The Resource Caught by Disorder : Bound States in Random Media, by Peter Stollmann, (electronic resource)

Caught by Disorder : Bound States in Random Media, by Peter Stollmann, (electronic resource)

Label
Caught by Disorder : Bound States in Random Media
Title
Caught by Disorder
Title remainder
Bound States in Random Media
Statement of responsibility
by Peter Stollmann
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
Disorder is one of the predominant topics in science today. The present text is devoted to the mathematical studyofsome particular cases ofdisordered systems. It deals with waves in disordered media. To understand the significance of the influence of disorder, let us start by describing the propagation of waves in a sufficiently ordered or regular environment. That they do in fact propagate is a basic experience that is verified by our senses; we hear sound (acoustic waves) see (electromagnetic waves) and use the fact that electromagnetic waves travel long distances in many aspects ofour daily lives. The discovery that disorder can suppress the transport properties of a medium is oneof the fundamental findings of physics. In its most prominent practical application, the semiconductor, it has revolutionized the technical progress in the past century. A lot of what we see in the world today depends on that relatively young device. The basic phenomenon of wave propagation in disordered media is called a metal-insulator transition: a disordered medium can exhibit good transport prop­ erties for waves ofrelatively high energy (like a metal) and suppress the propaga­ tion of waves of low energy (like an insulator). Here we are actually talking about quantum mechanical wave functions that are used to describe electronic transport properties. To give an initial idea of why such a phenomenon could occur, we have to recall that in physical theories waves are represented by solutions to certain partial differential equations. These equations link time derivatives to spatial derivatives
Member of
http://library.link/vocab/creatorName
Stollmann, Peter
Dewey number
515.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
C6n5ve9wxYo
Image bit depth
0
Language note
English
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Progress in Mathematical Physics,
Series volume
20
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Functional analysis
  • Mathematical statistics
  • Partial Differential Equations
  • Functional Analysis
  • Theoretical, Mathematical and Computational Physics
  • Statistical Theory and Methods
Label
Caught by Disorder : Bound States in Random Media, by Peter Stollmann, (electronic resource)
Instantiates
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Getting Started -- Prologue -- 1.1 Bound states versus extended states -- 1.2 Ergodic operator families -- 1.3 Some important examples -- 1.4 Our basic models (P+A) and (DIV) -- 1.5 Localization and Lifshitz tails: the heuristic picture -- 2 Analysis of Anderson-type Models -- Prologue -- 2.1 Lifshitz tails for (P+A) -- 2.2 Initial length scale estimates -- 2.3 Wegner estimates -- 2.4 Combes—Thomas estimates -- 2.5 Changing cubes -- 3 Multiscale Analysis -- Prologue -- 3.1 Idea of the proof and historical notes -- 3.2 Multiscale Analysis -- 3.3 Exponential localization -- 3.4 Dynamical localization -- 3.5 More models -- 4 Appendix -- 4.1 A short story of selfadjoint operators -- 4.2 Some basics from probability theory -- 5 Aftermath -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XVII, 166 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461201694
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0169-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089019
  • (SSID)ssj0001296073
  • (PQKBManifestationID)11886430
  • (PQKBTitleCode)TC0001296073
  • (PQKBWorkID)11347198
  • (PQKB)10428695
  • (DE-He213)978-1-4612-0169-4
  • (MiAaPQ)EBC3073874
  • (EXLCZ)993400000000089019
Label
Caught by Disorder : Bound States in Random Media, by Peter Stollmann, (electronic resource)
Publication
Note
Bibliographic Level Mode of Issuance: Monograph
Antecedent source
mixed
Bibliography note
Includes bibliographical references and indexes
Carrier category
online resource
Carrier category code
  • cr
Color
not applicable
Content category
text
Content type code
  • txt
Contents
1 Getting Started -- Prologue -- 1.1 Bound states versus extended states -- 1.2 Ergodic operator families -- 1.3 Some important examples -- 1.4 Our basic models (P+A) and (DIV) -- 1.5 Localization and Lifshitz tails: the heuristic picture -- 2 Analysis of Anderson-type Models -- Prologue -- 2.1 Lifshitz tails for (P+A) -- 2.2 Initial length scale estimates -- 2.3 Wegner estimates -- 2.4 Combes—Thomas estimates -- 2.5 Changing cubes -- 3 Multiscale Analysis -- Prologue -- 3.1 Idea of the proof and historical notes -- 3.2 Multiscale Analysis -- 3.3 Exponential localization -- 3.4 Dynamical localization -- 3.5 More models -- 4 Appendix -- 4.1 A short story of selfadjoint operators -- 4.2 Some basics from probability theory -- 5 Aftermath -- References -- Author Index
Dimensions
unknown
Edition
1st ed. 2001.
Extent
1 online resource (XVII, 166 p.)
File format
multiple file formats
Form of item
online
Isbn
9781461201694
Level of compression
uncompressed
Media category
computer
Media type code
  • c
Other control number
10.1007/978-1-4612-0169-4
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)3400000000089019
  • (SSID)ssj0001296073
  • (PQKBManifestationID)11886430
  • (PQKBTitleCode)TC0001296073
  • (PQKBWorkID)11347198
  • (PQKB)10428695
  • (DE-He213)978-1-4612-0169-4
  • (MiAaPQ)EBC3073874
  • (EXLCZ)993400000000089019

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