Existence and regularity properties of the integrated density of states of random Schrödinger operators:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in mathematics
1917 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Teilw. zugl.: Chemnitz, Techn. Univ., Habil.-Schr., 2006 |
| Physical Description: | X, 142 S. |
| ISBN: | 9783540726890 3540726896 |
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| 100 | 1 | |a Veselić, Ivan |d 1973- |e Verfasser |0 (DE-588)122989589 |4 aut | |
| 245 | 1 | 0 | |a Existence and regularity properties of the integrated density of states of random Schrödinger operators |c Ivan Veselic |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a X, 142 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1917 | |
| 500 | |a Teilw. zugl.: Chemnitz, Techn. Univ., Habil.-Schr., 2006 | ||
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Record in the Search Index
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| adam_text | Contents
Random Operators........................................ 1
1.1
Physical Background
..................................... 1
1.2
Model and Notation
..................................... 2
1.3
Transport Properties and Spectral Types
................... 6
1.4
Fluctuation Boundaries of the Spectrum
................... 10
Existence of the Integrated Density of States
.............. 13
2.1 Schrödinger
Operators on Manifolds: Motivation
............. 15
2.2
Random
Schrödinger
Operators on Manifolds: Definitions
..... 17
2.3
Non-Randomness of Spectra and Existence of the IDS
........ 21
2.4
Measurability
........................................... 26
2.5
Bounds on the Heat Kernels Uniform in
ω
.................. 30
2.6
Laplace Transform and Ergodic Theorem
................... 37
2.7
Approach Using Dirichlet-Neumann Bracketing
.............. 39
2.8
Independence of the Choice of Boundary Conditions
......... 42
Wegner Estimate
.......................................... 45
3.1
Continuity of the IDS
.................................... 46
3.2
Application to Anderson Localisation
...................... 50
3.3
Resonances of Hamiltonians on Disjoint Regions
............. 53
Wegner s Original Idea. Rigorous Implementation
......... 57
4.1
Spectral Averaging of the Trace of the Spectral Projection
.... 57
4.2
Improved Volume Estimates
.............................. 61
4.3
Sparse Potentials
........................................ 64
4.4
Locally Continuous Coupling Constants
.................... 66
4.5
Potentials with Small Support
............................ 69
4.6
Holder Continuous Coupling Constants
..................... 72
4.7
A Partial Integration Formula for Singular Distributions
...... 73
4.8
Coupling Constants with Bernoulli Disorder
................ 74
4.9
Single Site Potentials with Changing Sign
.................. 74
4.10
Uniform Wegner Estimates for Long Range Potentials
........ 75
X
Contents
5 Lipschitz
Continuity of the IDS
............................ 79
5.1
Partition of the Trace into Local Contributions
.............. 80
5.2
Spectral Averaging of Resolvents
.......................... 83
5.3
Stone s Formula and Spectral Averaging of Projection«
....... 84
5.4
Completion of the Proof of Theorem
5.0.1.................. 86
5.5
Single Site Potentials with Changing Sign
.................. 87
5.6
The Finite Section Method for Multi-Level Laurent Matrices
.. 95
5.7
Unbounded Coupling Constants and Magnetic Fields
........ 96
A Properties of the Spectral Shift Function
.................. 99
A.I The SSF for Trace Class Perturbations
..................... 99
A.
