scholarly journals Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

2019 ◽  
Vol 99 (22) ◽  
Author(s):  
Jagannath Sutradhar ◽  
Subroto Mukerjee ◽  
Rahul Pandit ◽  
Sumilan Banerjee
Keyword(s):  
Single Parameter ◽  
Localization Transition ◽  
Quasiperiodic Systems

scholarly journals On intermediate statistics across many-body localization transition

2021 ◽  
Author(s):  
Bitan De ◽  
Piotr Sierant ◽  
Jakub Zakrzewski
Keyword(s):  
Joint Probability ◽  
Single Parameter ◽  
Joint Probability Distribution ◽  
Many Body ◽  
Localization Transition ◽  
Physical Systems ◽  
Level Statistics ◽  
Interacting Systems ◽  
Many Body Systems ◽  
Two Parameter

Abstract The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

scholarly journals Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems

2017 ◽  
Vol 119 (26) ◽  
Author(s):  
Henrik P. Lüschen ◽  
Pranjal Bordia ◽  
Sebastian Scherg ◽  
Fabien Alet ◽  
Ehud Altman ◽  
...  
Keyword(s):  
Many Body ◽  
Slow Dynamics ◽  
Localization Transition ◽  
One Dimensional ◽  
Quasiperiodic Systems ◽  
The Many

The Calder´on-Zygmund Theory I: Ellipticity

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
Classical Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Differential Operators ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Single Parameter ◽  
Partial Differential ◽  
Translation Invariant ◽  
Partial Differential Operators

This chapter discusses a case for single-parameter singular integral operators, where ρ‎ is the usual distance on ℝn. There, we obtain the most classical theory of singular integrals, which is useful for studying elliptic partial differential operators. The chapter defines singular integral operators in three equivalent ways. This trichotomy can be seen three times, in increasing generality: Theorems 1.1.23, 1.1.26, and 1.2.10. This trichotomy is developed even when the operators are not translation invariant (many authors discuss such ideas only for translation invariant, or nearly translation invariant operators). It also presents these ideas in a slightly different way than is usual, which helps to motivate later results and definitions.

A parameter hierarchy for agreement

2017 ◽  
Author(s):  
András Bárány
Keyword(s):  
Full Range ◽  
Single Parameter

This chapter models some of the results of the previous chapter. It builds on the recently developed notion of parameter hierarchies. Parameter hierarchies are sets of dependent parameters giving rise to chains of implicational relations among languages. The languages discussed in this book are positioned on a parameter hierarchy of ϕ‎-probes: some languages do not show any kind of agreement, others with a single ϕ‎-probe can agree with one argument, yet others with more than one probe with more arguments. It is argued that this hierarchy restricts agreement across languages in some ways, but that other parameters are needed to account for the full range of data studied in the book. This chapter concludes that there is no single parameter that governs differential object and differential subject marking.

Other topics

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Photonic Crystals ◽  
Crystal Morphology ◽  
Three Dimensional ◽  
Icosahedral Quasicrystal ◽  
Crystal Surfaces ◽  
Decagonal Quasicrystal ◽  
System A ◽  
Fundamental Law ◽  
Quasiperiodic Systems ◽  
Aperiodic Crystals

The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

scholarly journals Study on the Influence of Geometric Characteristics of Grain Membranes on Permeability Properties in Porous Sandstone

Membranes ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 587
Author(s):  
Run Shi ◽  
Huaiguang Xiao ◽  
Chengmeng Shao ◽  
Mingzheng Huang ◽  
Lei He
Keyword(s):  
Fluid Flow ◽  
Single Parameter ◽  
Control Group ◽  
Porous Rock ◽  
Permeability Characteristics ◽  
Natural Rock ◽  
Porous Sandstone ◽  
Novel Method ◽  
Boltzmann Method ◽  
Flow Laws

Studying the influence of grain characteristics on fluid flow in complex porous rock is one of the most important premises to reveal the permeability mechanism. Previous studies have mainly investigated the fluid flow laws in complex rock structures using an uncontrollable one single parameter of natural rock models or oversimplified control group models. In order to solve these problems, this paper proposes a novel method to reconstruct models that can independently control one single parameter of rock grain membranes based on mapping and reverse-mapping ideas. The lattice Boltzmann method is used to analyze the influence of grain parameters (grain radius, space, roundness, orientation, and model resolution) on the permeability characteristics (porosity, connectivity, permeability, flow path, and flow velocity). Results show that the grain radius and space have highly positive and negative correlations with permeability properties. The effect of grain roundness and resolution on permeability properties shows a strong regularity, while grain orientation on permeability properties shows strong randomness. This study is of great significance to reveal the fluid flow laws of natural rock structures.

scholarly journals A single parameter approach to enhance the microstructural and mechanical properties of beta Ti-Nb alloy via open-air fiber laser nitriding

2020 ◽  
Vol 383 ◽  
pp. 125269 ◽  
Author(s):  
Chi-Wai Chan ◽  
Xianwen Chang ◽  
Mohammad Amin Bozorgzadeh ◽  
Graham C. Smith ◽  
Seunghwan Lee
Keyword(s):  
Mechanical Properties ◽  
Fiber Laser ◽  
Single Parameter ◽  
Laser Nitriding ◽  
Parameter Approach

Adsorption energy as a promising single-parameter descriptor for single atom catalysis in the oxygen evolution reaction

2021 ◽  
Author(s):  
Hai-Cai Huang ◽  
Jun Li ◽  
Yang Zhao ◽  
Jing Chen ◽  
Yu-Xiang Bu ◽  
...  
Keyword(s):  
Oxygen Evolution ◽  
Adsorption Energy ◽  
Oxygen Evolution Reaction ◽  
Single Parameter ◽  
Single Atom ◽  
Highly Efficient

A highly efficient and reliable single-parameter descriptor for offering a strategy to rationally design SACs for the OER.

SPECKLE STATISTICS IN THE PHOTON LOCALIZATION TRANSITION

2010 ◽  
Vol 24 (12n13) ◽  
pp. 1950-1988 ◽  
Author(s):  
Azriel Z. Genack ◽  
Jing Wang
Keyword(s):  
Steady State ◽  
Probability Distributions ◽  
Speckle Pattern ◽  
Frequency Variation ◽  
Localization Transition ◽  
Classical Waves ◽  
Speckle Patterns ◽  
The Many ◽  
Photon Localization ◽  
State Propagation

We review the statistics of speckle in the Anderson localization transition for classical waves. Probability distributions of local and integrated transmission and of the evolution of the structure of the speckle pattern are related to their corresponding correlation functions. Steady state and pulse transport can be described in terms of modes whose speckle patterns are obtained by decomposing the frequency variation of the transmitted field. At the same time, transmission can be purposefully manipulated by adjusting the incident field and the eigenchannels of the transmission matrix can be found by analyzing sets of speckle patterns for different inputs. The many aspects of steady state propagation are reflected in diverse, but simply related, parameters so that a single localization parameter encapsulates the character of transport on both sides of the divide separating localized from diffusive waves.

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