05775nam 22009375 450 991029997540332120200705110151.01-4614-8226-710.1007/978-1-4614-8226-0(CKB)3710000000078542(Springer)9781461482260(MH)013879492-8(SSID)ssj0001010517(PQKBManifestationID)11562138(PQKBTitleCode)TC0001010517(PQKBWorkID)11000141(PQKB)11678425(DE-He213)978-1-4614-8226-0(MiAaPQ)EBC6311571(MiAaPQ)EBC1466241(Au-PeEL)EBL1466241(CaPaEBR)ebr10976287(OCoLC)869771902(PPN)172420873(EXLCZ)99371000000007854220130920d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierMulti-scale Analysis for Random Quantum Systems with Interaction /by Victor Chulaevsky, Yuri Suhov1st ed. 2014.New York, NY :Springer New York :Imprint: Birkhäuser,2014.1 online resource (XI, 238 p. 5 illus.)online resourceProgress in Mathematical Physics,1544-9998 ;65Bibliographic Level Mode of Issuance: Monograph1-4614-8225-9 Includes bibliographical references (pages [229]-235) and index.Preface -- Part I Single-particle Localisation -- A Brief History of Anderson Localization.- Single-Particle MSA Techniques -- Part II Multi-particle Localization -- Multi-particle Eigenvalue Concentration Bounds -- Multi-particle MSA Techniques -- References -- Index.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.Progress in Mathematical Physics,1544-9998 ;65Functional analysisPhysicsProbabilitiesApplied mathematicsEngineering mathematicsSolid state physicsSpectrum analysisMicroscopyFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Mathematical Methods in Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P19013Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Applications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Solid State Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/P25013Spectroscopy and Microscopyhttps://scigraph.springernature.com/ontologies/product-market-codes/P31090Functional analysis.Physics.Probabilities.Applied mathematics.Engineering mathematics.Solid state physics.Spectrum analysis.Microscopy.Functional Analysis.Mathematical Methods in Physics.Probability Theory and Stochastic Processes.Applications of Mathematics.Solid State Physics.Spectroscopy and Microscopy.515.7Chulaevsky Victorauthttp://id.loc.gov/vocabulary/relators/aut721745Suhov Yuriauthttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910299975403321Multi-scale Analysis for Random Quantum Systems with Interaction2504065UNINAThis Record contains information from the Harvard Library Bibliographic Dataset, which is provided by the Harvard Library under its Bibliographic Dataset Use Terms and includes data made available by, among others the Library of Congress