrödinger equation with a quasiperiodic dichotomous potential specified by the Fibonacci sequence is known to have a singular continuous eigenvalue spectrum with all states being critically localized. This equation can be transformed into a quasiperiodic skew product dynamical system. In this iterative mapping which is entirely equivalent to the Schrödinger problem, critically lo...

متن کامل

Transmission properties of one dimensional fractal structures

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...

متن کامل

A Critique on Power Spectrum – Area Fractal Method for Geochemical Anomaly Mapping

Power spectrum – area fractal (S-A fractal) method has been frequently applied for geochemical anomaly mapping. Some researchers have performed this method for separation of geochemical anomaly, background and noise and have delineated their distribution maps. In this research, surface geochemical data of Zafarghand Cu-Mo mineralization area have been utilized and some defects of S-A fractal me...

متن کامل

Application of fractal modeling and PCA method for hydrothermal alteration mapping in the Saveh area (Central Iran) based on ASTER multispectral data

The aim of this study is determination and separation of alteration zones using Concentration-Area (C-A) fractal model based on remote sensing data which has been extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images. The studied area is on the SW part of Saveh, 1:250,000 geological map, which is located in Urumieh-Dokhtar magmatic belt, Central Iran. The ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Physical review. E, Statistical, nonlinear, and soft matter physics

دوره 64 4 Pt 2  شماره 

صفحات  -

تاریخ انتشار 2001