scholarly journals Multiparticle Localization at Low Energy for Multidimensional Continuous Anderson Models

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Trésor Ekanga
Keyword(s):  
Probability Distribution ◽  
Anderson Model ◽  
Multiscale Analysis ◽  
Random Potential ◽  
Particle Interaction ◽  
Low Energy ◽  
Dynamical Localization ◽  
Hölder Continuous ◽  
The Continuum ◽  
Number Of Particles

We study the multiparticle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multiparticle lower spectral edges are almost surely constant in absence of ergodicity. We stress that this result is not quite obvious and has to be handled carefully. In addition, we prove the spectral exponential and the strong dynamical localization of the continuous multiparticle Anderson model at low energy. The proof based on the multiparticle multiscale analysis bounds needs the values of the external random potential to be independent and identically distributed, whose common probability distribution is at least Log-Hölder continuous.

Localization in the multi-particle tight-binding Anderson model at low energy

2019 ◽  
Vol 32 (03) ◽  
pp. 2050009
Author(s):  
Trésor Ekanga
Keyword(s):  
Anderson Model ◽  
Particle Interaction ◽  
Tight Binding ◽  
Low Energy ◽  
Dynamical Localization ◽  
Scale Analysis ◽  
Hölder Continuous ◽  
Multi Scale ◽  
Spectral Edge ◽  
Marginal Probability Distribution

We consider the multi-particle tight-binding Anderson model and prove that its lower spectral edge is non-random under some mild assumptions on the inter-particle interaction and the random external potential. We also adapt to the low energy regime the multi-particle multi-scale analysis initially developed by Chulaevsky and Suhov in the high disorder limit, if the marginal probability distribution of the i.i.d. random variables is log-Hölder continuous and we obtain the spectral exponential and strong dynamical localization near the bottom of the spectrum.

scholarly journals LOCALIZATION ON A QUANTUM GRAPH WITH A RANDOM POTENTIAL ON THE EDGES

2007 ◽  
Vol 19 (09) ◽  
pp. 923-939 ◽  
Author(s):  
PAVEL EXNER ◽  
MARIO HELM ◽  
PETER STOLLMANN
Keyword(s):  
Multiscale Analysis ◽  
Random Potential ◽  
Schrödinger Operators ◽  
Quantum Graph ◽  
Dynamical Localization ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Cubic Lattice ◽  
Lattice Quantum

We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schrödinger operators.

scholarly journals Dynamical Localization for the One-Dimensional Continuum Anderson Model in a Decaying Random Potential

2020 ◽  
Vol 21 (10) ◽  
pp. 3095-3118 ◽  
Author(s):  
Olivier Bourget ◽  
Gregorio R. Moreno Flores ◽  
Amal Taarabt
Keyword(s):  
Anderson Model ◽  
Random Potential ◽  
Dynamical Localization ◽  
One Dimensional ◽  
The One

scholarly journals ANDERSON LOCALIZATION FOR A MULTI-PARTICLE QUANTUM GRAPH

2014 ◽  
Vol 26 (01) ◽  
pp. 1350020 ◽  
Author(s):  
MOSTAFA SABRI
Keyword(s):  
Single Particle ◽  
Anderson Localization ◽  
Multiscale Analysis ◽  
Random Potential ◽  
Particle Systems ◽  
Quantum Graph ◽  
Dynamical Localization ◽  
Quantum Graphs ◽  
Spectral Edge ◽  
Schmidt Norm

We study a multi-particle quantum graph with random potential. Taking the approach of multiscale analysis, we prove exponential and strong dynamical localization of any order in the Hilbert–Schmidt norm near the spectral edge. Apart from the results on multi-particle systems, we also prove Lifshitz-type asymptotics for single-particle systems. This shows in particular that localization for single-particle quantum graphs holds under a weaker assumption on the random potential than previously known.

A Convex Complementarity Approach for Simulating Large Granular Flows

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Alessandro Tasora ◽  
Mihai Anitescu
Keyword(s):  
Granular Flow ◽  
Complementarity Problems ◽  
Particle Interaction ◽  
Granular Flows ◽  
Rigid Bodies ◽  
Integration Time ◽  
Frictional Contacts ◽  
Physical Experiments ◽  
Dense Granular Flow ◽  
Number Of Particles

Aiming at the simulation of dense granular flows, we propose and test a numerical method based on successive convex complementarity problems. This approach originates from a multibody description of the granular flow: all the particles are simulated as rigid bodies with arbitrary shapes and frictional contacts. Unlike the discrete element method (DEM), the proposed approach does not require small integration time steps typical of stiff particle interaction; this fact, together with the development of optimized algorithms that can run also on parallel computing architectures, allows an efficient application of the proposed methodology to granular flows with a large number of particles. We present an application to the analysis of the refueling flow in pebble-bed nuclear reactors. Extensive validation of our method against both DEM and physical experiments results indicates that essential collective characteristics of dense granular flow are accurately predicted.

scholarly journals Low-energy scale of the periodic Anderson model

2000 ◽  
Vol 61 (19) ◽  
pp. 12799-12809 ◽  
Author(s):  
Th. Pruschke ◽  
R. Bulla ◽  
M. Jarrell
Keyword(s):  
Anderson Model ◽  
Energy Scale ◽  
Low Energy ◽  
Periodic Anderson Model

scholarly journals Influence of Particle Contact Number on Triboelectric Separation Selectivity

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 716
Author(s):  
Johann Landauer ◽  
Petra Foerst
Keyword(s):  
Protein Content ◽  
Particle Interaction ◽  
Decisive Role ◽  
Contact Number ◽  
Separation Selectivity ◽  
Fine Powders ◽  
Powder Composition ◽  
Triboelectric Charging ◽  
The Impact ◽  
Number Of Particles

Triboelectric separation is a promising technology to separate fine powders. To enable triboelectric separation for its application in industry, the impact of the process and product parameters must be examined. In this study, with regards to different wall materials in the charging step (PTFE, POM, PE, PVC, and PMMA), the influence of the powder composition of a binary starch-protein mixture with a protein content of 15 wt.%, 30 wt.% and 45 wt.% was studied. By increasing the protein content in the feed, the separation selectivity increased. No dependency of the empirical triboelectric series was determined for all powder compositions. The variation in the protein content of the initial powder and turbulent flow profiles results in a variation in the contact number of particles calculated. An increase in the contact number of particles leads to an increase in the protein content separated on the cathode, whereas the protein content on the anode is only slightly affected. These findings underpin the assumption that particle-particle interaction plays a decisive role in triboelectric charging of fine powders.

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