On Lifshits tails in magnetic fields:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin
Logos-Verl.
2001
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache |
| Physical Description: | 142, VIII S. graph. Darst. : 21 cm |
| ISBN: | 3897227118 |
Staff View
MARC
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| 245 | 1 | 0 | |a On Lifshits tails in magnetic fields |c Simone Warzel |
| 264 | 1 | |a Berlin |b Logos-Verl. |c 2001 | |
| 300 | |a 142, VIII S. |b graph. Darst. : 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache | ||
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Record in the Search Index
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|---|---|
| adam_text |
CONTENTS
ABSTRACT
III
ZUSAMMENFASSUNG
IV
1.
INTRODUCTION
1
1.1.
THE
LIFSHITS-POISSON
MODEL
WITH
A
CONSTANT
MAGNETIC
FIELD
.
.
4
1.2.
THE
LIFSHITS
TAILS AND
THEIR
HEURISTIC
DERIVATION
.
7
1.2.1.
THE
CASE
OF
VANISHING
MAGNETIC
FIELD
.
7
1.2.2.
THE
PRESENCE
OF
A
CONSTANT
MAGNETIC
FIELD
.
10
1.2.3.
THE
METHOD
OF
OPTIMAL
FLUCTUATIONS
.
13
1.3.
SHORT
OVERVIEW
.
14
2.
THE
RANDOM
SCHRODINGER
OPERATOR
WITH
A
CONSTANT
MAGNETIC
FIELD
15
2.1.
THE
POISSON
POTENTIAL
.
15
2.2.
THE
RANDOM
MAGNETIC
SCHRODINGER
OPERATOR
.
20
2.3.
THE
INTEGRATED
DENSITY
OF
STATES
.
22
2.3.1.
DEFINITION
AND
SELF-AVERAGING
.
22
2.3.2.
FURTHER
PROPERTIES
.
25
3.
MAGNETIC
LIFSHITS
TAILS
IN
TWO
SPACE
DIMENSIONS
29
3.1.
THE
LANDAU
HAMILTONIAN
.
29
3.2.
THE
LANDAU-LIFSHITS
TAILS
.
31
3.2.1.
LIFSHITS
TAILS
CAUSED
BY
SUPER-GAUSSIAN
AND
GAUSSIAN
DECAY
.
34
3.2.2.
LIFSHITS
TAILS
CAUSED
BY
SUB-GAUSSIAN
DECAY
.
35
3.2.3.
CLASSICAL
VERSUS
QUANTUM
LIFSHITS
TAILS
.
40
3.3.
RESTRICTION
TO
A
SINGLE
LANDAU
BAND
AND
STRONG-MAGNETIC
FIELD
ASYMPTOTICS
.
41
3.3.1.
THE
RESTRICTED
LANDAU-LIFSHITS
TAILS
.
42
3.3.2.
STRONG-MAGNETIC
FIELD
ASYMPTOTICS
.
45
VI
CONTENTS
4.
ON
MAGNETIC
LIFSHITS
TAILS
IN
THREE
SPACE
DIMENSIONS
49
4.1.
THE
MAGNETIC
HAMILTONIAN
.
49
4.2.
THE
MAGNETIC
LIFSHITS
TAILS
.
50
4.2.1.
LIFSHITS
TAILS
CAUSED
BY
SUPER-GAUSSIAN
AND
GAUSSIAN
DECAY
.
52
4.2.2.
LIFSHITS
TAILS
CAUSED
BY
STRETCHED-GAUSSIAN
DECAY
.
54
4.3.
STRONG-MAGNETIC
FIELD
ASYMPTOTICS
.
55
5.
BOUNDS
ON
THE
LAPLACE
TRANSFORM
OF
THE
INTEGRATED
DENSITY
OF
STATES
59
5.1.
APPROXIMATION
FORMULA
.
59
5.2.
BOUNDS
FOR
ARBITRARY
SPACE
DIMENSION
.
61
5.3.
BOUNDS
FOR
THE
CASE
OF
TWO
SPACE
DIMENSIONS
.
65
5.3.1.
BASIC
INEQUALITIES
.
66
5.3.2.
PROOF
OF
THE
STRONG-MAGNETIC
FIELD
ASYMPTOTICS
.
69
5.4.
BOUNDS
FOR
THE
CASE
OF
THREE
SPACE
DIMENSIONS
.
70
5.4.1.
BASIC
INEQUALITIES
.
70
5.4.2.
PROOF
OF
THE
STRONG-MAGNETIC
FIELD
ASYMPTOTICS
.
75
6.
PROOF
OF
MAGNETIC
LIFSHITS
TAILS
IN
TWO
SPACE
DIMENSIONS
77
6.1.
PREPARATORY
RESULTS
.
77
6.1.1.
