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[Download] "Multi-scale Analysis for Random Quantum Systems with Interaction" by Victor Chulaevsky & Yuri Suhov " eBook PDF Kindle ePub Free

Multi-scale Analysis for Random Quantum Systems with Interaction

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eBook details

  • Title: Multi-scale Analysis for Random Quantum Systems with Interaction
  • Author : Victor Chulaevsky & Yuri Suhov
  • Release Date : January 20, 2013
  • Genre: Mathematics,Books,Science & Nature,Physics,
  • Pages : * pages
  • Size : 5552 KB

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.


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