{"product_id":"9781493939527","title":"Multi-scale Analysis for Random Quantum Systems with Interaction","description":"\u003cp\u003eThe 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. \u003ci\u003eMulti-scale Analysis for Random Quantum Systems with Interaction\u003c\/i\u003e presents the progress that had been recently achieved in this area. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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 Z\u003ci\u003e\u003csup\u003ed\u003c\/sup\u003e\u003c\/i\u003e. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis book includes the following cutting-edge features:\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e* an introduction to the state-of-the-art single-particle localization theory \u003c\/p\u003e\u003cp\u003e* an extensive discussion of relevant technical aspects of the localization theory\u003c\/p\u003e\u003cp\u003e* a thorough comparison of the multi-particle model with its single-particle counterpart \u003c\/p\u003e\u003cp\u003e* a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eRequired 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. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e","brand":"Springer New York","offers":[{"title":"Default Title","offer_id":47048524890352,"sku":"9781493939527","price":109.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9781493939527_p0.jpg?v=1763665853","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9781493939527","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}