Caught by disorder : bound states in random media / Peter Stollmann

Englisch

Boston ; Berlin [u.a.] : Birkhäuser, 2001

XVI, 166 S. : graph. Darst. ; 24 cm

Hier auch später erschienene, unveränderte Nachdrucke

Hier auch später erschienene, unveränderte Nachdrucke

0-8176-4210-2 (acid-free paper)

3-7643-4210-2 (acid-free paper)

978-1-4612-6644-0

Weitere Ausgaben: 978-1-4612-0169-4 (Fernzugriff)

Machine generated contents note: 1 Getting Started 1 -- Prologue1 -- 1.1 Bound states versus extended states7 -- 1.2 Ergodic operator families11 -- 1.3 Some important examples18 -- 1.4 Our basic models (P+A) and (DIV)21 -- 1.5 Localization and Lifshitz tails: the heuristic picture31 -- 2 Analysis of Anderson-type Models 37 -- Prologue37 -- 2.1 Lifshitz tails for (P+A)39 -- 2.2 Initial length scale estimates44 -- 2.3 Wegner estimates48 -- 2.4 Combes-Thomas estimates54 -- 2.5 Changing cubes62 -- 3 Multiscale Analysis 69 -- Prologue 69 -- 3.1 Idea of the proof and historical notes71 -- 3.2 M ultiscale Analysis76 -- 3.3 Exponential localization90 -- 3.4 Dynamical localization98 -- 3.5 More models108 -- 4 Appendix 111 -- 4.1 A short story of selfadjoint operators111 -- 4.1.1 Welcome to Hilbert space111 -- 4.1.2 Selfadjoint operators and forms114 -- 4.1.3 Schrodinger operators116 -- 4.1.4 Spectra and the Spectral Theorem120 -- 4.1.5 Spectral Types and the RAGE theorem126 -- 4.1.6 Sectorial forms and form-bounded perturbations128 -- 4.1.7 The min-max principle130 -- 4.1.8 Weyl asymptotics131 -- 4.1.9 Auxiliary results from Sobolev space132 -- 4.1.10 Analytic perturbation theory132 -- 4.1.11 Generalized eigenfunction expansions134 -- 4.2 Some basics from probability theory137 -- 4.2.1 Measurable sets and random variables137 -- 4.2.2 Measure and probability138 -- 4.2.3 Independence 139 -- 4.2.4 Product measures140 -- 4.2.5 Ergodicity 142 -- 4.2.6 Monotone class arguments142 -- 5 Aftermath 145 -- References 147 -- Author Index 161 -- Subject Index 165

9780817642105

*Ungeordnetes System / Inhomogenes Medium / Wellenausbreitung / Zufallsoperator

*Order-disorder models ; Selfadjoint operators ; Wave-motion, Theory of

Klassifikation der Library of Congress: QC173.4.O4 ; QC173.4.O4S76 2001

Dewey Dezimal-Klassifikation: 530.413 ; 530.4/13

Regensburger Verbund-Klassifikation: UG 3100: U Physik / UG Thermodynamik, statistische Physik, Quantenstatistik / Statistische Mechanik, Ising-Modell, Order-Disorder-Modell, Percolation Theory, Cellulare Automaten

Mathematics Subject Classification: *82C44

Mathematics Subject Classification: 82-02

Mathematics Subject Classification: 60H25

Mathematics Subject Classification: 81Q10

Mathematics Subject Classification: 47B80

http://www.loc.gov/catdir/toc/fy02/2001035885.html [Table of contents]

http://www.loc.gov/catdir/enhancements/fy0812/2001035885-d.html [Publisher description]

https://zbmath.org/?q=an:0983.82016 [Zentralblatt MATH]

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