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001 978-1-4614-8226-0
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020 _a9781461482260
_9978-1-4614-8226-0
024 7 _a10.1007/978-1-4614-8226-0
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
082 0 4 _a515.7
_223
100 1 _aChulaevsky, Victor.
_eauthor.
245 1 0 _aMulti-scale Analysis for Random Quantum Systems with Interaction
_h[electronic resource] /
_cby Victor Chulaevsky, Yuri Suhov.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Birkhäuser,
_c2014.
300 _aXI, 238 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematical Physics,
_x1544-9998 ;
_v65
505 0 _aPreface -- 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.
520 _aThe 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.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aDistribution (Probability theory).
650 0 _aMathematical physics.
650 1 4 _aMathematics.
650 2 4 _aFunctional Analysis.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aApplications of Mathematics.
650 2 4 _aSolid State Physics.
650 2 4 _aSpectroscopy and Microscopy.
700 1 _aSuhov, Yuri.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461482253
830 0 _aProgress in Mathematical Physics,
_x1544-9998 ;
_v65
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8226-0
912 _aZDB-2-SMA
999 _c92132
_d92132