2
The SSF for
Schrödinger
Operators and the
Invariance
Principle
...............................................102
A.3 Singular Value Estimates
.................................103
A.4 Bounds on the SSF for
Schrödinger
Operators
...............108
References
.....................................................113
Index
..........................................................139
|
| adam_txt |
Contents
Random Operators. 1
1.1
Physical Background
. 1
1.2
Model and Notation
. 2
1.3
Transport Properties and Spectral Types
. 6
1.4
Fluctuation Boundaries of the Spectrum
. 10
Existence of the Integrated Density of States
. 13
2.1 Schrödinger
Operators on Manifolds: Motivation
. 15
2.2
Random
Schrödinger
Operators on Manifolds: Definitions
. 17
2.3
Non-Randomness of Spectra and Existence of the IDS
. 21
2.4
Measurability
. 26
2.5
Bounds on the Heat Kernels Uniform in
ω
. 30
2.6
Laplace Transform and Ergodic Theorem
. 37
2.7
Approach Using Dirichlet-Neumann Bracketing
. 39
2.8
Independence of the Choice of Boundary Conditions
. 42
Wegner Estimate
. 45
3.1
Continuity of the IDS
. 46
3.2
Application to Anderson Localisation
. 50
3.3
Resonances of Hamiltonians on Disjoint Regions
. 53
Wegner's Original Idea. Rigorous Implementation
. 57
4.1
Spectral Averaging of the Trace of the Spectral Projection
. 57
4.2
Improved Volume Estimates
. 61
4.3
Sparse Potentials
. 64
4.4
Locally Continuous Coupling Constants
. 66
4.5
Potentials with Small Support
. 69
4.6
Holder Continuous Coupling Constants
. 72
4.7
A Partial Integration Formula for Singular Distributions
. 73
4.8
Coupling Constants with Bernoulli Disorder
. 74
4.9
Single Site Potentials with Changing Sign
. 74
4.10
Uniform Wegner Estimates for Long Range Potentials
. 75
X
Contents
5 Lipschitz
Continuity of the IDS
. 79
5.1
Partition of the Trace into Local Contributions
. 80
5.2
Spectral Averaging of Resolvents
. 83
5.3
Stone's Formula and Spectral Averaging of Projection«
. 84
5.4
Completion of the Proof of Theorem
5.0.1. 86
5.5
Single Site Potentials with Changing Sign
. 87
5.6
The Finite Section Method for Multi-Level Laurent Matrices
. 95
5.7
Unbounded Coupling Constants and Magnetic Fields
. 96
A Properties of the Spectral Shift Function
. 99
A.I The SSF for Trace Class Perturbations
. 99
A.
2
The SSF for
Schrödinger
Operators and the
Invariance
Principle
.102
A.3 Singular Value Estimates
.103
A.4 Bounds on the SSF for
Schrödinger
Operators
.108
References
.113
Index
.139 |
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| author | Veselić, Ivan 1973- |
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| dewey-full | 510 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| language | English |
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| spelling | Veselić, Ivan 1973- Verfasser (DE-588)122989589 aut Existence and regularity properties of the integrated density of states of random Schrödinger operators Ivan Veselic Berlin [u.a.] Springer 2008 X, 142 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1917 Teilw. zugl.: Chemnitz, Techn. Univ., Habil.-Schr., 2006 Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Zufälliger Hamilton-Operator (DE-588)4279525-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Lecture notes in mathematics 1917 (DE-604)BV000676446 1917 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016284379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Veselić, Ivan 1973- Existence and regularity properties of the integrated density of states of random Schrödinger operators Lecture notes in mathematics Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4279525-4 (DE-588)4116561-5 (DE-588)4113937-9 |
| title | Existence and regularity properties of the integrated density of states of random Schrödinger operators |
| title_auth | Existence and regularity properties of the integrated density of states of random Schrödinger operators |
| title_exact_search | Existence and regularity properties of the integrated density of states of random Schrödinger operators |
| title_exact_search_txtP | Existence and regularity properties of the integrated density of states of random Schrödinger operators |
| title_full | Existence and regularity properties of the integrated density of states of random Schrödinger operators Ivan Veselic |
| title_fullStr | Existence and regularity properties of the integrated density of states of random Schrödinger operators Ivan Veselic |
| title_full_unstemmed | Existence and regularity properties of the integrated density of states of random Schrödinger operators Ivan Veselic |
| title_short | Existence and regularity properties of the integrated density of states of random Schrödinger operators |
| title_sort | existence and regularity properties of the integrated density of states of random schrodinger operators |
| topic | Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Zufälliger Hamilton-Operator Spektraltheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016284379&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT veselicivan existenceandregularitypropertiesoftheintegrateddensityofstatesofrandomschrodingeroperators |