scholarly journals Anderson Localization for Electric Quantum Walks and Skew-Shift CMV Matrices

2021 ◽  
Author(s):  
C. Cedzich ◽  
A. H. Werner
Keyword(s):  
Electric Fields ◽  
Anderson Localization ◽  
Quantum Walks ◽  
Discrete Version ◽  
Band Matrices ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Coupling Principle ◽  
Almost All

AbstractWe consider the spectral and dynamical properties of one-dimensional quantum walks placed into homogenous electric fields according to a discrete version of the minimal coupling principle. We show that for all irrational fields the absolutely continuous spectrum of these systems is empty, and prove Anderson localization for almost all (irrational) fields. This result closes a gap which was left open in the original study of electric quantum walks: a spectral and dynamical characterization of these systems for typical fields. Additionally, we derive an analytic and explicit expression for the Lyapunov exponent of this model. Making use of a connection between quantum walks and CMV matrices our result implies Anderson localization for CMV matrices with a particular choice of skew-shift Verblunsky coefficients as well as for quasi-periodic unitary band matrices.

scholarly journals Necessary Condition for Rectifiability Involving Wasserstein Distance W2

2020 ◽  
Author(s):  
Damian Dąbrowski
Keyword(s):  
Hausdorff Measure ◽  
Radon Measure ◽  
Recent Article ◽  
Wasserstein Distance ◽  
Necessary Condition ◽  
Absolutely Continuous ◽  
Dimensional Hausdorff Measure ◽  
Almost All

Abstract A Radon measure $\mu $ is $n$-rectifiable if it is absolutely continuous with respect to $n$-dimensional Hausdorff measure and $\mu $-almost all of ${\operatorname{supp}}\mu $ can be covered by Lipschitz images of $\mathbb{R}^n$. In this paper, we give a necessary condition for rectifiability in terms of the so-called $\alpha _2$ numbers — coefficients quantifying flatness using Wasserstein distance $W_2$. In a recent article, we showed that the same condition is also sufficient for rectifiability, and so we get a new characterization of rectifiable measures.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Characterization of Minimum Route MTM in One-Dimensional Multi-Hop Wireless Networks

2009 ◽  
Vol E92-A (9) ◽  
pp. 2227-2235 ◽  
Author(s):  
Kazuyuki MIYAKITA ◽  
Keisuke NAKANO ◽  
Masakazu SENGOKU ◽  
Shoji SHINODA
Keyword(s):  
Wireless Networks ◽  
One Dimensional

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

A Thorough Theoretical Exploration of Intriguing Characteristics of Cyclo[18]carbon: Geometry, Bonding Nature, Aromaticity, Weak Interaction, Reactivity, Excited States, Vibrations, Molecular Dynamics and Various Molecular Properties

2019 ◽  
Author(s):  
Tian Lu ◽  
Qinxue Chen ◽  
Zeyu Liu
Keyword(s):  
Molecular Dynamics ◽  
Excited States ◽  
Electronic Excitation ◽  
Ring Structure ◽  
Molecular Properties ◽  
Molecular Vibration ◽  
Full Characterization ◽  
Long Time ◽  
Almost All

Although cyclo[18]carbon has been theoretically and experimentally investigated since long time ago, only very recently it was prepared and directly observed by means of STM/AFM in condensed phase (Kaiser et al., <i>Science</i>, <b>365</b>, 1299 (2019)). The unique ring structure and dual 18-center π delocalization feature bring a variety of unusual characteristics and properties to the cyclo[18]carbon, which are quite worth to be explored. In this work, we present an extremely comprehensive and detailed investigation on almost all aspects of the cyclo[18]carbon, including (1) Geometric characteristics (2) Bonding nature (3) Electron delocalization and aromaticity (4) Intermolecular interaction (5) Reactivity (6) Electronic excitation and UV/Vis spectrum (7) Molecular vibration and IR/Raman spectrum (8) Molecular dynamics (9) Response to external field (10) Electron ionization, affinity and accompanied process (11) Various molecular properties. We believe that our full characterization of the cyclo[18]carbon will greatly deepen researchers' understanding of this system, and thereby help them to utilize it in practice and design its various valuable derivatives.

Physicochemical and bacteriological characterization of hospital effluents and their impact on the environment

2019 ◽  
Author(s):  
Chem Int
Keyword(s):  
Human Health ◽  
Fecal Coliforms ◽  
Chemical Pollution ◽  
Hospital Effluents ◽  
Biological Contaminants ◽  
Almost All ◽  
Direct Discharge ◽  
Significant Chemical

Liquid effluents discharged by hospitals may contain chemical and biological contaminants whose main source is the different substances used for the treatment of patients. This type of rejection can present a sanitary potentially dangerous risk for human health and can provoke a strong degradation of diverse environmental compartments mainly water and soils. The present study focuses on the quality of the liquid effluents of Hassani Abdelkader’s hospital of Sidi Bel-Abbes (West of Algeria). The results reveal a significant chemical pollution (COD: 879 mgO2/L, BOD5: 850 mgO2/L, NH4+ : 47.9 mg/l, NO2- : 4.2 mg/l, NO3- : 56.8 mg/l with respect to WHO standard of 90 mgO2/L, 30 mgO2/L, 0.5 mg/l, 1 mg/l and 1 mg/l respectively). However, these effluents are biodegradable since the ratio COD/BOD5 do not exceeded the value of 2 in almost all samples. The presence of pathogen germs is put into evidence such as pseudomonas, the clostridium, the staphylococcus, the fecal coliforms and fecal streptococcus. These results show that the direct discharge of these effluents constitutes a major threat to human health and the environment.

Solvothermal Synthesis and Characterization of an One-Dimensional Zinc Phosphate

2002 ◽  
Vol 37 (2-3) ◽  
pp. 169-175 ◽  
Author(s):  
K. Yanxiong ◽  
L. Jianmin ◽  
Z. Yugen ◽  
H. Gaofei ◽  
J. Zheng ◽  
...  
Keyword(s):  
Solvothermal Synthesis ◽  
Zinc Phosphate ◽  
Synthesis And Characterization ◽  
One Dimensional

scholarly journals Anomalous Anderson localization behavior in gain-loss balanced non-Hermitian systems

Nanophotonics ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 443-452
Author(s):  
Tianshu Jiang ◽  
Anan Fang ◽  
Zhao-Qing Zhang ◽  
Che Ting Chan
Keyword(s):  
Wave Propagation ◽  
Electromagnetic Waves ◽  
Anderson Localization ◽  
Random Media ◽  
Normal Incidence ◽  
Disordered Media ◽  
One Dimensional ◽  
Gain Loss ◽  
The Waves ◽  
Localization Behavior

AbstractIt has been shown recently that the backscattering of wave propagation in one-dimensional disordered media can be entirely suppressed for normal incidence by adding sample-specific gain and loss components to the medium. Here, we study the Anderson localization behaviors of electromagnetic waves in such gain-loss balanced random non-Hermitian systems when the waves are obliquely incident on the random media. We also study the case of normal incidence when the sample-specific gain-loss profile is slightly altered so that the Anderson localization occurs. Our results show that the Anderson localization in the non-Hermitian system behaves differently from random Hermitian systems in which the backscattering is suppressed.

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