ANDERSON LOCALIZATION FOR A MULTI-PARTICLE QUANTUM GRAPH-Reference-Cited by-同舟云学术

ANDERSON LOCALIZATION FOR A MULTI-PARTICLE QUANTUM GRAPH

Published:2014-01-13 Issue:01 Volume:26 Page:1350020
ISSN:0129-055X
Container-title:Reviews in Mathematical Physics
language:en
Short-container-title:Rev. Math. Phys.

Author:

SABRI MOSTAFA¹²

Affiliation:

1. Institut de Mathématiques de Jussieu, Université Paris Diderot-Paris 7, Bâtiment Sophie Germain, 75013, Paris, France

2. Department of Mathematics, Faculty of Science, Cairo University, Cairo 12613, Egypt

Abstract

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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0129055X13500207

Reference39 articles.

1. Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder

2. Functional Analysis

3. Quantum graphs with singular two-particle interactions

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Multiparticle Localization at Low Energy for Multidimensional Continuous Anderson Models;Advances in Mathematical Physics;2020-05-05

2. Spectra and Quantum Transport on Graphs;Graph Theory - Advanced Algorithms and Applications;2018-01-31