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.

Manifestation of the DX Centre in Heavily δ-Doped GaAs(Si)

1992 ◽  
Vol 281 ◽  
Author(s):  
S. Arscott ◽  
M. Missous ◽  
L. Dobaczewski ◽  
P. C. Harness ◽  
D. K. Maude ◽  
...  
Keyword(s):  
Molecular Beam Epitaxy ◽  
Transport Properties ◽  
Electron Concentration ◽  
Low Temperatures ◽  
Molecular Beam ◽  
Wave Functions ◽  
Potential Well ◽  
Electronic Wave ◽  
Hall Measurements ◽  
Electronic Wave Functions

ABSTRACTShubnikov-de Haas and Hall measurements have been performed on singly delta doped GaAs(Si) structures, grown by molecular beam epitaxy, enabling us to study the effects of illumination and temperature upon bulk and individual subband, mobilities and carrier concentrations. In a highly doped sample, where the peak 3D electron concentration approaches 2×1019cm−3, we have observed novel changes in subband transport characteristics, not observed in the lower doped samples, which we attribute to the presence of DX centre phenomena. This paper explains the variations in individual subband transport properties due to a possible shift of the electronic wave functions contained in the potential well. This shift occurs due to a recombination-autoionization(R-A) process involving filled DX centres and free holes upon sample illumination at low temperatures.

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.

scholarly journals Chemical Bonding and Physical Properties in Quasicrystals and Their Related Approximant Phases: Known Facts and Current Perspectives

2019 ◽  
Vol 9 (10) ◽  
pp. 2132 ◽  
Author(s):  
Enrique Maciá Barber
Keyword(s):  
Physical Properties ◽  
Transport Properties ◽  
Chemical Bonding ◽  
Structural Design ◽  
Wave Functions ◽  
Underlying Structure ◽  
Transmission Characteristics ◽  
Covalent Bonds ◽  
Self Similar ◽  
Metallic Bonding

Quasicrystals are a class of ordered solids made of typical metallic atoms but they do not exhibit the physical properties that usually signal the presence of metallic bonding, and their electrical and thermal transport properties resemble a more semiconductor-like than metallic character. In this paper I first review a number of experimental results and numerical simulations suggesting that the origin of the unusual properties of these compounds can be traced back to two main features. For one thing, we have the formation of covalent bonds among certain atoms grouped into clusters at a local scale. Thus, the nature of chemical bonding among certain constituent atoms should play a significant role in the onset of non-metallic physical properties of quasicrystals bearing transition-metal elements. On the other hand, the self-similar symmetry of the underlying structure gives rise to the presence of an extended chemical bonding network due to a hierarchical nesting of clusters. This novel structural design leads to the existence of quite diverse wave functions, whose transmission characteristics range from extended to almost localized ones. Finally, the potential of quasicrystals as thermoelectric materials is discussed on the basis of their specific transport properties.

Self-similar elastic regime of filtration through moving boundary

2018 ◽  
Vol 13 (3) ◽  
pp. 64-72 ◽  
Author(s):  
S.V. Khabirov ◽  
S.S. Khabirov
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Elastic Regime ◽  
Self Similar ◽  
The One ◽  
The Relationship

The one-dimensional problem of elastic filtration of fluid through moving boundary is considered. The boundary conditions for invariant problem is introduced. The problem is reduced to overdetermine boundary problem for Veber equation. The exact solutions are obtained. For arbitrary invariant filtration law the relationship between overdetermine invariant boundary conditions is obtained.

A Model Dielectric Function for Semiconductors

1975 ◽  
Vol 53 (23) ◽  
pp. 2549-2554 ◽  
Author(s):  
R. D. Grimes ◽  
E. R. Cowley
Keyword(s):  
Dielectric Function ◽  
Energy Gap ◽  
Interpolation Formula ◽  
Electron System ◽  
Wave Functions ◽  
Three Dimensions ◽  
Energy Bands ◽  
One Dimensional ◽  
Energy Gaps ◽  
The Relationship

The microscopic dielectric function is calculated for a simple model of a semiconductor, originally proposed by Penn, in which the energy bands and wave functions are those of a one-dimensional, nearly free electron system, isotropically extended to three dimensions. The dielectric function is evaluated numerically so that all unnecessary approximations are avoided. The relationship between the static dielectric constant and the energy gap is found to be[Formula: see text]where S0 is about 0.6. The results for finite wave vectors, for a range of energy gaps, have been fitted to an interpolation formula to facilitate their use.

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.)

Trace Maps

1997 ◽  
Vol 11 (30) ◽  
pp. 3525-3542 ◽  
Author(s):  
Yshai Avishai ◽  
Daniel Berend ◽  
Vadim Tkachenko
Keyword(s):  
General Class ◽  
Wave Functions ◽  
Transfer Matrices ◽  
One Dimensional ◽  
Trace Map ◽  
Underlying Space ◽  
Substitution Potentials ◽  
Discrete Schrödinger Operators ◽  
Quasiperiodic Systems ◽  
Trace Maps

Trace maps for products of transfer matrices prove to be an important tool in the investigation of electronic spectra and wave functions of one-dimensional quasiperiodic systems. These systems belong to a general class of substitution sequences. In this work we review the various stages of development in constructing trace maps for products of (2×2) matrices generated by arbitrary substitution sequences. The dimension of the underlying space of the trace map obtained by means of this construction is the minimal possible, namely 3r-3 for an alphabet of size r≥2. In conclusion, we describe some results from the spectral theory of discrete Schrödinger operators with substitution potentials.

Electronic Wave Functions in One-Dimensional Disordered Systems

1972 ◽  
Vol 6 (12) ◽  
pp. 4482-4490 ◽  
Author(s):  
B. Y. Tong ◽  
T. C. Wong
Keyword(s):  
Disordered Systems ◽  
Wave Functions ◽  
One Dimensional ◽  
Electronic Wave ◽  
Electronic Wave Functions
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