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Multi-scale analysis for random quantum systems with interaction
The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems wi...
Autores principales: | , |
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Lenguaje: | eng |
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Springer
2014
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/978-1-4614-8226-0 http://cds.cern.ch/record/2023321 |
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author | Chulaevsky, Victor Suhov, Yuri |
author_facet | Chulaevsky, Victor Suhov, Yuri |
author_sort | Chulaevsky, Victor |
collection | CERN |
description | The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: * an introduction to the state-of-the-art single-particle localization theory * an extensive discussion of relevant technical aspects of the localization theory * a thorough comparison of the multi-particle model with its single-particle counterpart * a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists. |
id | cern-2023321 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2014 |
publisher | Springer |
record_format | invenio |
spelling | cern-20233212021-04-21T20:13:56Zdoi:10.1007/978-1-4614-8226-0http://cds.cern.ch/record/2023321engChulaevsky, VictorSuhov, YuriMulti-scale analysis for random quantum systems with interactionMathematical Physics and MathematicsThe study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: * an introduction to the state-of-the-art single-particle localization theory * an extensive discussion of relevant technical aspects of the localization theory * a thorough comparison of the multi-particle model with its single-particle counterpart * a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.Springeroai:cds.cern.ch:20233212014 |
spellingShingle | Mathematical Physics and Mathematics Chulaevsky, Victor Suhov, Yuri Multi-scale analysis for random quantum systems with interaction |
title | Multi-scale analysis for random quantum systems with interaction |
title_full | Multi-scale analysis for random quantum systems with interaction |
title_fullStr | Multi-scale analysis for random quantum systems with interaction |
title_full_unstemmed | Multi-scale analysis for random quantum systems with interaction |
title_short | Multi-scale analysis for random quantum systems with interaction |
title_sort | multi-scale analysis for random quantum systems with interaction |
topic | Mathematical Physics and Mathematics |
url | https://dx.doi.org/10.1007/978-1-4614-8226-0 http://cds.cern.ch/record/2023321 |
work_keys_str_mv | AT chulaevskyvictor multiscaleanalysisforrandomquantumsystemswithinteraction AT suhovyuri multiscaleanalysisforrandomquantumsystemswithinteraction |