ASYMPTOTIC
EVALUATION
OF
CERTAIN
INTEGRALS
.
78
6.1.2.
LONG-DISTANCE
FALL-OFF
OF
CERTAIN
CONVOLUTIONS
.
79
6.2.
PROOF
OF
THE
LIFSHITS
TAILS
.
84
6.2.1.
PROOF
OF
THE
LANDAU-LIFSHITS
TAILS
.
84
6.2.2.
PROOF
OF
THE
RESTRICTED
LANDAU-LIFSHITS
TAILS
.
86
7.
PROOF
OF
MAGNETIC
LIFSHITS
TAILS
IN
THREE
SPACE
DIMENSIONS
87
7.1.
ASYMPTOTIC
EVALUATION
OF
THE
LOWER
BOUND
.
87
7.2.
ASYMPTOTIC
EVALUATION
OF
THE
UPPER
BOUND
.
94
7.3.
PROOF
OF
THE
LIFSHITS
TAILS
.
97
8.
OUTLOOK
101
A.
ELEMENTARY
FACTS
ABOUT
REGULARLY
VARYING
FUNCTIONS
105
B.
AN
ABELIAN
AND
TAUBERIAN
THEOREM
OF
EXPONENTIAL
TYPE
109
B.L.
AN
ABELIAN
AND
TAUBERIAN
THEOREM
FOR
THE
LAPLACE
TRANSFORM
.
109
B.2.
RELATION
WITH
THE
ASYMPTOTICS
OF
THE
LEGENDRE
TRANSFORM
.
113
CONTENTS
VII
C.
RESTRICTED
RANDOM
OPERATORS
115
C.L.
DEFINITION
AND
BASIC
PROPERTIES
.
115
C.2.
APPROXIMATION
FORMULA
.
118
BIBLIOGRAPHY
121
CITATION
INDEX
134
SYMBOL
INDEX
137 |
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| author_GND | (DE-588)123039703 |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV013833131 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T00:41:34Z |
| institution | BVB |
| isbn | 3897227118 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009461339 |
| oclc_num | 76241707 |
| open_access_boolean | |
| owner | DE-29 DE-29T |
| owner_facet | DE-29 DE-29T |
| physical | 142, VIII S. graph. Darst. : 21 cm |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Logos-Verl. |
| record_format | marc |
| spelling | Warzel, Simone 1973- Verfasser (DE-588)123039703 aut On Lifshits tails in magnetic fields Simone Warzel Berlin Logos-Verl. 2001 142, VIII S. graph. Darst. : 21 cm txt rdacontent n rdamedia nc rdacarrier Zugl.: Erlangen-Nürnberg, Univ., Diss., 2001. - Enth. Zsfassung in dt. Sprache Magnetfeld (DE-588)4074450-4 gnd rswk-swf Zustandsdichte (DE-588)4191170-2 gnd rswk-swf Ungeordnetes System (DE-588)4124353-5 gnd rswk-swf Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd rswk-swf Störstelle (DE-588)4193400-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Ungeordnetes System (DE-588)4124353-5 s Störstelle (DE-588)4193400-3 s Zufälliger Hamilton-Operator (DE-588)4279525-4 s Zustandsdichte (DE-588)4191170-2 s Magnetfeld (DE-588)4074450-4 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009461339&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Warzel, Simone 1973- On Lifshits tails in magnetic fields Magnetfeld (DE-588)4074450-4 gnd Zustandsdichte (DE-588)4191170-2 gnd Ungeordnetes System (DE-588)4124353-5 gnd Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd Störstelle (DE-588)4193400-3 gnd |
| subject_GND | (DE-588)4074450-4 (DE-588)4191170-2 (DE-588)4124353-5 (DE-588)4279525-4 (DE-588)4193400-3 (DE-588)4113937-9 |
| title | On Lifshits tails in magnetic fields |
| title_auth | On Lifshits tails in magnetic fields |
| title_exact_search | On Lifshits tails in magnetic fields |
| title_full | On Lifshits tails in magnetic fields Simone Warzel |
| title_fullStr | On Lifshits tails in magnetic fields Simone Warzel |
| title_full_unstemmed | On Lifshits tails in magnetic fields Simone Warzel |
| title_short | On Lifshits tails in magnetic fields |
| title_sort | on lifshits tails in magnetic fields |
| topic | Magnetfeld (DE-588)4074450-4 gnd Zustandsdichte (DE-588)4191170-2 gnd Ungeordnetes System (DE-588)4124353-5 gnd Zufälliger Hamilton-Operator (DE-588)4279525-4 gnd Störstelle (DE-588)4193400-3 gnd |
| topic_facet | Magnetfeld Zustandsdichte Ungeordnetes System Zufälliger Hamilton-Operator Störstelle Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009461339&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT warzelsimone onlifshitstailsinmagneticfields |