Self-similarities in one-dimensional periodic and quasiperiodic systems

1989 ◽  
Vol 39 (1) ◽  
pp. 475-487 ◽  
Author(s):  
T. Odagaki ◽  
Hideaki Aoyama
Keyword(s):  
One Dimensional ◽  
Quasiperiodic Systems

scholarly journals On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-35 ◽  
Author(s):  
Enrique Maciá
Keyword(s):  
Transport Properties ◽  
Wave Functions ◽  
Critical States ◽  
One Dimensional ◽  
Precise Nature ◽  
Self Similar ◽  
Electronic Wave Functions ◽  
Quasiperiodic Systems ◽  
The Relationship ◽  
Singular Continuous Spectra

The interest in the precise nature of critical states and their role in the physics of aperiodic systems has witnessed a renewed interest in the last few years. In this work we present a review on the notion of critical wave functions and, in the light of the obtained results, we suggest the convenience of some conceptual revisions in order to properly describe the relationship between the transport properties and the wave functions distribution amplitudes for eigen functions belonging to singular continuous spectra related to both fractal and quasiperiodic distribution of atoms through the space.

scholarly journals Interaction instability of localization in quasiperiodic systems

2018 ◽  
Vol 115 (18) ◽  
pp. 4595-4600 ◽  
Author(s):  
Marko Žnidarič ◽  
Marko Ljubotina
Keyword(s):  
Transport Properties ◽  
Quantum Systems ◽  
Theoretical Physics ◽  
Solvable Models ◽  
Many Body ◽  
Small Perturbations ◽  
One Dimensional ◽  
Quasiperiodic Potential ◽  
Quasiperiodic Systems ◽  
Small Interactions

Integrable models form pillars of theoretical physics because they allow for full analytical understanding. Despite being rare, many realistic systems can be described by models that are close to integrable. Therefore, an important question is how small perturbations influence the behavior of solvable models. This is particularly true for many-body interacting quantum systems where no general theorems about their stability are known. Here, we show that no such theorem can exist by providing an explicit example of a one-dimensional many-body system in a quasiperiodic potential whose transport properties discontinuously change from localization to diffusion upon switching on interaction. This demonstrates an inherent instability of a possible many-body localization in a quasiperiodic potential at small interactions. We also show how the transport properties can be strongly modified by engineering potential at only a few lattice sites.

Phonon properties of a class of one-dimensional quasiperiodic systems

1990 ◽  
Vol 41 (11) ◽  
pp. 7491-7496 ◽  
Author(s):  
J. Q. You ◽  
Q. B. Yang ◽  
J. R. Yan
Keyword(s):  
One Dimensional ◽  
Quasiperiodic Systems ◽  
Phonon Properties

ELECTRONIC SPECTRAL AND WAVEFUNCTION PROPERTIES OF ONE-DIMENSIONAL QUASIPERIODIC SYSTEMS: A SCALING APPROACH

1992 ◽  
Vol 06 (03n04) ◽  
pp. 281-320 ◽  
Author(s):  
HISASHI HIRAMOTO ◽  
MAHITO KOHMOTO
Keyword(s):  
Finite Difference ◽  
Finite Number ◽  
Smooth Function ◽  
Wave Functions ◽  
Continuous Part ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Dense Point ◽  
Quasiperiodic Systems ◽  
Localized Wavefunctions

We review the results of the scaling and multifractal analyses for the spectra and wave-functions of the finite-difference Schrödinger equation: [Formula: see text] Here V is a function of period 1 and ω is irrational. For the Fibonacci model, V takes only two values (it is constant except for discontinuities) and the spectrum is purely singular continuous (critical wavefunctions). When V is a smooth function, the spectrum is purely absolutely continuous (extended wavefunctions) for λ small and purely dense point (localized wavefunctions) for λ large. For an intermediate λ, the spectrum is a mixture of absolutely continuous parts and dense point parts which are separated by a finite number of mobility edges. There is no singular continuous part. (An exception is the Harper model V (x) = cos (2πx), where the spectrum is always pure and the singular continuous one appears at λ = 2.)

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