Multifractal analysis of mobility edge in a one-dimensional quasiperiodic system

We investigate the gap formation probability of the effective one-dimensional gas model recently proposed for the energy level statistics for disordered solids at the mobility edge. It is found that in order to get the correct form for the gap probability of this model, the thermodynamic limit must be taken very carefully.

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Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials

Physical Review B ◽

10.1103/physrevb.101.064203 ◽

2020 ◽

Vol 101 (6) ◽

Cited By ~ 4

Author(s):

Xiao Li ◽

S. Das Sarma

Keyword(s):

Intermediate Phase ◽

Mobility Edge ◽

One Dimensional

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NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

International Journal of Modern Physics B ◽

10.1142/s0217979291000444 ◽

1991 ◽

Vol 05 (05) ◽

pp. 825-841 ◽

Cited By ~ 1

Author(s):

WLODZIMIERZ SALEJDA

Keyword(s):

Vibrational Spectrum ◽

Multifractal Analysis ◽

Scaling Laws ◽

Model Parameters ◽

Local Scaling ◽

One Dimensional ◽

Dynamic Matrix ◽

Numerical Studies ◽

Wide Range ◽

The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

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EQUIVALENCE IN GEOMETRIC SCALING OF TRANSPORT PROPERTIES AND WAVEFUNCTIONS

International Journal of Modern Physics B ◽

10.1142/s021797929300233x ◽

1993 ◽

Vol 07 (05) ◽

pp. 1309-1319 ◽

Cited By ~ 1

Author(s):

CHAITALI BASU ◽

ABHIJIT MOOKERJEE

Keyword(s):

Transport Properties ◽

Anderson Model ◽

Multifractal Analysis ◽

Resonance State ◽

Electron States ◽

One Dimensional ◽

Geometric Scaling ◽

Multifractal Scaling

The transport properties and wavefunction behave identically with respect to multifractal scaling. To establish the above statement, we carried out multifractal analysis on normalised transmittance and normalised wavefunction of two types of electron states, namely the resonance state and the localised state of a one-dimensional Anderson model.

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MULTIFRACTAL ANALYSIS OF ONE-DIMENSIONAL BIASED WALKS

Fractals ◽

10.1142/s0218348x18500305 ◽

2018 ◽

Vol 26 (03) ◽

pp. 1850030 ◽

Cited By ~ 6

Author(s):

YUFEI CHEN ◽

MEIFENG DAI ◽

XIAOQIAN WANG ◽

YU SUN ◽

WEIYI SU

Keyword(s):

Random Walk ◽

Hausdorff Dimension ◽

Multifractal Analysis ◽

Infinite Sequence ◽

Real Numbers ◽

One Dimensional ◽

Dimension Formula ◽

Sum Of Digits ◽

Packing Dimensions ◽

Dyadic System

For an infinite sequence [Formula: see text] of [Formula: see text] and [Formula: see text] with probability [Formula: see text] and [Formula: see text], we mainly study the multifractal analysis of one-dimensional biased walks. Let [Formula: see text] and [Formula: see text]. The Hausdorff and packing dimensions of the sets [Formula: see text] are [Formula: see text], which is the development of the theorem of Besicovitch [On the sum of digits of real numbers represented in the dyadic system, Math. Ann. 110 (1934) 321–330] on random walk, saying that: For any [Formula: see text], the set [Formula: see text] has Hausdorff dimension [Formula: see text].

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