Quantum ergodicity and delocalization of Schrödinger Eigenfunctions:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
EMS Press
[2022]
|
| Edition: | 1. Auflage |
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 134 Seiten Illustrationen 24 cm x 17 cm |
| ISBN: | 9783985470150 3985470154 |
Staff View
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| 245 | 1 | 0 | |a Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |c Nalini Anantharaman |
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Record in the Search Index
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|---|---|
| adam_text | |
| adam_txt |
CONTENTS
1
INTRODUCTION
.
1
1.1
HISTORY
OF
THE
PROBLEM
.
1
1.2
CONJECTURES,
SCOPE
OF
THE
BOOK
.
3
2
HIGH
FREQUENCY
DELOCALISATION
.
15
2.1
L
P
-NORMS
AS
MEASURES
OF
DELOCALISATION?
.
16
2.2
THE
SHNIRELMAN
THEOREM
.
18
2.3
OVERVIEW
OF
PSEUDO-DIFFERENTIAL
OPERATORS
.
20
2.4
THE
GEODESIC
FLOW
AND
THE
ERGODICITY
ASSUMPTION
.
32
2.5
PROOF
OF
THE
QUANTUM
ERGODICITY
THEOREM
.
34
3
ENTROPY
AND
SUPPORT
OF
SEMICLASSICAL
MEASURES
.
37
3.1
QUANTUM
UNIQUE
ERGODICITY
CONJECTURE
.
37
3.2
STATEMENT
OF
RESULTS
.
38
3.3
WHAT
IS
ENTROPY?
.
41
3.4
PROOF
OF
THE
ENTROPY
RESULT
(THEOREM
3.1)
.
45
3.5
A
FEW
WORDS
ON
DYATLOV
AND
JIN
'
S
RESULT
.
55
4
QUANTUM
ERGODICITY
ON
REGULAR
GRAPHS
.
57
4.1
REGULAR
GRAPHS:
QUANTUM
ERGODICITY
.
58
4.2
HARMONIC
ANALYSIS
ON
THE
(Q
+
L)-REGULAR
TREE
.
66
4.3
PROOF
OF
THEOREM
4.2
.
71
5
QUANTUM
ERGODICITY
ON
THE
SPHERE
.
.
81
6
QUANTUM
ERGODICITY
ON
NON-REGULAR
GRAPHS
.
85
6.1
INTRODUCTION
.
85
6.2
A
PROOF
BASED
ON
THE
NON-BACKTRACKING
RANDOM
WALK
.
89
6.3
ADAPTATION
TO
NON-REGULAR
GRAPHS
.
99
6.4
TREES
OF
FINITE
CONE
TYPE AND
THEIR
STOCHASTIC
PERTURBATIONS
.
107
6.5
THE
MEASURE
(A}
Y
:
ONE
EXAMPLE
.
115
7
BACKHAUSZ
AND
SZEGEDY
'
S
THEOREM
.
117
7.1
GAUSSIANITY
OF
EIGENFUNCTIONS
.
117
7.2
ELEMENTS
OF
THE
PROOF
.
120
REFERENCES
.
127 |
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| index_date | 2024-07-03T21:09:11Z |
| indexdate | 2025-05-14T14:00:43Z |
| institution | BVB |
| institution_GND | (DE-588)1066118477 |
| isbn | 9783985470150 3985470154 |
| language | English |
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| publisher | EMS Press |
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| series2 | Zurich lectures in advanced mathematics |
| spelling | Anantharaman, Nalini 1976- Verfasser (DE-588)1227362226 aut Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman Berlin EMS Press [2022] © 2022 134 Seiten Illustrationen 24 cm x 17 cm txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Schrödinger operators on manifolds and graphs quantum chaos Laplacian quantum ergodicity European Mathematical Society Publishing House ETH-Zentrum SEW A27 (DE-588)1066118477 pbl Erscheint auch als Online-Ausgabe 978-3-98547-515-5 (DE-604)BV048319890 DNB Datenaustausch https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p vlb 20220713 DE-101 https://d-nb.info/provenance/plan#vlb |
| spellingShingle | Anantharaman, Nalini 1976- Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_auth | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_exact_search | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_exact_search_txtP | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_full | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_fullStr | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_full_unstemmed | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions Nalini Anantharaman |
| title_short | Quantum ergodicity and delocalization of Schrödinger Eigenfunctions |
| title_sort | quantum ergodicity and delocalization of schrodinger eigenfunctions |
| url | https://bvbr.bib-bvb.de:443/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033973503&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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